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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 29 Nov 2008 04:05:22 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Nov/29/t1227956784m3ny5uhbqwq44ex.htm/, Retrieved Sun, 19 May 2024 06:08:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=26202, Retrieved Sun, 19 May 2024 06:08:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact224

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
F    D  [Multiple Regression] [Seatbelt law: q1] [2008-11-24 23:03:38] [8d78428855b119373cac369316c08983]
- RMPD      [Central Tendency] [Verbetering seatb...] [2008-11-29 11:05:22] [e4cb5a8878d0401c2e8d19a1768b515b] [Current]
-    D        [Central Tendency] [Central tendency q2] [2008-11-29 13:43:47] [73d6180dc45497329efd1b6934a84aba]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
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Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26202&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26202&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9553976186712.729637752726055.30.322358320316019
Geometric MeanNaN
Harmonic Mean-40.6195863705367
Quadratic Mean409713300139596
Winsorized Mean ( 1 / 64 )9660989286401.01296158025273810.326210619397163
Winsorized Mean ( 2 / 64 )9751183850666.9929457748962279.50.331022708597093
Winsorized Mean ( 3 / 64 )10133697991392.229330852774278.10.345496193696728
Winsorized Mean ( 4 / 64 )10637828318105.729156631773913.70.364851070610403
Winsorized Mean ( 5 / 64 )10639465385802.029113546452821.80.365447246457697
Winsorized Mean ( 6 / 64 )9937685436017.0528962456352845.00.343123018122076
Winsorized Mean ( 7 / 64 )8999288735873.6228797779774439.40.312499394271404
Winsorized Mean ( 8 / 64 )9350244586762.9928715629572609.50.325615169366920
Winsorized Mean ( 9 / 64 )9041812183796.9728613369798426.80.315999557112428
Winsorized Mean ( 10 / 64 )7853480474747.9628320064497573.10.277311532091354
Winsorized Mean ( 11 / 64 )7366819823445.1927758739486165.10.265387404464702
Winsorized Mean ( 12 / 64 )5836763260543.7527139765163413.10.215063145366204
Winsorized Mean ( 13 / 64 )6690288078686.6326932334056955.00.24841100160641
Winsorized Mean ( 14 / 64 )3832663512091.9125881636180673.10.148084282049909
Winsorized Mean ( 15 / 64 )-701136478941.29225278514836938.4-0.0277364585484568
Winsorized Mean ( 16 / 64 )-448416488506.1324926511912375.8-0.0179895402165553
Winsorized Mean ( 17 / 64 )1081318314395.1124631250579453.30.0439002603991662
Winsorized Mean ( 18 / 64 )245258992959.42724508182870699.00.0100072287796028
Winsorized Mean ( 19 / 64 )2632078621725.3224068017701134.90.109360008556135
Winsorized Mean ( 20 / 64 )5479509615139.0723537013855804.00.232803942280378
Winsorized Mean ( 21 / 64 )7343945366576.0722603295012584.70.324905964483817
Winsorized Mean ( 22 / 64 )10048308442038.421972045930979.00.457322384706608
Winsorized Mean ( 23 / 64 )14412884302870.820619451960953.90.698994538272102
Winsorized Mean ( 24 / 64 )13871654974175.220536514772569.90.675462955997928
Winsorized Mean ( 25 / 64 )14878414736402.020300972273070.50.73289173229099
Winsorized Mean ( 26 / 64 )24321555589901.419080390917558.71.27468853730452
Winsorized Mean ( 27 / 64 )25269418449645.718922364503253.21.33542604811895
Winsorized Mean ( 28 / 64 )26500201044696187836540640151.41081181299351
Winsorized Mean ( 29 / 64 )25073182776199.818570305073848.21.35017613746741
Winsorized Mean ( 30 / 64 )18375342260219.617768690229724.21.03414162904819
Winsorized Mean ( 31 / 64 )20165186767304.117449812210565.11.15561053173368
Winsorized Mean ( 32 / 64 )19094491399939.117178002624658.41.11156645025363
Winsorized Mean ( 33 / 64 )18303484992669.316975313281963.21.07824136666257
Winsorized Mean ( 34 / 64 )16732176290265.516566496432389.41.01000089901642
Winsorized Mean ( 35 / 64 )16559121028366.216398552677091.21.00979161725043
Winsorized Mean ( 36 / 64 )17523257447132.215974440824774.81.09695592098318
Winsorized Mean ( 37 / 64 )16958064372451.415260619660863.31.11123039229798
Winsorized Mean ( 38 / 64 )16724440358821.715135147725957.71.10500674731692
Winsorized Mean ( 39 / 64 )18330855142223.114938503513011.31.22708778200287
Winsorized Mean ( 40 / 64 )19820243600588.114744118379227.51.34428136635908
Winsorized Mean ( 41 / 64 )21305729201079.314574495356938.81.46185021705989
Winsorized Mean ( 42 / 64 )22056878098139.914474647638689.61.52382832720457
Winsorized Mean ( 43 / 64 )23275589064149.214358659130077.61.62101411094808
Winsorized Mean ( 44 / 64 )24391735035137.114116478362046.31.72789093777929
Winsorized Mean ( 45 / 64 )24756467081076.113919018028066.01.77860730054072
Winsorized Mean ( 46 / 64 )25124142604229.813814671348888.11.81865655502922
Winsorized Mean ( 47 / 64 )25612950739315.413562921017105.31.88845387413322
Winsorized Mean ( 48 / 64 )25769388338419.613489848092437.11.91028009817745
Winsorized Mean ( 49 / 64 )25695285805472.913330172022495.81.92760346694026
Winsorized Mean ( 50 / 64 )25283494454223.913293512795795.21.90194231145745
Winsorized Mean ( 51 / 64 )2330581498735912972813871209.11.7965119378674
Winsorized Mean ( 52 / 64 )23963900567949.512635406341744.61.89656746445724
Winsorized Mean ( 53 / 64 )24370362698492.812602447326868.21.93378016716924
Winsorized Mean ( 54 / 64 )21687483948869.212264575507510.11.76830286018371
Winsorized Mean ( 55 / 64 )19826856714986.012064511367024.11.64340321060815
Winsorized Mean ( 56 / 64 )17879091661436.411883349016284.51.50454990734814
Winsorized Mean ( 57 / 64 )16311570140632.511740933061276.11.38929078766586
Winsorized Mean ( 58 / 64 )15877975456569.711702326529802.71.35682211704935
Winsorized Mean ( 59 / 64 )17018508328495.411508152405015.71.47882194548258
Winsorized Mean ( 60 / 64 )17328588123009.811478629424857.41.50963912864754
Winsorized Mean ( 61 / 64 )16769664181863.411395819966405.01.47156275119304
Winsorized Mean ( 62 / 64 )12350100446148.911023802341972.21.1203122174213
Winsorized Mean ( 63 / 64 )12403238336213.810991822568747.11.12840598168677
Winsorized Mean ( 64 / 64 )14981550148741.810764198247414.71.39179433566639
Trimmed Mean ( 1 / 64 )9809617841800.1829075467868090.90.337384694420200
Trimmed Mean ( 2 / 64 )9961408706888.6928497539539964.70.349553290132956
Trimmed Mean ( 3 / 64 )10069911858487.027967349822736.70.360059566684449
Trimmed Mean ( 4 / 64 )10047725377476.527448837403806.90.366052857892005
Trimmed Mean ( 5 / 64 )9892093832695.1426945806559434.60.367110697201662
Trimmed Mean ( 6 / 64 )9732654568032.3526417270125539.40.368420147947957
Trimmed Mean ( 7 / 64 )9695795086147.4625882580984611.20.374606964116608
Trimmed Mean ( 8 / 64 )9804341530345.9925339652781504.20.386916964288569
Trimmed Mean ( 9 / 64 )9866975591529.8524769739963443.60.39834796837157
Trimmed Mean ( 10 / 64 )9969321440550.9824171868733497.00.412434865937182
Trimmed Mean ( 11 / 64 )10208287008453.423570895231595.70.433088642079648
Trimmed Mean ( 12 / 64 )10503504378324.423001909694823.60.456636188806887
Trimmed Mean ( 13 / 64 )10953310751122.622470430658296.10.487454420330774
Trimmed Mean ( 14 / 64 )11337222736632.721922372513023.20.51715309234426
Trimmed Mean ( 15 / 64 )11972529337652.121457967728489.80.557952621102888
Trimmed Mean ( 16 / 64 )12986422602979.521024726426788.30.617673797002805
Trimmed Mean ( 17 / 64 )14006790128915.220595324556871.80.68009562511321
Trimmed Mean ( 18 / 64 )14942570893767.320162749944861.50.741097862872393
Trimmed Mean ( 19 / 64 )15960566523260.519706246246850.20.809924240432729
Trimmed Mean ( 20 / 64 )16846670982088.319257284015094.60.87482071557356
Trimmed Mean ( 21 / 64 )17574169309573.118824575661667.70.93357585453356
Trimmed Mean ( 22 / 64 )18206152255858.618447744461331.60.9869039705109
Trimmed Mean ( 23 / 64 )18693794227294.918099578162529.21.03283038198072
Trimmed Mean ( 24 / 64 )18941962918565.917846708975090.71.06137007921202
Trimmed Mean ( 25 / 64 )19227614070362.517579086020185.31.09377780211578
Trimmed Mean ( 26 / 64 )19466198719539.817308751578734.21.12464487291251
Trimmed Mean ( 27 / 64 )19206380291694.417119058585948.81.12192970164018
Trimmed Mean ( 28 / 64 )18889358688664.216924874762362.11.11607081020598
Trimmed Mean ( 29 / 64 )18499891275988.8167238077768391.10620090369668
Trimmed Mean ( 30 / 64 )18170196404504.916521549194389.41.09978768883703
Trimmed Mean ( 31 / 64 )18160096916223.516365391474673.51.10966468136906
Trimmed Mean ( 32 / 64 )18063076439558.416218725429973.51.1137173828824
Trimmed Mean ( 33 / 64 )1801396144144516078277035563.21.12039128331974
Trimmed Mean ( 34 / 64 )18000376758689.615938805157436.41.12934292005516
Trimmed Mean ( 35 / 64 )18059078419716.015815965869825.51.14182583399285
Trimmed Mean ( 36 / 64 )18127647900463.415692174843542.11.15520302833763
Trimmed Mean ( 37 / 64 )18154964983099.815586691614524.11.16477347676415
Trimmed Mean ( 38 / 64 )18208507601283.515521710825779.91.17309926757823
Trimmed Mean ( 39 / 64 )18274283434744.515456158690562.21.18233021545664
Trimmed Mean ( 40 / 64 )18271796766283.915395075211085.51.18685985717867
Trimmed Mean ( 41 / 64 )18204228177150.615338373095511.01.18684218096626
Trimmed Mean ( 42 / 64 )18069745747928.715284303521493.21.18224201204317
Trimmed Mean ( 43 / 64 )17897793948458.715227710944834.21.17534368844388
Trimmed Mean ( 44 / 64 )17666904712722.415169304485966.71.16464830204090
Trimmed Mean ( 45 / 64 )17379211436897.215118258753374.61.14955113021980
Trimmed Mean ( 46 / 64 )17064448529412.315071687254907.51.13221885783597
Trimmed Mean ( 47 / 64 )16721178506704.915022607666757.81.11306764295693
Trimmed Mean ( 48 / 64 )16342805220210.8149820065330971.09082886755573
Trimmed Mean ( 49 / 64 )15941674023691.314936482641223.81.06729773043710
Trimmed Mean ( 50 / 64 )15526258437599.414892326979927.21.04256765638618
Trimmed Mean ( 51 / 64 )15109949700890.114839533411362.41.01822269488073
Trimmed Mean ( 52 / 64 )14759324447993.014801037726890.20.997181732817194
Trimmed Mean ( 53 / 64 )14364136922270.414778531731215.70.97195967661185
Trimmed Mean ( 54 / 64 )13932601578821.514747798460860.20.944724164477688
Trimmed Mean ( 55 / 64 )13596346516705.614734933275435.50.922728746886961
Trimmed Mean ( 56 / 64 )13324469708053.314729249327122.40.90462652998328
Trimmed Mean ( 57 / 64 )13124266545267.314729575761462.20.89101456537567
Trimmed Mean ( 58 / 64 )12983001011954.714732713289287.40.881236250039223
Trimmed Mean ( 59 / 64 )12853496097377.314728925390274.20.872670324330972
Trimmed Mean ( 60 / 64 )12665246956987.814731575702231.40.859734709510359
Trimmed Mean ( 61 / 64 )12452065646541.114725149208543.90.84563256169357
Trimmed Mean ( 62 / 64 )12252215376825.114713567250182.10.832715490981525
Trimmed Mean ( 63 / 64 )12247622528997.614726353739188.40.831680587463093
Trimmed Mean ( 64 / 64 )12240212252463.514729636531787.60.830992144717773
Median31923419683984
Midrange-14731981046597.5
Midmean - Weighted Average at Xnp14257146597969.4
Midmean - Weighted Average at X(n+1)p16342805220210.8
Midmean - Empirical Distribution Function14257146597969.4
Midmean - Empirical Distribution Function - Averaging16342805220210.8
Midmean - Empirical Distribution Function - Interpolation16342805220210.8
Midmean - Closest Observation14257146597969.4
Midmean - True Basic - Statistics Graphics Toolkit16342805220210.8
Midmean - MS Excel (old versions)16721178506704.9
Number of observations192

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9553976186712.7 & 29637752726055.3 & 0.322358320316019 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -40.6195863705367 &  &  \tabularnewline
Quadratic Mean & 409713300139596 &  &  \tabularnewline
Winsorized Mean ( 1 / 64 ) & 9660989286401.01 & 29615802527381 & 0.326210619397163 \tabularnewline
Winsorized Mean ( 2 / 64 ) & 9751183850666.99 & 29457748962279.5 & 0.331022708597093 \tabularnewline
Winsorized Mean ( 3 / 64 ) & 10133697991392.2 & 29330852774278.1 & 0.345496193696728 \tabularnewline
Winsorized Mean ( 4 / 64 ) & 10637828318105.7 & 29156631773913.7 & 0.364851070610403 \tabularnewline
Winsorized Mean ( 5 / 64 ) & 10639465385802.0 & 29113546452821.8 & 0.365447246457697 \tabularnewline
Winsorized Mean ( 6 / 64 ) & 9937685436017.05 & 28962456352845.0 & 0.343123018122076 \tabularnewline
Winsorized Mean ( 7 / 64 ) & 8999288735873.62 & 28797779774439.4 & 0.312499394271404 \tabularnewline
Winsorized Mean ( 8 / 64 ) & 9350244586762.99 & 28715629572609.5 & 0.325615169366920 \tabularnewline
Winsorized Mean ( 9 / 64 ) & 9041812183796.97 & 28613369798426.8 & 0.315999557112428 \tabularnewline
Winsorized Mean ( 10 / 64 ) & 7853480474747.96 & 28320064497573.1 & 0.277311532091354 \tabularnewline
Winsorized Mean ( 11 / 64 ) & 7366819823445.19 & 27758739486165.1 & 0.265387404464702 \tabularnewline
Winsorized Mean ( 12 / 64 ) & 5836763260543.75 & 27139765163413.1 & 0.215063145366204 \tabularnewline
Winsorized Mean ( 13 / 64 ) & 6690288078686.63 & 26932334056955.0 & 0.24841100160641 \tabularnewline
Winsorized Mean ( 14 / 64 ) & 3832663512091.91 & 25881636180673.1 & 0.148084282049909 \tabularnewline
Winsorized Mean ( 15 / 64 ) & -701136478941.292 & 25278514836938.4 & -0.0277364585484568 \tabularnewline
Winsorized Mean ( 16 / 64 ) & -448416488506.13 & 24926511912375.8 & -0.0179895402165553 \tabularnewline
Winsorized Mean ( 17 / 64 ) & 1081318314395.11 & 24631250579453.3 & 0.0439002603991662 \tabularnewline
Winsorized Mean ( 18 / 64 ) & 245258992959.427 & 24508182870699.0 & 0.0100072287796028 \tabularnewline
Winsorized Mean ( 19 / 64 ) & 2632078621725.32 & 24068017701134.9 & 0.109360008556135 \tabularnewline
Winsorized Mean ( 20 / 64 ) & 5479509615139.07 & 23537013855804.0 & 0.232803942280378 \tabularnewline
Winsorized Mean ( 21 / 64 ) & 7343945366576.07 & 22603295012584.7 & 0.324905964483817 \tabularnewline
Winsorized Mean ( 22 / 64 ) & 10048308442038.4 & 21972045930979.0 & 0.457322384706608 \tabularnewline
Winsorized Mean ( 23 / 64 ) & 14412884302870.8 & 20619451960953.9 & 0.698994538272102 \tabularnewline
Winsorized Mean ( 24 / 64 ) & 13871654974175.2 & 20536514772569.9 & 0.675462955997928 \tabularnewline
Winsorized Mean ( 25 / 64 ) & 14878414736402.0 & 20300972273070.5 & 0.73289173229099 \tabularnewline
Winsorized Mean ( 26 / 64 ) & 24321555589901.4 & 19080390917558.7 & 1.27468853730452 \tabularnewline
Winsorized Mean ( 27 / 64 ) & 25269418449645.7 & 18922364503253.2 & 1.33542604811895 \tabularnewline
Winsorized Mean ( 28 / 64 ) & 26500201044696 & 18783654064015 & 1.41081181299351 \tabularnewline
Winsorized Mean ( 29 / 64 ) & 25073182776199.8 & 18570305073848.2 & 1.35017613746741 \tabularnewline
Winsorized Mean ( 30 / 64 ) & 18375342260219.6 & 17768690229724.2 & 1.03414162904819 \tabularnewline
Winsorized Mean ( 31 / 64 ) & 20165186767304.1 & 17449812210565.1 & 1.15561053173368 \tabularnewline
Winsorized Mean ( 32 / 64 ) & 19094491399939.1 & 17178002624658.4 & 1.11156645025363 \tabularnewline
Winsorized Mean ( 33 / 64 ) & 18303484992669.3 & 16975313281963.2 & 1.07824136666257 \tabularnewline
Winsorized Mean ( 34 / 64 ) & 16732176290265.5 & 16566496432389.4 & 1.01000089901642 \tabularnewline
Winsorized Mean ( 35 / 64 ) & 16559121028366.2 & 16398552677091.2 & 1.00979161725043 \tabularnewline
Winsorized Mean ( 36 / 64 ) & 17523257447132.2 & 15974440824774.8 & 1.09695592098318 \tabularnewline
Winsorized Mean ( 37 / 64 ) & 16958064372451.4 & 15260619660863.3 & 1.11123039229798 \tabularnewline
Winsorized Mean ( 38 / 64 ) & 16724440358821.7 & 15135147725957.7 & 1.10500674731692 \tabularnewline
Winsorized Mean ( 39 / 64 ) & 18330855142223.1 & 14938503513011.3 & 1.22708778200287 \tabularnewline
Winsorized Mean ( 40 / 64 ) & 19820243600588.1 & 14744118379227.5 & 1.34428136635908 \tabularnewline
Winsorized Mean ( 41 / 64 ) & 21305729201079.3 & 14574495356938.8 & 1.46185021705989 \tabularnewline
Winsorized Mean ( 42 / 64 ) & 22056878098139.9 & 14474647638689.6 & 1.52382832720457 \tabularnewline
Winsorized Mean ( 43 / 64 ) & 23275589064149.2 & 14358659130077.6 & 1.62101411094808 \tabularnewline
Winsorized Mean ( 44 / 64 ) & 24391735035137.1 & 14116478362046.3 & 1.72789093777929 \tabularnewline
Winsorized Mean ( 45 / 64 ) & 24756467081076.1 & 13919018028066.0 & 1.77860730054072 \tabularnewline
Winsorized Mean ( 46 / 64 ) & 25124142604229.8 & 13814671348888.1 & 1.81865655502922 \tabularnewline
Winsorized Mean ( 47 / 64 ) & 25612950739315.4 & 13562921017105.3 & 1.88845387413322 \tabularnewline
Winsorized Mean ( 48 / 64 ) & 25769388338419.6 & 13489848092437.1 & 1.91028009817745 \tabularnewline
Winsorized Mean ( 49 / 64 ) & 25695285805472.9 & 13330172022495.8 & 1.92760346694026 \tabularnewline
Winsorized Mean ( 50 / 64 ) & 25283494454223.9 & 13293512795795.2 & 1.90194231145745 \tabularnewline
Winsorized Mean ( 51 / 64 ) & 23305814987359 & 12972813871209.1 & 1.7965119378674 \tabularnewline
Winsorized Mean ( 52 / 64 ) & 23963900567949.5 & 12635406341744.6 & 1.89656746445724 \tabularnewline
Winsorized Mean ( 53 / 64 ) & 24370362698492.8 & 12602447326868.2 & 1.93378016716924 \tabularnewline
Winsorized Mean ( 54 / 64 ) & 21687483948869.2 & 12264575507510.1 & 1.76830286018371 \tabularnewline
Winsorized Mean ( 55 / 64 ) & 19826856714986.0 & 12064511367024.1 & 1.64340321060815 \tabularnewline
Winsorized Mean ( 56 / 64 ) & 17879091661436.4 & 11883349016284.5 & 1.50454990734814 \tabularnewline
Winsorized Mean ( 57 / 64 ) & 16311570140632.5 & 11740933061276.1 & 1.38929078766586 \tabularnewline
Winsorized Mean ( 58 / 64 ) & 15877975456569.7 & 11702326529802.7 & 1.35682211704935 \tabularnewline
Winsorized Mean ( 59 / 64 ) & 17018508328495.4 & 11508152405015.7 & 1.47882194548258 \tabularnewline
Winsorized Mean ( 60 / 64 ) & 17328588123009.8 & 11478629424857.4 & 1.50963912864754 \tabularnewline
Winsorized Mean ( 61 / 64 ) & 16769664181863.4 & 11395819966405.0 & 1.47156275119304 \tabularnewline
Winsorized Mean ( 62 / 64 ) & 12350100446148.9 & 11023802341972.2 & 1.1203122174213 \tabularnewline
Winsorized Mean ( 63 / 64 ) & 12403238336213.8 & 10991822568747.1 & 1.12840598168677 \tabularnewline
Winsorized Mean ( 64 / 64 ) & 14981550148741.8 & 10764198247414.7 & 1.39179433566639 \tabularnewline
Trimmed Mean ( 1 / 64 ) & 9809617841800.18 & 29075467868090.9 & 0.337384694420200 \tabularnewline
Trimmed Mean ( 2 / 64 ) & 9961408706888.69 & 28497539539964.7 & 0.349553290132956 \tabularnewline
Trimmed Mean ( 3 / 64 ) & 10069911858487.0 & 27967349822736.7 & 0.360059566684449 \tabularnewline
Trimmed Mean ( 4 / 64 ) & 10047725377476.5 & 27448837403806.9 & 0.366052857892005 \tabularnewline
Trimmed Mean ( 5 / 64 ) & 9892093832695.14 & 26945806559434.6 & 0.367110697201662 \tabularnewline
Trimmed Mean ( 6 / 64 ) & 9732654568032.35 & 26417270125539.4 & 0.368420147947957 \tabularnewline
Trimmed Mean ( 7 / 64 ) & 9695795086147.46 & 25882580984611.2 & 0.374606964116608 \tabularnewline
Trimmed Mean ( 8 / 64 ) & 9804341530345.99 & 25339652781504.2 & 0.386916964288569 \tabularnewline
Trimmed Mean ( 9 / 64 ) & 9866975591529.85 & 24769739963443.6 & 0.39834796837157 \tabularnewline
Trimmed Mean ( 10 / 64 ) & 9969321440550.98 & 24171868733497.0 & 0.412434865937182 \tabularnewline
Trimmed Mean ( 11 / 64 ) & 10208287008453.4 & 23570895231595.7 & 0.433088642079648 \tabularnewline
Trimmed Mean ( 12 / 64 ) & 10503504378324.4 & 23001909694823.6 & 0.456636188806887 \tabularnewline
Trimmed Mean ( 13 / 64 ) & 10953310751122.6 & 22470430658296.1 & 0.487454420330774 \tabularnewline
Trimmed Mean ( 14 / 64 ) & 11337222736632.7 & 21922372513023.2 & 0.51715309234426 \tabularnewline
Trimmed Mean ( 15 / 64 ) & 11972529337652.1 & 21457967728489.8 & 0.557952621102888 \tabularnewline
Trimmed Mean ( 16 / 64 ) & 12986422602979.5 & 21024726426788.3 & 0.617673797002805 \tabularnewline
Trimmed Mean ( 17 / 64 ) & 14006790128915.2 & 20595324556871.8 & 0.68009562511321 \tabularnewline
Trimmed Mean ( 18 / 64 ) & 14942570893767.3 & 20162749944861.5 & 0.741097862872393 \tabularnewline
Trimmed Mean ( 19 / 64 ) & 15960566523260.5 & 19706246246850.2 & 0.809924240432729 \tabularnewline
Trimmed Mean ( 20 / 64 ) & 16846670982088.3 & 19257284015094.6 & 0.87482071557356 \tabularnewline
Trimmed Mean ( 21 / 64 ) & 17574169309573.1 & 18824575661667.7 & 0.93357585453356 \tabularnewline
Trimmed Mean ( 22 / 64 ) & 18206152255858.6 & 18447744461331.6 & 0.9869039705109 \tabularnewline
Trimmed Mean ( 23 / 64 ) & 18693794227294.9 & 18099578162529.2 & 1.03283038198072 \tabularnewline
Trimmed Mean ( 24 / 64 ) & 18941962918565.9 & 17846708975090.7 & 1.06137007921202 \tabularnewline
Trimmed Mean ( 25 / 64 ) & 19227614070362.5 & 17579086020185.3 & 1.09377780211578 \tabularnewline
Trimmed Mean ( 26 / 64 ) & 19466198719539.8 & 17308751578734.2 & 1.12464487291251 \tabularnewline
Trimmed Mean ( 27 / 64 ) & 19206380291694.4 & 17119058585948.8 & 1.12192970164018 \tabularnewline
Trimmed Mean ( 28 / 64 ) & 18889358688664.2 & 16924874762362.1 & 1.11607081020598 \tabularnewline
Trimmed Mean ( 29 / 64 ) & 18499891275988.8 & 16723807776839 & 1.10620090369668 \tabularnewline
Trimmed Mean ( 30 / 64 ) & 18170196404504.9 & 16521549194389.4 & 1.09978768883703 \tabularnewline
Trimmed Mean ( 31 / 64 ) & 18160096916223.5 & 16365391474673.5 & 1.10966468136906 \tabularnewline
Trimmed Mean ( 32 / 64 ) & 18063076439558.4 & 16218725429973.5 & 1.1137173828824 \tabularnewline
Trimmed Mean ( 33 / 64 ) & 18013961441445 & 16078277035563.2 & 1.12039128331974 \tabularnewline
Trimmed Mean ( 34 / 64 ) & 18000376758689.6 & 15938805157436.4 & 1.12934292005516 \tabularnewline
Trimmed Mean ( 35 / 64 ) & 18059078419716.0 & 15815965869825.5 & 1.14182583399285 \tabularnewline
Trimmed Mean ( 36 / 64 ) & 18127647900463.4 & 15692174843542.1 & 1.15520302833763 \tabularnewline
Trimmed Mean ( 37 / 64 ) & 18154964983099.8 & 15586691614524.1 & 1.16477347676415 \tabularnewline
Trimmed Mean ( 38 / 64 ) & 18208507601283.5 & 15521710825779.9 & 1.17309926757823 \tabularnewline
Trimmed Mean ( 39 / 64 ) & 18274283434744.5 & 15456158690562.2 & 1.18233021545664 \tabularnewline
Trimmed Mean ( 40 / 64 ) & 18271796766283.9 & 15395075211085.5 & 1.18685985717867 \tabularnewline
Trimmed Mean ( 41 / 64 ) & 18204228177150.6 & 15338373095511.0 & 1.18684218096626 \tabularnewline
Trimmed Mean ( 42 / 64 ) & 18069745747928.7 & 15284303521493.2 & 1.18224201204317 \tabularnewline
Trimmed Mean ( 43 / 64 ) & 17897793948458.7 & 15227710944834.2 & 1.17534368844388 \tabularnewline
Trimmed Mean ( 44 / 64 ) & 17666904712722.4 & 15169304485966.7 & 1.16464830204090 \tabularnewline
Trimmed Mean ( 45 / 64 ) & 17379211436897.2 & 15118258753374.6 & 1.14955113021980 \tabularnewline
Trimmed Mean ( 46 / 64 ) & 17064448529412.3 & 15071687254907.5 & 1.13221885783597 \tabularnewline
Trimmed Mean ( 47 / 64 ) & 16721178506704.9 & 15022607666757.8 & 1.11306764295693 \tabularnewline
Trimmed Mean ( 48 / 64 ) & 16342805220210.8 & 14982006533097 & 1.09082886755573 \tabularnewline
Trimmed Mean ( 49 / 64 ) & 15941674023691.3 & 14936482641223.8 & 1.06729773043710 \tabularnewline
Trimmed Mean ( 50 / 64 ) & 15526258437599.4 & 14892326979927.2 & 1.04256765638618 \tabularnewline
Trimmed Mean ( 51 / 64 ) & 15109949700890.1 & 14839533411362.4 & 1.01822269488073 \tabularnewline
Trimmed Mean ( 52 / 64 ) & 14759324447993.0 & 14801037726890.2 & 0.997181732817194 \tabularnewline
Trimmed Mean ( 53 / 64 ) & 14364136922270.4 & 14778531731215.7 & 0.97195967661185 \tabularnewline
Trimmed Mean ( 54 / 64 ) & 13932601578821.5 & 14747798460860.2 & 0.944724164477688 \tabularnewline
Trimmed Mean ( 55 / 64 ) & 13596346516705.6 & 14734933275435.5 & 0.922728746886961 \tabularnewline
Trimmed Mean ( 56 / 64 ) & 13324469708053.3 & 14729249327122.4 & 0.90462652998328 \tabularnewline
Trimmed Mean ( 57 / 64 ) & 13124266545267.3 & 14729575761462.2 & 0.89101456537567 \tabularnewline
Trimmed Mean ( 58 / 64 ) & 12983001011954.7 & 14732713289287.4 & 0.881236250039223 \tabularnewline
Trimmed Mean ( 59 / 64 ) & 12853496097377.3 & 14728925390274.2 & 0.872670324330972 \tabularnewline
Trimmed Mean ( 60 / 64 ) & 12665246956987.8 & 14731575702231.4 & 0.859734709510359 \tabularnewline
Trimmed Mean ( 61 / 64 ) & 12452065646541.1 & 14725149208543.9 & 0.84563256169357 \tabularnewline
Trimmed Mean ( 62 / 64 ) & 12252215376825.1 & 14713567250182.1 & 0.832715490981525 \tabularnewline
Trimmed Mean ( 63 / 64 ) & 12247622528997.6 & 14726353739188.4 & 0.831680587463093 \tabularnewline
Trimmed Mean ( 64 / 64 ) & 12240212252463.5 & 14729636531787.6 & 0.830992144717773 \tabularnewline
Median & 31923419683984 &  &  \tabularnewline
Midrange & -14731981046597.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 14257146597969.4 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16342805220210.8 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 14257146597969.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16342805220210.8 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16342805220210.8 &  &  \tabularnewline
Midmean - Closest Observation & 14257146597969.4 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16342805220210.8 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16721178506704.9 &  &  \tabularnewline
Number of observations & 192 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=26202&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]9553976186712.7[/C][C]29637752726055.3[/C][C]0.322358320316019[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-40.6195863705367[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]409713300139596[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 64 )[/C][C]9660989286401.01[/C][C]29615802527381[/C][C]0.326210619397163[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 64 )[/C][C]9751183850666.99[/C][C]29457748962279.5[/C][C]0.331022708597093[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 64 )[/C][C]10133697991392.2[/C][C]29330852774278.1[/C][C]0.345496193696728[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 64 )[/C][C]10637828318105.7[/C][C]29156631773913.7[/C][C]0.364851070610403[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 64 )[/C][C]10639465385802.0[/C][C]29113546452821.8[/C][C]0.365447246457697[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 64 )[/C][C]9937685436017.05[/C][C]28962456352845.0[/C][C]0.343123018122076[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 64 )[/C][C]8999288735873.62[/C][C]28797779774439.4[/C][C]0.312499394271404[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 64 )[/C][C]9350244586762.99[/C][C]28715629572609.5[/C][C]0.325615169366920[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 64 )[/C][C]9041812183796.97[/C][C]28613369798426.8[/C][C]0.315999557112428[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 64 )[/C][C]7853480474747.96[/C][C]28320064497573.1[/C][C]0.277311532091354[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 64 )[/C][C]7366819823445.19[/C][C]27758739486165.1[/C][C]0.265387404464702[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 64 )[/C][C]5836763260543.75[/C][C]27139765163413.1[/C][C]0.215063145366204[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 64 )[/C][C]6690288078686.63[/C][C]26932334056955.0[/C][C]0.24841100160641[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 64 )[/C][C]3832663512091.91[/C][C]25881636180673.1[/C][C]0.148084282049909[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 64 )[/C][C]-701136478941.292[/C][C]25278514836938.4[/C][C]-0.0277364585484568[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 64 )[/C][C]-448416488506.13[/C][C]24926511912375.8[/C][C]-0.0179895402165553[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 64 )[/C][C]1081318314395.11[/C][C]24631250579453.3[/C][C]0.0439002603991662[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 64 )[/C][C]245258992959.427[/C][C]24508182870699.0[/C][C]0.0100072287796028[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 64 )[/C][C]2632078621725.32[/C][C]24068017701134.9[/C][C]0.109360008556135[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 64 )[/C][C]5479509615139.07[/C][C]23537013855804.0[/C][C]0.232803942280378[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 64 )[/C][C]7343945366576.07[/C][C]22603295012584.7[/C][C]0.324905964483817[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 64 )[/C][C]10048308442038.4[/C][C]21972045930979.0[/C][C]0.457322384706608[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 64 )[/C][C]14412884302870.8[/C][C]20619451960953.9[/C][C]0.698994538272102[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 64 )[/C][C]13871654974175.2[/C][C]20536514772569.9[/C][C]0.675462955997928[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 64 )[/C][C]14878414736402.0[/C][C]20300972273070.5[/C][C]0.73289173229099[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 64 )[/C][C]24321555589901.4[/C][C]19080390917558.7[/C][C]1.27468853730452[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 64 )[/C][C]25269418449645.7[/C][C]18922364503253.2[/C][C]1.33542604811895[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 64 )[/C][C]26500201044696[/C][C]18783654064015[/C][C]1.41081181299351[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 64 )[/C][C]25073182776199.8[/C][C]18570305073848.2[/C][C]1.35017613746741[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 64 )[/C][C]18375342260219.6[/C][C]17768690229724.2[/C][C]1.03414162904819[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 64 )[/C][C]20165186767304.1[/C][C]17449812210565.1[/C][C]1.15561053173368[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 64 )[/C][C]19094491399939.1[/C][C]17178002624658.4[/C][C]1.11156645025363[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 64 )[/C][C]18303484992669.3[/C][C]16975313281963.2[/C][C]1.07824136666257[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 64 )[/C][C]16732176290265.5[/C][C]16566496432389.4[/C][C]1.01000089901642[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 64 )[/C][C]16559121028366.2[/C][C]16398552677091.2[/C][C]1.00979161725043[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 64 )[/C][C]17523257447132.2[/C][C]15974440824774.8[/C][C]1.09695592098318[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 64 )[/C][C]16958064372451.4[/C][C]15260619660863.3[/C][C]1.11123039229798[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 64 )[/C][C]16724440358821.7[/C][C]15135147725957.7[/C][C]1.10500674731692[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 64 )[/C][C]18330855142223.1[/C][C]14938503513011.3[/C][C]1.22708778200287[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 64 )[/C][C]19820243600588.1[/C][C]14744118379227.5[/C][C]1.34428136635908[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 64 )[/C][C]21305729201079.3[/C][C]14574495356938.8[/C][C]1.46185021705989[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 64 )[/C][C]22056878098139.9[/C][C]14474647638689.6[/C][C]1.52382832720457[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 64 )[/C][C]23275589064149.2[/C][C]14358659130077.6[/C][C]1.62101411094808[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 64 )[/C][C]24391735035137.1[/C][C]14116478362046.3[/C][C]1.72789093777929[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 64 )[/C][C]24756467081076.1[/C][C]13919018028066.0[/C][C]1.77860730054072[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 64 )[/C][C]25124142604229.8[/C][C]13814671348888.1[/C][C]1.81865655502922[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 64 )[/C][C]25612950739315.4[/C][C]13562921017105.3[/C][C]1.88845387413322[/C][/ROW]
[ROW][C]Winsorized Mean ( 48 / 64 )[/C][C]25769388338419.6[/C][C]13489848092437.1[/C][C]1.91028009817745[/C][/ROW]
[ROW][C]Winsorized Mean ( 49 / 64 )[/C][C]25695285805472.9[/C][C]13330172022495.8[/C][C]1.92760346694026[/C][/ROW]
[ROW][C]Winsorized Mean ( 50 / 64 )[/C][C]25283494454223.9[/C][C]13293512795795.2[/C][C]1.90194231145745[/C][/ROW]
[ROW][C]Winsorized Mean ( 51 / 64 )[/C][C]23305814987359[/C][C]12972813871209.1[/C][C]1.7965119378674[/C][/ROW]
[ROW][C]Winsorized Mean ( 52 / 64 )[/C][C]23963900567949.5[/C][C]12635406341744.6[/C][C]1.89656746445724[/C][/ROW]
[ROW][C]Winsorized Mean ( 53 / 64 )[/C][C]24370362698492.8[/C][C]12602447326868.2[/C][C]1.93378016716924[/C][/ROW]
[ROW][C]Winsorized Mean ( 54 / 64 )[/C][C]21687483948869.2[/C][C]12264575507510.1[/C][C]1.76830286018371[/C][/ROW]
[ROW][C]Winsorized Mean ( 55 / 64 )[/C][C]19826856714986.0[/C][C]12064511367024.1[/C][C]1.64340321060815[/C][/ROW]
[ROW][C]Winsorized Mean ( 56 / 64 )[/C][C]17879091661436.4[/C][C]11883349016284.5[/C][C]1.50454990734814[/C][/ROW]
[ROW][C]Winsorized Mean ( 57 / 64 )[/C][C]16311570140632.5[/C][C]11740933061276.1[/C][C]1.38929078766586[/C][/ROW]
[ROW][C]Winsorized Mean ( 58 / 64 )[/C][C]15877975456569.7[/C][C]11702326529802.7[/C][C]1.35682211704935[/C][/ROW]
[ROW][C]Winsorized Mean ( 59 / 64 )[/C][C]17018508328495.4[/C][C]11508152405015.7[/C][C]1.47882194548258[/C][/ROW]
[ROW][C]Winsorized Mean ( 60 / 64 )[/C][C]17328588123009.8[/C][C]11478629424857.4[/C][C]1.50963912864754[/C][/ROW]
[ROW][C]Winsorized Mean ( 61 / 64 )[/C][C]16769664181863.4[/C][C]11395819966405.0[/C][C]1.47156275119304[/C][/ROW]
[ROW][C]Winsorized Mean ( 62 / 64 )[/C][C]12350100446148.9[/C][C]11023802341972.2[/C][C]1.1203122174213[/C][/ROW]
[ROW][C]Winsorized Mean ( 63 / 64 )[/C][C]12403238336213.8[/C][C]10991822568747.1[/C][C]1.12840598168677[/C][/ROW]
[ROW][C]Winsorized Mean ( 64 / 64 )[/C][C]14981550148741.8[/C][C]10764198247414.7[/C][C]1.39179433566639[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 64 )[/C][C]9809617841800.18[/C][C]29075467868090.9[/C][C]0.337384694420200[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 64 )[/C][C]9961408706888.69[/C][C]28497539539964.7[/C][C]0.349553290132956[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 64 )[/C][C]10069911858487.0[/C][C]27967349822736.7[/C][C]0.360059566684449[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 64 )[/C][C]10047725377476.5[/C][C]27448837403806.9[/C][C]0.366052857892005[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 64 )[/C][C]9892093832695.14[/C][C]26945806559434.6[/C][C]0.367110697201662[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 64 )[/C][C]9732654568032.35[/C][C]26417270125539.4[/C][C]0.368420147947957[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 64 )[/C][C]9695795086147.46[/C][C]25882580984611.2[/C][C]0.374606964116608[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 64 )[/C][C]9804341530345.99[/C][C]25339652781504.2[/C][C]0.386916964288569[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 64 )[/C][C]9866975591529.85[/C][C]24769739963443.6[/C][C]0.39834796837157[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 64 )[/C][C]9969321440550.98[/C][C]24171868733497.0[/C][C]0.412434865937182[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 64 )[/C][C]10208287008453.4[/C][C]23570895231595.7[/C][C]0.433088642079648[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 64 )[/C][C]10503504378324.4[/C][C]23001909694823.6[/C][C]0.456636188806887[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 64 )[/C][C]10953310751122.6[/C][C]22470430658296.1[/C][C]0.487454420330774[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 64 )[/C][C]11337222736632.7[/C][C]21922372513023.2[/C][C]0.51715309234426[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 64 )[/C][C]11972529337652.1[/C][C]21457967728489.8[/C][C]0.557952621102888[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 64 )[/C][C]12986422602979.5[/C][C]21024726426788.3[/C][C]0.617673797002805[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 64 )[/C][C]14006790128915.2[/C][C]20595324556871.8[/C][C]0.68009562511321[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 64 )[/C][C]14942570893767.3[/C][C]20162749944861.5[/C][C]0.741097862872393[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 64 )[/C][C]15960566523260.5[/C][C]19706246246850.2[/C][C]0.809924240432729[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 64 )[/C][C]16846670982088.3[/C][C]19257284015094.6[/C][C]0.87482071557356[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 64 )[/C][C]17574169309573.1[/C][C]18824575661667.7[/C][C]0.93357585453356[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 64 )[/C][C]18206152255858.6[/C][C]18447744461331.6[/C][C]0.9869039705109[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 64 )[/C][C]18693794227294.9[/C][C]18099578162529.2[/C][C]1.03283038198072[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 64 )[/C][C]18941962918565.9[/C][C]17846708975090.7[/C][C]1.06137007921202[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 64 )[/C][C]19227614070362.5[/C][C]17579086020185.3[/C][C]1.09377780211578[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 64 )[/C][C]19466198719539.8[/C][C]17308751578734.2[/C][C]1.12464487291251[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 64 )[/C][C]19206380291694.4[/C][C]17119058585948.8[/C][C]1.12192970164018[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 64 )[/C][C]18889358688664.2[/C][C]16924874762362.1[/C][C]1.11607081020598[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 64 )[/C][C]18499891275988.8[/C][C]16723807776839[/C][C]1.10620090369668[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 64 )[/C][C]18170196404504.9[/C][C]16521549194389.4[/C][C]1.09978768883703[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 64 )[/C][C]18160096916223.5[/C][C]16365391474673.5[/C][C]1.10966468136906[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 64 )[/C][C]18063076439558.4[/C][C]16218725429973.5[/C][C]1.1137173828824[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 64 )[/C][C]18013961441445[/C][C]16078277035563.2[/C][C]1.12039128331974[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 64 )[/C][C]18000376758689.6[/C][C]15938805157436.4[/C][C]1.12934292005516[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 64 )[/C][C]18059078419716.0[/C][C]15815965869825.5[/C][C]1.14182583399285[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 64 )[/C][C]18127647900463.4[/C][C]15692174843542.1[/C][C]1.15520302833763[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 64 )[/C][C]18154964983099.8[/C][C]15586691614524.1[/C][C]1.16477347676415[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 64 )[/C][C]18208507601283.5[/C][C]15521710825779.9[/C][C]1.17309926757823[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 64 )[/C][C]18274283434744.5[/C][C]15456158690562.2[/C][C]1.18233021545664[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 64 )[/C][C]18271796766283.9[/C][C]15395075211085.5[/C][C]1.18685985717867[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 64 )[/C][C]18204228177150.6[/C][C]15338373095511.0[/C][C]1.18684218096626[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 64 )[/C][C]18069745747928.7[/C][C]15284303521493.2[/C][C]1.18224201204317[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 64 )[/C][C]17897793948458.7[/C][C]15227710944834.2[/C][C]1.17534368844388[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 64 )[/C][C]17666904712722.4[/C][C]15169304485966.7[/C][C]1.16464830204090[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 64 )[/C][C]17379211436897.2[/C][C]15118258753374.6[/C][C]1.14955113021980[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 64 )[/C][C]17064448529412.3[/C][C]15071687254907.5[/C][C]1.13221885783597[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 64 )[/C][C]16721178506704.9[/C][C]15022607666757.8[/C][C]1.11306764295693[/C][/ROW]
[ROW][C]Trimmed Mean ( 48 / 64 )[/C][C]16342805220210.8[/C][C]14982006533097[/C][C]1.09082886755573[/C][/ROW]
[ROW][C]Trimmed Mean ( 49 / 64 )[/C][C]15941674023691.3[/C][C]14936482641223.8[/C][C]1.06729773043710[/C][/ROW]
[ROW][C]Trimmed Mean ( 50 / 64 )[/C][C]15526258437599.4[/C][C]14892326979927.2[/C][C]1.04256765638618[/C][/ROW]
[ROW][C]Trimmed Mean ( 51 / 64 )[/C][C]15109949700890.1[/C][C]14839533411362.4[/C][C]1.01822269488073[/C][/ROW]
[ROW][C]Trimmed Mean ( 52 / 64 )[/C][C]14759324447993.0[/C][C]14801037726890.2[/C][C]0.997181732817194[/C][/ROW]
[ROW][C]Trimmed Mean ( 53 / 64 )[/C][C]14364136922270.4[/C][C]14778531731215.7[/C][C]0.97195967661185[/C][/ROW]
[ROW][C]Trimmed Mean ( 54 / 64 )[/C][C]13932601578821.5[/C][C]14747798460860.2[/C][C]0.944724164477688[/C][/ROW]
[ROW][C]Trimmed Mean ( 55 / 64 )[/C][C]13596346516705.6[/C][C]14734933275435.5[/C][C]0.922728746886961[/C][/ROW]
[ROW][C]Trimmed Mean ( 56 / 64 )[/C][C]13324469708053.3[/C][C]14729249327122.4[/C][C]0.90462652998328[/C][/ROW]
[ROW][C]Trimmed Mean ( 57 / 64 )[/C][C]13124266545267.3[/C][C]14729575761462.2[/C][C]0.89101456537567[/C][/ROW]
[ROW][C]Trimmed Mean ( 58 / 64 )[/C][C]12983001011954.7[/C][C]14732713289287.4[/C][C]0.881236250039223[/C][/ROW]
[ROW][C]Trimmed Mean ( 59 / 64 )[/C][C]12853496097377.3[/C][C]14728925390274.2[/C][C]0.872670324330972[/C][/ROW]
[ROW][C]Trimmed Mean ( 60 / 64 )[/C][C]12665246956987.8[/C][C]14731575702231.4[/C][C]0.859734709510359[/C][/ROW]
[ROW][C]Trimmed Mean ( 61 / 64 )[/C][C]12452065646541.1[/C][C]14725149208543.9[/C][C]0.84563256169357[/C][/ROW]
[ROW][C]Trimmed Mean ( 62 / 64 )[/C][C]12252215376825.1[/C][C]14713567250182.1[/C][C]0.832715490981525[/C][/ROW]
[ROW][C]Trimmed Mean ( 63 / 64 )[/C][C]12247622528997.6[/C][C]14726353739188.4[/C][C]0.831680587463093[/C][/ROW]
[ROW][C]Trimmed Mean ( 64 / 64 )[/C][C]12240212252463.5[/C][C]14729636531787.6[/C][C]0.830992144717773[/C][/ROW]
[ROW][C]Median[/C][C]31923419683984[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-14731981046597.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]14257146597969.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16342805220210.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]14257146597969.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16342805220210.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16342805220210.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]14257146597969.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16342805220210.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16721178506704.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]192[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=26202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=26202&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9553976186712.729637752726055.30.322358320316019
Geometric MeanNaN
Harmonic Mean-40.6195863705367
Quadratic Mean409713300139596
Winsorized Mean ( 1 / 64 )9660989286401.01296158025273810.326210619397163
Winsorized Mean ( 2 / 64 )9751183850666.9929457748962279.50.331022708597093
Winsorized Mean ( 3 / 64 )10133697991392.229330852774278.10.345496193696728
Winsorized Mean ( 4 / 64 )10637828318105.729156631773913.70.364851070610403
Winsorized Mean ( 5 / 64 )10639465385802.029113546452821.80.365447246457697
Winsorized Mean ( 6 / 64 )9937685436017.0528962456352845.00.343123018122076
Winsorized Mean ( 7 / 64 )8999288735873.6228797779774439.40.312499394271404
Winsorized Mean ( 8 / 64 )9350244586762.9928715629572609.50.325615169366920
Winsorized Mean ( 9 / 64 )9041812183796.9728613369798426.80.315999557112428
Winsorized Mean ( 10 / 64 )7853480474747.9628320064497573.10.277311532091354
Winsorized Mean ( 11 / 64 )7366819823445.1927758739486165.10.265387404464702
Winsorized Mean ( 12 / 64 )5836763260543.7527139765163413.10.215063145366204
Winsorized Mean ( 13 / 64 )6690288078686.6326932334056955.00.24841100160641
Winsorized Mean ( 14 / 64 )3832663512091.9125881636180673.10.148084282049909
Winsorized Mean ( 15 / 64 )-701136478941.29225278514836938.4-0.0277364585484568
Winsorized Mean ( 16 / 64 )-448416488506.1324926511912375.8-0.0179895402165553
Winsorized Mean ( 17 / 64 )1081318314395.1124631250579453.30.0439002603991662
Winsorized Mean ( 18 / 64 )245258992959.42724508182870699.00.0100072287796028
Winsorized Mean ( 19 / 64 )2632078621725.3224068017701134.90.109360008556135
Winsorized Mean ( 20 / 64 )5479509615139.0723537013855804.00.232803942280378
Winsorized Mean ( 21 / 64 )7343945366576.0722603295012584.70.324905964483817
Winsorized Mean ( 22 / 64 )10048308442038.421972045930979.00.457322384706608
Winsorized Mean ( 23 / 64 )14412884302870.820619451960953.90.698994538272102
Winsorized Mean ( 24 / 64 )13871654974175.220536514772569.90.675462955997928
Winsorized Mean ( 25 / 64 )14878414736402.020300972273070.50.73289173229099
Winsorized Mean ( 26 / 64 )24321555589901.419080390917558.71.27468853730452
Winsorized Mean ( 27 / 64 )25269418449645.718922364503253.21.33542604811895
Winsorized Mean ( 28 / 64 )26500201044696187836540640151.41081181299351
Winsorized Mean ( 29 / 64 )25073182776199.818570305073848.21.35017613746741
Winsorized Mean ( 30 / 64 )18375342260219.617768690229724.21.03414162904819
Winsorized Mean ( 31 / 64 )20165186767304.117449812210565.11.15561053173368
Winsorized Mean ( 32 / 64 )19094491399939.117178002624658.41.11156645025363
Winsorized Mean ( 33 / 64 )18303484992669.316975313281963.21.07824136666257
Winsorized Mean ( 34 / 64 )16732176290265.516566496432389.41.01000089901642
Winsorized Mean ( 35 / 64 )16559121028366.216398552677091.21.00979161725043
Winsorized Mean ( 36 / 64 )17523257447132.215974440824774.81.09695592098318
Winsorized Mean ( 37 / 64 )16958064372451.415260619660863.31.11123039229798
Winsorized Mean ( 38 / 64 )16724440358821.715135147725957.71.10500674731692
Winsorized Mean ( 39 / 64 )18330855142223.114938503513011.31.22708778200287
Winsorized Mean ( 40 / 64 )19820243600588.114744118379227.51.34428136635908
Winsorized Mean ( 41 / 64 )21305729201079.314574495356938.81.46185021705989
Winsorized Mean ( 42 / 64 )22056878098139.914474647638689.61.52382832720457
Winsorized Mean ( 43 / 64 )23275589064149.214358659130077.61.62101411094808
Winsorized Mean ( 44 / 64 )24391735035137.114116478362046.31.72789093777929
Winsorized Mean ( 45 / 64 )24756467081076.113919018028066.01.77860730054072
Winsorized Mean ( 46 / 64 )25124142604229.813814671348888.11.81865655502922
Winsorized Mean ( 47 / 64 )25612950739315.413562921017105.31.88845387413322
Winsorized Mean ( 48 / 64 )25769388338419.613489848092437.11.91028009817745
Winsorized Mean ( 49 / 64 )25695285805472.913330172022495.81.92760346694026
Winsorized Mean ( 50 / 64 )25283494454223.913293512795795.21.90194231145745
Winsorized Mean ( 51 / 64 )2330581498735912972813871209.11.7965119378674
Winsorized Mean ( 52 / 64 )23963900567949.512635406341744.61.89656746445724
Winsorized Mean ( 53 / 64 )24370362698492.812602447326868.21.93378016716924
Winsorized Mean ( 54 / 64 )21687483948869.212264575507510.11.76830286018371
Winsorized Mean ( 55 / 64 )19826856714986.012064511367024.11.64340321060815
Winsorized Mean ( 56 / 64 )17879091661436.411883349016284.51.50454990734814
Winsorized Mean ( 57 / 64 )16311570140632.511740933061276.11.38929078766586
Winsorized Mean ( 58 / 64 )15877975456569.711702326529802.71.35682211704935
Winsorized Mean ( 59 / 64 )17018508328495.411508152405015.71.47882194548258
Winsorized Mean ( 60 / 64 )17328588123009.811478629424857.41.50963912864754
Winsorized Mean ( 61 / 64 )16769664181863.411395819966405.01.47156275119304
Winsorized Mean ( 62 / 64 )12350100446148.911023802341972.21.1203122174213
Winsorized Mean ( 63 / 64 )12403238336213.810991822568747.11.12840598168677
Winsorized Mean ( 64 / 64 )14981550148741.810764198247414.71.39179433566639
Trimmed Mean ( 1 / 64 )9809617841800.1829075467868090.90.337384694420200
Trimmed Mean ( 2 / 64 )9961408706888.6928497539539964.70.349553290132956
Trimmed Mean ( 3 / 64 )10069911858487.027967349822736.70.360059566684449
Trimmed Mean ( 4 / 64 )10047725377476.527448837403806.90.366052857892005
Trimmed Mean ( 5 / 64 )9892093832695.1426945806559434.60.367110697201662
Trimmed Mean ( 6 / 64 )9732654568032.3526417270125539.40.368420147947957
Trimmed Mean ( 7 / 64 )9695795086147.4625882580984611.20.374606964116608
Trimmed Mean ( 8 / 64 )9804341530345.9925339652781504.20.386916964288569
Trimmed Mean ( 9 / 64 )9866975591529.8524769739963443.60.39834796837157
Trimmed Mean ( 10 / 64 )9969321440550.9824171868733497.00.412434865937182
Trimmed Mean ( 11 / 64 )10208287008453.423570895231595.70.433088642079648
Trimmed Mean ( 12 / 64 )10503504378324.423001909694823.60.456636188806887
Trimmed Mean ( 13 / 64 )10953310751122.622470430658296.10.487454420330774
Trimmed Mean ( 14 / 64 )11337222736632.721922372513023.20.51715309234426
Trimmed Mean ( 15 / 64 )11972529337652.121457967728489.80.557952621102888
Trimmed Mean ( 16 / 64 )12986422602979.521024726426788.30.617673797002805
Trimmed Mean ( 17 / 64 )14006790128915.220595324556871.80.68009562511321
Trimmed Mean ( 18 / 64 )14942570893767.320162749944861.50.741097862872393
Trimmed Mean ( 19 / 64 )15960566523260.519706246246850.20.809924240432729
Trimmed Mean ( 20 / 64 )16846670982088.319257284015094.60.87482071557356
Trimmed Mean ( 21 / 64 )17574169309573.118824575661667.70.93357585453356
Trimmed Mean ( 22 / 64 )18206152255858.618447744461331.60.9869039705109
Trimmed Mean ( 23 / 64 )18693794227294.918099578162529.21.03283038198072
Trimmed Mean ( 24 / 64 )18941962918565.917846708975090.71.06137007921202
Trimmed Mean ( 25 / 64 )19227614070362.517579086020185.31.09377780211578
Trimmed Mean ( 26 / 64 )19466198719539.817308751578734.21.12464487291251
Trimmed Mean ( 27 / 64 )19206380291694.417119058585948.81.12192970164018
Trimmed Mean ( 28 / 64 )18889358688664.216924874762362.11.11607081020598
Trimmed Mean ( 29 / 64 )18499891275988.8167238077768391.10620090369668
Trimmed Mean ( 30 / 64 )18170196404504.916521549194389.41.09978768883703
Trimmed Mean ( 31 / 64 )18160096916223.516365391474673.51.10966468136906
Trimmed Mean ( 32 / 64 )18063076439558.416218725429973.51.1137173828824
Trimmed Mean ( 33 / 64 )1801396144144516078277035563.21.12039128331974
Trimmed Mean ( 34 / 64 )18000376758689.615938805157436.41.12934292005516
Trimmed Mean ( 35 / 64 )18059078419716.015815965869825.51.14182583399285
Trimmed Mean ( 36 / 64 )18127647900463.415692174843542.11.15520302833763
Trimmed Mean ( 37 / 64 )18154964983099.815586691614524.11.16477347676415
Trimmed Mean ( 38 / 64 )18208507601283.515521710825779.91.17309926757823
Trimmed Mean ( 39 / 64 )18274283434744.515456158690562.21.18233021545664
Trimmed Mean ( 40 / 64 )18271796766283.915395075211085.51.18685985717867
Trimmed Mean ( 41 / 64 )18204228177150.615338373095511.01.18684218096626
Trimmed Mean ( 42 / 64 )18069745747928.715284303521493.21.18224201204317
Trimmed Mean ( 43 / 64 )17897793948458.715227710944834.21.17534368844388
Trimmed Mean ( 44 / 64 )17666904712722.415169304485966.71.16464830204090
Trimmed Mean ( 45 / 64 )17379211436897.215118258753374.61.14955113021980
Trimmed Mean ( 46 / 64 )17064448529412.315071687254907.51.13221885783597
Trimmed Mean ( 47 / 64 )16721178506704.915022607666757.81.11306764295693
Trimmed Mean ( 48 / 64 )16342805220210.8149820065330971.09082886755573
Trimmed Mean ( 49 / 64 )15941674023691.314936482641223.81.06729773043710
Trimmed Mean ( 50 / 64 )15526258437599.414892326979927.21.04256765638618
Trimmed Mean ( 51 / 64 )15109949700890.114839533411362.41.01822269488073
Trimmed Mean ( 52 / 64 )14759324447993.014801037726890.20.997181732817194
Trimmed Mean ( 53 / 64 )14364136922270.414778531731215.70.97195967661185
Trimmed Mean ( 54 / 64 )13932601578821.514747798460860.20.944724164477688
Trimmed Mean ( 55 / 64 )13596346516705.614734933275435.50.922728746886961
Trimmed Mean ( 56 / 64 )13324469708053.314729249327122.40.90462652998328
Trimmed Mean ( 57 / 64 )13124266545267.314729575761462.20.89101456537567
Trimmed Mean ( 58 / 64 )12983001011954.714732713289287.40.881236250039223
Trimmed Mean ( 59 / 64 )12853496097377.314728925390274.20.872670324330972
Trimmed Mean ( 60 / 64 )12665246956987.814731575702231.40.859734709510359
Trimmed Mean ( 61 / 64 )12452065646541.114725149208543.90.84563256169357
Trimmed Mean ( 62 / 64 )12252215376825.114713567250182.10.832715490981525
Trimmed Mean ( 63 / 64 )12247622528997.614726353739188.40.831680587463093
Trimmed Mean ( 64 / 64 )12240212252463.514729636531787.60.830992144717773
Median31923419683984
Midrange-14731981046597.5
Midmean - Weighted Average at Xnp14257146597969.4
Midmean - Weighted Average at X(n+1)p16342805220210.8
Midmean - Empirical Distribution Function14257146597969.4
Midmean - Empirical Distribution Function - Averaging16342805220210.8
Midmean - Empirical Distribution Function - Interpolation16342805220210.8
Midmean - Closest Observation14257146597969.4
Midmean - True Basic - Statistics Graphics Toolkit16342805220210.8
Midmean - MS Excel (old versions)16721178506704.9
Number of observations192


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')