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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 06 Mar 2012 13:38:19 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/06/t1331059244f5rwv5lim9ak0mn.htm/, Retrieved Wed, 01 May 2024 19:48:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163550, Retrieved Wed, 01 May 2024 19:48:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords1EUR = Wisselkoers USD
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Gemiddelde wissel...] [2012-03-06 18:38:19] [dfc1948741ef97fe204bd83461871a05] [Current]
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Dataseries X:
1,322
1,3661
1,3898
1,3067
1,2894
1,277
1,2208
1,2565
1,3406
1,3569
1,3686
1,4272
1,4614
1,4914
1,4816
1,4562
1,4268
1,4088
1,4016
1,365
1,319
1,305
1,2785
1,3239
1,3449
1,2732
1,3322
1,437
1,4975
1,577
1,5553
1,5557
1,575
1,5527
1,4748
1,4718
1,457
1,4684
1,4227
1,3896
1,3622
1,3716
1,3419
1,3511
1,3516
1,3242
1,3074
1,2999
1,3213
1,2881
1,2611
1,2727
1,2811
1,2684
1,265
1,277
1,2271
1,202
1,1938
1,2103
1,1856
1,1786
1,2015
1,2256
1,2292
1,2037
1,2165
1,2694
1,2938
1,3201
1,3014
1,3119




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163550&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163550&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163550&T=0

As an alternative you can also use a 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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.343620833333330.0120451592133667111.548615467224
Geometric Mean1.33986978971738
Harmonic Mean1.33620150494423
Quadratic Mean1.34744871511353
Winsorized Mean ( 1 / 24 )1.343690277777780.0120192184653776111.795145553631
Winsorized Mean ( 2 / 24 )1.343381944444440.0118374315667286113.485931206587
Winsorized Mean ( 3 / 24 )1.343686111111110.0117773866410899114.090345512064
Winsorized Mean ( 4 / 24 )1.343569444444440.011736262011605114.48018484215
Winsorized Mean ( 5 / 24 )1.339854166666670.010838615169163123.618575413461
Winsorized Mean ( 6 / 24 )1.339895833333330.0106397158861186125.933422252512
Winsorized Mean ( 7 / 24 )1.339545833333330.0103498450045284129.426656413428
Winsorized Mean ( 8 / 24 )1.339268055555560.0101262092008461132.257593043175
Winsorized Mean ( 9 / 24 )1.339493055555560.00995800460619726134.514203249307
Winsorized Mean ( 10 / 24 )1.339229166666670.00983664331923782136.146968351236
Winsorized Mean ( 11 / 24 )1.338480555555560.00958967755688924139.575136662858
Winsorized Mean ( 12 / 24 )1.342297222222220.00877531414759471152.962868296874
Winsorized Mean ( 13 / 24 )1.342983333333330.00863602519347934155.509427455973
Winsorized Mean ( 14 / 24 )1.340008333333330.00786460438622311170.384709456041
Winsorized Mean ( 15 / 24 )1.3386750.00742077397215768180.395603615287
Winsorized Mean ( 16 / 24 )1.338808333333330.00737629322100987181.501506680891
Winsorized Mean ( 17 / 24 )1.338619444444440.00711185328280567188.223714862176
Winsorized Mean ( 18 / 24 )1.335269444444440.00652985908117978204.486716764368
Winsorized Mean ( 19 / 24 )1.334372222222220.00609797813481139218.822073927212
Winsorized Mean ( 20 / 24 )1.331094444444440.00560102791010722237.651814239748
Winsorized Mean ( 21 / 24 )1.331473611111110.0055331523222046240.635632922646
Winsorized Mean ( 22 / 24 )1.326768055555560.00464073185198437285.896297797993
Winsorized Mean ( 23 / 24 )1.328045833333330.0042056523266393315.776419491757
Winsorized Mean ( 24 / 24 )1.327645833333330.00403521467854638329.014919675004
Trimmed Mean ( 1 / 24 )1.342644285714290.0116888087964327114.865792494103
Trimmed Mean ( 2 / 24 )1.341536764705880.0112943978872968118.778953786882
Trimmed Mean ( 3 / 24 )1.34053030303030.0109397593905471122.53745765091
Trimmed Mean ( 4 / 24 )1.3393468750.0105394546354001127.079333925057
Trimmed Mean ( 5 / 24 )1.338120967741940.0100684868254621132.901893893129
Trimmed Mean ( 6 / 24 )1.3377050.0097990693161788136.513474579813
Trimmed Mean ( 7 / 24 )1.337251724137930.00952677833228496140.367674936465
Trimmed Mean ( 8 / 24 )1.336830357142860.00926912866624728144.22395084565
Trimmed Mean ( 9 / 24 )1.336424074074070.00900570513141212148.397494096558
Trimmed Mean ( 10 / 24 )1.335951923076920.00871658216293532153.265568786544
Trimmed Mean ( 11 / 24 )1.335480.00838106271572394159.344947687179
Trimmed Mean ( 12 / 24 )1.335070833333330.00801522540438489166.56684821402
Trimmed Mean ( 13 / 24 )1.334128260869570.00773514263132815172.476232754417
Trimmed Mean ( 14 / 24 )1.333013636363640.00739849678385905180.173577864061
Trimmed Mean ( 15 / 24 )1.332157142857140.00715247911737414186.251105525242
Trimmed Mean ( 16 / 24 )1.3313750.00693243098479706192.050235035838
Trimmed Mean ( 17 / 24 )1.330494736842110.00664027642075797200.367372159822
Trimmed Mean ( 18 / 24 )1.329538888888890.00630697557606715210.80450888918
Trimmed Mean ( 19 / 24 )1.328864705882350.00601901011391319220.777948654817
Trimmed Mean ( 20 / 24 )1.32821250.00573739633752724231.500914676647
Trimmed Mean ( 21 / 24 )1.327866666666670.00549137742771701241.809397395348
Trimmed Mean ( 22 / 24 )1.3274250.00514106721313261258.200281180755
Trimmed Mean ( 23 / 24 )1.327507692307690.00494335583019322268.543826887696
Trimmed Mean ( 24 / 24 )1.32743750.00478566629657501277.377781428266
Median1.32295
Midrange1.3778
Midmean - Weighted Average at Xnp1.3280027027027
Midmean - Weighted Average at X(n+1)p1.32953888888889
Midmean - Empirical Distribution Function1.3280027027027
Midmean - Empirical Distribution Function - Averaging1.32953888888889
Midmean - Empirical Distribution Function - Interpolation1.32953888888889
Midmean - Closest Observation1.3280027027027
Midmean - True Basic - Statistics Graphics Toolkit1.32953888888889
Midmean - MS Excel (old versions)1.33049473684211
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.34362083333333 & 0.0120451592133667 & 111.548615467224 \tabularnewline
Geometric Mean & 1.33986978971738 &  &  \tabularnewline
Harmonic Mean & 1.33620150494423 &  &  \tabularnewline
Quadratic Mean & 1.34744871511353 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.34369027777778 & 0.0120192184653776 & 111.795145553631 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.34338194444444 & 0.0118374315667286 & 113.485931206587 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.34368611111111 & 0.0117773866410899 & 114.090345512064 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.34356944444444 & 0.011736262011605 & 114.48018484215 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.33985416666667 & 0.010838615169163 & 123.618575413461 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.33989583333333 & 0.0106397158861186 & 125.933422252512 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.33954583333333 & 0.0103498450045284 & 129.426656413428 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.33926805555556 & 0.0101262092008461 & 132.257593043175 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.33949305555556 & 0.00995800460619726 & 134.514203249307 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.33922916666667 & 0.00983664331923782 & 136.146968351236 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.33848055555556 & 0.00958967755688924 & 139.575136662858 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.34229722222222 & 0.00877531414759471 & 152.962868296874 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.34298333333333 & 0.00863602519347934 & 155.509427455973 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.34000833333333 & 0.00786460438622311 & 170.384709456041 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.338675 & 0.00742077397215768 & 180.395603615287 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.33880833333333 & 0.00737629322100987 & 181.501506680891 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.33861944444444 & 0.00711185328280567 & 188.223714862176 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.33526944444444 & 0.00652985908117978 & 204.486716764368 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.33437222222222 & 0.00609797813481139 & 218.822073927212 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.33109444444444 & 0.00560102791010722 & 237.651814239748 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.33147361111111 & 0.0055331523222046 & 240.635632922646 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.32676805555556 & 0.00464073185198437 & 285.896297797993 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.32804583333333 & 0.0042056523266393 & 315.776419491757 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.32764583333333 & 0.00403521467854638 & 329.014919675004 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.34264428571429 & 0.0116888087964327 & 114.865792494103 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.34153676470588 & 0.0112943978872968 & 118.778953786882 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.3405303030303 & 0.0109397593905471 & 122.53745765091 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.339346875 & 0.0105394546354001 & 127.079333925057 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.33812096774194 & 0.0100684868254621 & 132.901893893129 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.337705 & 0.0097990693161788 & 136.513474579813 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.33725172413793 & 0.00952677833228496 & 140.367674936465 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.33683035714286 & 0.00926912866624728 & 144.22395084565 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.33642407407407 & 0.00900570513141212 & 148.397494096558 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.33595192307692 & 0.00871658216293532 & 153.265568786544 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.33548 & 0.00838106271572394 & 159.344947687179 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.33507083333333 & 0.00801522540438489 & 166.56684821402 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.33412826086957 & 0.00773514263132815 & 172.476232754417 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.33301363636364 & 0.00739849678385905 & 180.173577864061 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.33215714285714 & 0.00715247911737414 & 186.251105525242 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.331375 & 0.00693243098479706 & 192.050235035838 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.33049473684211 & 0.00664027642075797 & 200.367372159822 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.32953888888889 & 0.00630697557606715 & 210.80450888918 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.32886470588235 & 0.00601901011391319 & 220.777948654817 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.3282125 & 0.00573739633752724 & 231.500914676647 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.32786666666667 & 0.00549137742771701 & 241.809397395348 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.327425 & 0.00514106721313261 & 258.200281180755 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.32750769230769 & 0.00494335583019322 & 268.543826887696 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.3274375 & 0.00478566629657501 & 277.377781428266 \tabularnewline
Median & 1.32295 &  &  \tabularnewline
Midrange & 1.3778 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.3280027027027 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.32953888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.3280027027027 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.32953888888889 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.32953888888889 &  &  \tabularnewline
Midmean - Closest Observation & 1.3280027027027 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.32953888888889 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.33049473684211 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163550&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]1.34362083333333[/C][C]0.0120451592133667[/C][C]111.548615467224[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.33986978971738[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.33620150494423[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.34744871511353[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.34369027777778[/C][C]0.0120192184653776[/C][C]111.795145553631[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.34338194444444[/C][C]0.0118374315667286[/C][C]113.485931206587[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.34368611111111[/C][C]0.0117773866410899[/C][C]114.090345512064[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.34356944444444[/C][C]0.011736262011605[/C][C]114.48018484215[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.33985416666667[/C][C]0.010838615169163[/C][C]123.618575413461[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.33989583333333[/C][C]0.0106397158861186[/C][C]125.933422252512[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.33954583333333[/C][C]0.0103498450045284[/C][C]129.426656413428[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.33926805555556[/C][C]0.0101262092008461[/C][C]132.257593043175[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.33949305555556[/C][C]0.00995800460619726[/C][C]134.514203249307[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.33922916666667[/C][C]0.00983664331923782[/C][C]136.146968351236[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.33848055555556[/C][C]0.00958967755688924[/C][C]139.575136662858[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.34229722222222[/C][C]0.00877531414759471[/C][C]152.962868296874[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.34298333333333[/C][C]0.00863602519347934[/C][C]155.509427455973[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.34000833333333[/C][C]0.00786460438622311[/C][C]170.384709456041[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.338675[/C][C]0.00742077397215768[/C][C]180.395603615287[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.33880833333333[/C][C]0.00737629322100987[/C][C]181.501506680891[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.33861944444444[/C][C]0.00711185328280567[/C][C]188.223714862176[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.33526944444444[/C][C]0.00652985908117978[/C][C]204.486716764368[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.33437222222222[/C][C]0.00609797813481139[/C][C]218.822073927212[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.33109444444444[/C][C]0.00560102791010722[/C][C]237.651814239748[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.33147361111111[/C][C]0.0055331523222046[/C][C]240.635632922646[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.32676805555556[/C][C]0.00464073185198437[/C][C]285.896297797993[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.32804583333333[/C][C]0.0042056523266393[/C][C]315.776419491757[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.32764583333333[/C][C]0.00403521467854638[/C][C]329.014919675004[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.34264428571429[/C][C]0.0116888087964327[/C][C]114.865792494103[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.34153676470588[/C][C]0.0112943978872968[/C][C]118.778953786882[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.3405303030303[/C][C]0.0109397593905471[/C][C]122.53745765091[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.339346875[/C][C]0.0105394546354001[/C][C]127.079333925057[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.33812096774194[/C][C]0.0100684868254621[/C][C]132.901893893129[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.337705[/C][C]0.0097990693161788[/C][C]136.513474579813[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.33725172413793[/C][C]0.00952677833228496[/C][C]140.367674936465[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.33683035714286[/C][C]0.00926912866624728[/C][C]144.22395084565[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.33642407407407[/C][C]0.00900570513141212[/C][C]148.397494096558[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.33595192307692[/C][C]0.00871658216293532[/C][C]153.265568786544[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.33548[/C][C]0.00838106271572394[/C][C]159.344947687179[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.33507083333333[/C][C]0.00801522540438489[/C][C]166.56684821402[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.33412826086957[/C][C]0.00773514263132815[/C][C]172.476232754417[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.33301363636364[/C][C]0.00739849678385905[/C][C]180.173577864061[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.33215714285714[/C][C]0.00715247911737414[/C][C]186.251105525242[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.331375[/C][C]0.00693243098479706[/C][C]192.050235035838[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.33049473684211[/C][C]0.00664027642075797[/C][C]200.367372159822[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.32953888888889[/C][C]0.00630697557606715[/C][C]210.80450888918[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.32886470588235[/C][C]0.00601901011391319[/C][C]220.777948654817[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.3282125[/C][C]0.00573739633752724[/C][C]231.500914676647[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.32786666666667[/C][C]0.00549137742771701[/C][C]241.809397395348[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.327425[/C][C]0.00514106721313261[/C][C]258.200281180755[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.32750769230769[/C][C]0.00494335583019322[/C][C]268.543826887696[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.3274375[/C][C]0.00478566629657501[/C][C]277.377781428266[/C][/ROW]
[ROW][C]Median[/C][C]1.32295[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.3778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.3280027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.32953888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.3280027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.32953888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.32953888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.3280027027027[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.32953888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.33049473684211[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163550&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163550&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.343620833333330.0120451592133667111.548615467224
Geometric Mean1.33986978971738
Harmonic Mean1.33620150494423
Quadratic Mean1.34744871511353
Winsorized Mean ( 1 / 24 )1.343690277777780.0120192184653776111.795145553631
Winsorized Mean ( 2 / 24 )1.343381944444440.0118374315667286113.485931206587
Winsorized Mean ( 3 / 24 )1.343686111111110.0117773866410899114.090345512064
Winsorized Mean ( 4 / 24 )1.343569444444440.011736262011605114.48018484215
Winsorized Mean ( 5 / 24 )1.339854166666670.010838615169163123.618575413461
Winsorized Mean ( 6 / 24 )1.339895833333330.0106397158861186125.933422252512
Winsorized Mean ( 7 / 24 )1.339545833333330.0103498450045284129.426656413428
Winsorized Mean ( 8 / 24 )1.339268055555560.0101262092008461132.257593043175
Winsorized Mean ( 9 / 24 )1.339493055555560.00995800460619726134.514203249307
Winsorized Mean ( 10 / 24 )1.339229166666670.00983664331923782136.146968351236
Winsorized Mean ( 11 / 24 )1.338480555555560.00958967755688924139.575136662858
Winsorized Mean ( 12 / 24 )1.342297222222220.00877531414759471152.962868296874
Winsorized Mean ( 13 / 24 )1.342983333333330.00863602519347934155.509427455973
Winsorized Mean ( 14 / 24 )1.340008333333330.00786460438622311170.384709456041
Winsorized Mean ( 15 / 24 )1.3386750.00742077397215768180.395603615287
Winsorized Mean ( 16 / 24 )1.338808333333330.00737629322100987181.501506680891
Winsorized Mean ( 17 / 24 )1.338619444444440.00711185328280567188.223714862176
Winsorized Mean ( 18 / 24 )1.335269444444440.00652985908117978204.486716764368
Winsorized Mean ( 19 / 24 )1.334372222222220.00609797813481139218.822073927212
Winsorized Mean ( 20 / 24 )1.331094444444440.00560102791010722237.651814239748
Winsorized Mean ( 21 / 24 )1.331473611111110.0055331523222046240.635632922646
Winsorized Mean ( 22 / 24 )1.326768055555560.00464073185198437285.896297797993
Winsorized Mean ( 23 / 24 )1.328045833333330.0042056523266393315.776419491757
Winsorized Mean ( 24 / 24 )1.327645833333330.00403521467854638329.014919675004
Trimmed Mean ( 1 / 24 )1.342644285714290.0116888087964327114.865792494103
Trimmed Mean ( 2 / 24 )1.341536764705880.0112943978872968118.778953786882
Trimmed Mean ( 3 / 24 )1.34053030303030.0109397593905471122.53745765091
Trimmed Mean ( 4 / 24 )1.3393468750.0105394546354001127.079333925057
Trimmed Mean ( 5 / 24 )1.338120967741940.0100684868254621132.901893893129
Trimmed Mean ( 6 / 24 )1.3377050.0097990693161788136.513474579813
Trimmed Mean ( 7 / 24 )1.337251724137930.00952677833228496140.367674936465
Trimmed Mean ( 8 / 24 )1.336830357142860.00926912866624728144.22395084565
Trimmed Mean ( 9 / 24 )1.336424074074070.00900570513141212148.397494096558
Trimmed Mean ( 10 / 24 )1.335951923076920.00871658216293532153.265568786544
Trimmed Mean ( 11 / 24 )1.335480.00838106271572394159.344947687179
Trimmed Mean ( 12 / 24 )1.335070833333330.00801522540438489166.56684821402
Trimmed Mean ( 13 / 24 )1.334128260869570.00773514263132815172.476232754417
Trimmed Mean ( 14 / 24 )1.333013636363640.00739849678385905180.173577864061
Trimmed Mean ( 15 / 24 )1.332157142857140.00715247911737414186.251105525242
Trimmed Mean ( 16 / 24 )1.3313750.00693243098479706192.050235035838
Trimmed Mean ( 17 / 24 )1.330494736842110.00664027642075797200.367372159822
Trimmed Mean ( 18 / 24 )1.329538888888890.00630697557606715210.80450888918
Trimmed Mean ( 19 / 24 )1.328864705882350.00601901011391319220.777948654817
Trimmed Mean ( 20 / 24 )1.32821250.00573739633752724231.500914676647
Trimmed Mean ( 21 / 24 )1.327866666666670.00549137742771701241.809397395348
Trimmed Mean ( 22 / 24 )1.3274250.00514106721313261258.200281180755
Trimmed Mean ( 23 / 24 )1.327507692307690.00494335583019322268.543826887696
Trimmed Mean ( 24 / 24 )1.32743750.00478566629657501277.377781428266
Median1.32295
Midrange1.3778
Midmean - Weighted Average at Xnp1.3280027027027
Midmean - Weighted Average at X(n+1)p1.32953888888889
Midmean - Empirical Distribution Function1.3280027027027
Midmean - Empirical Distribution Function - Averaging1.32953888888889
Midmean - Empirical Distribution Function - Interpolation1.32953888888889
Midmean - Closest Observation1.3280027027027
Midmean - True Basic - Statistics Graphics Toolkit1.32953888888889
Midmean - MS Excel (old versions)1.33049473684211
Number of observations72



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')