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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 24 Dec 2010 14:57:15 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/24/t129320254972yyg26os8t6tpk.htm/, Retrieved Tue, 30 Apr 2024 06:47:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115042, Retrieved Tue, 30 Apr 2024 06:47:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Mean Plot] [Colombia Coffee] [2008-01-07 13:38:24] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [Paper uitvoer cen...] [2010-11-30 13:39:00] [247f085ab5b7724f755ad01dc754a3e8]
-    D      [Central Tendency] [paperCTuit] [2010-12-22 19:59:22] [7e261c986c934df955dd3ac53e9d45c6]
-               [Central Tendency] [Kristof Nagels] [2010-12-24 14:57:15] [fff0a1ca5ad3b1801f382406d5a383a7] [Current]
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Post a new message
Dataseries X:
15
14,4
13
13,7
13,6
15,2
12,9
14
14,1
13,2
11,3
13,3
14,4
13,3
11,6
13,2
13,1
14,6
14
14,3
13,8
13,7
11
14,4
15,6
13,7
12,6
13,2
13,3
14,3
14
13,4
13,9
13,7
10,5
14,5
15
13,5
13,5
13,2
13,8
16,2
14,7
13,9
16
14,4
12,3
15,9
15,9
15,5
15,1
14,5
15,1
17,4
16,2
15,6
17,2
14,9
13,8
17,5
16,2
17,5
16,6
16,2
16,6
19,6
15,9
18
18,3
16,3
14,9
18,2
18,4
18,5
16
17,4
17,2
19,6
17,2
18,3
19,3
18,1
16,2
18,4
20,5
19
16,5
18,7
19
19,2
20,5
19,3
20,6
20,1
16,1
20,4
19,7
15,6
14,4
13,7
14,1
15
14,2
13,6
15,4
14,8
12,5
16,2
16,1
16
15,8
15,2
15,7
18,9
17,4
17
19,8
17,7
16
19,6
19,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115042&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115042&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115042&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean15.71735537190080.21179307201263474.2109041742557
Geometric Mean15.5481040815154
Harmonic Mean15.3809402533699
Quadratic Mean15.8876686939565
Winsorized Mean ( 1 / 40 )15.72066115702480.21082586313502474.5670427871387
Winsorized Mean ( 2 / 40 )15.72561983471070.20992760435707874.9097284412495
Winsorized Mean ( 3 / 40 )15.73057851239670.20819254628705175.5578371701539
Winsorized Mean ( 4 / 40 )15.74380165289260.20282404458195677.6229548392173
Winsorized Mean ( 5 / 40 )15.73966942148760.19951897849772478.8880814246306
Winsorized Mean ( 6 / 40 )15.73966942148760.19802217415850579.4843783953655
Winsorized Mean ( 7 / 40 )15.75702479338840.19582004742323780.4668623092092
Winsorized Mean ( 8 / 40 )15.75702479338840.19392575631364681.2528727122962
Winsorized Mean ( 9 / 40 )15.76446280991740.19305739131610681.6568726141397
Winsorized Mean ( 10 / 40 )15.77272727272730.19212097313817582.0978939211568
Winsorized Mean ( 11 / 40 )15.74545454545450.1877039753685283.8845022570322
Winsorized Mean ( 12 / 40 )15.74545454545450.1877039753685283.8845022570322
Winsorized Mean ( 13 / 40 )15.73471074380170.18602226955683784.5850917811432
Winsorized Mean ( 14 / 40 )15.72314049586780.18117978959536786.7819778960036
Winsorized Mean ( 15 / 40 )15.72314049586780.18117978959536786.7819778960036
Winsorized Mean ( 16 / 40 )15.70991735537190.17920241475137687.6657682161691
Winsorized Mean ( 17 / 40 )15.69586776859500.17352843184532790.4512741899578
Winsorized Mean ( 18 / 40 )15.68099173553720.16767045128343593.5226905844586
Winsorized Mean ( 19 / 40 )15.66528925619830.16548913534453694.660529971254
Winsorized Mean ( 20 / 40 )15.68181818181820.16371210368375995.7889968362422
Winsorized Mean ( 21 / 40 )15.66446280991740.16132995595638097.0958103661338
Winsorized Mean ( 22 / 40 )15.68264462809920.15941818149827998.3742536811492
Winsorized Mean ( 23 / 40 )15.66363636363640.1568368456175199.872171631381
Winsorized Mean ( 24 / 40 )15.64380165289260.154183589549857101.462170510916
Winsorized Mean ( 25 / 40 )15.62314049586780.151461022136694103.149577861477
Winsorized Mean ( 26 / 40 )15.55867768595040.143224714216435108.631235684917
Winsorized Mean ( 27 / 40 )15.53636363636360.135344677834711114.791094004725
Winsorized Mean ( 28 / 40 )15.53636363636360.135344677834711114.791094004725
Winsorized Mean ( 29 / 40 )15.51239669421490.132472619177945117.098890249748
Winsorized Mean ( 30 / 40 )15.53719008264460.129834246053251119.669428944595
Winsorized Mean ( 31 / 40 )15.53719008264460.129834246053251119.669428944595
Winsorized Mean ( 32 / 40 )15.51074380165290.120820209145112128.378720012176
Winsorized Mean ( 33 / 40 )15.51074380165290.120820209145112128.378720012176
Winsorized Mean ( 34 / 40 )15.51074380165290.120820209145112128.378720012176
Winsorized Mean ( 35 / 40 )15.48181818181820.111148524463252139.289462065120
Winsorized Mean ( 36 / 40 )15.36280991735540.0980887060681991156.621598277318
Winsorized Mean ( 37 / 40 )15.39338842975210.0948446281807894162.301109983896
Winsorized Mean ( 38 / 40 )15.39338842975210.0882703050036697174.389206303435
Winsorized Mean ( 39 / 40 )15.32892561983470.0817039439563894187.615491707680
Winsorized Mean ( 40 / 40 )15.32892561983470.075024679286925204.318442484914
Trimmed Mean ( 1 / 40 )15.72016806722690.20675317029091076.0335043235755
Trimmed Mean ( 2 / 40 )15.71965811965810.20224294654113477.7266074713805
Trimmed Mean ( 3 / 40 )15.71652173913040.19776373901201779.4712004215062
Trimmed Mean ( 4 / 40 )15.71150442477880.19349712694478781.1976109043826
Trimmed Mean ( 5 / 40 )15.70270270270270.19046672904255382.4432843554239
Trimmed Mean ( 6 / 40 )15.69449541284400.18796094033255683.4987066199818
Trimmed Mean ( 7 / 40 )15.68598130841120.1854971283341884.5618552118626
Trimmed Mean ( 8 / 40 )15.67428571428570.18317023333474785.5722320648062
Trimmed Mean ( 9 / 40 )15.66213592233010.18089880986752686.5795409809473
Trimmed Mean ( 10 / 40 )15.64851485148510.17847324929976587.6798899156129
Trimmed Mean ( 11 / 40 )15.63333333333330.17586843154875688.8922087702778
Trimmed Mean ( 12 / 40 )15.62061855670100.17361960572503789.9703607289577
Trimmed Mean ( 13 / 40 )15.60736842105260.17105326901423191.242736902936
Trimmed Mean ( 14 / 40 )15.59462365591400.16837621775218192.6177334548899
Trimmed Mean ( 15 / 40 )15.58241758241760.16600302604442493.8682742942744
Trimmed Mean ( 16 / 40 )15.56966292134830.16327380775316595.3592198014164
Trimmed Mean ( 17 / 40 )15.55747126436780.16041439406694696.9830129949262
Trimmed Mean ( 18 / 40 )15.54588235294120.15788831408050298.4612600588971
Trimmed Mean ( 19 / 40 )15.53493975903610.15573504756314199.752367897391
Trimmed Mean ( 20 / 40 )15.52469135802470.153513690870099101.129034615951
Trimmed Mean ( 21 / 40 )15.51265822784810.151122244481231102.649734200941
Trimmed Mean ( 22 / 40 )15.50129870129870.14863808140235104.288877756287
Trimmed Mean ( 23 / 40 )15.4880.145935441730764106.129119947256
Trimmed Mean ( 24 / 40 )15.47534246575340.143103522122369108.140891546473
Trimmed Mean ( 25 / 40 )15.46338028169010.140124110504032110.354886293785
Trimmed Mean ( 26 / 40 )15.45217391304350.136975126951801112.81007184962
Trimmed Mean ( 27 / 40 )15.44477611940300.134424810841378114.895278801083
Trimmed Mean ( 28 / 40 )15.43846153846150.132445422498584116.564704519151
Trimmed Mean ( 29 / 40 )15.43174603174600.130024720892378118.683169829828
Trimmed Mean ( 30 / 40 )15.42622950819670.127500169063303120.989874927442
Trimmed Mean ( 31 / 40 )15.42622950819670.124766867957738123.640432437737
Trimmed Mean ( 32 / 40 )15.41052631578950.121387245930022126.953422476307
Trimmed Mean ( 33 / 40 )15.40363636363640.118689920442175129.780492785323
Trimmed Mean ( 34 / 40 )15.39622641509430.115301153738135133.530549486619
Trimmed Mean ( 35 / 40 )15.38823529411760.111025418704979138.601011134287
Trimmed Mean ( 36 / 40 )15.38163265306120.107486491375089143.102937460158
Trimmed Mean ( 37 / 40 )15.38297872340430.105462250588218145.862416529189
Trimmed Mean ( 38 / 40 )15.38222222222220.103391424965775148.776576271331
Trimmed Mean ( 39 / 40 )15.38139534883720.101879122671189150.97691210475
Trimmed Mean ( 40 / 40 )15.38536585365850.101004767794358152.323164436976
Median15.5
Midrange15.55
Midmean - Weighted Average at Xnp15.4580645161290
Midmean - Weighted Average at X(n+1)p15.4580645161290
Midmean - Empirical Distribution Function15.4580645161290
Midmean - Empirical Distribution Function - Averaging15.4580645161290
Midmean - Empirical Distribution Function - Interpolation15.4580645161290
Midmean - Closest Observation15.3815384615385
Midmean - True Basic - Statistics Graphics Toolkit15.4580645161290
Midmean - MS Excel (old versions)15.4580645161290
Number of observations121

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 15.7173553719008 & 0.211793072012634 & 74.2109041742557 \tabularnewline
Geometric Mean & 15.5481040815154 &  &  \tabularnewline
Harmonic Mean & 15.3809402533699 &  &  \tabularnewline
Quadratic Mean & 15.8876686939565 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 15.7206611570248 & 0.210825863135024 & 74.5670427871387 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 15.7256198347107 & 0.209927604357078 & 74.9097284412495 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 15.7305785123967 & 0.208192546287051 & 75.5578371701539 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 15.7438016528926 & 0.202824044581956 & 77.6229548392173 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 15.7396694214876 & 0.199518978497724 & 78.8880814246306 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 15.7396694214876 & 0.198022174158505 & 79.4843783953655 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 15.7570247933884 & 0.195820047423237 & 80.4668623092092 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 15.7570247933884 & 0.193925756313646 & 81.2528727122962 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 15.7644628099174 & 0.193057391316106 & 81.6568726141397 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 15.7727272727273 & 0.192120973138175 & 82.0978939211568 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 15.7454545454545 & 0.18770397536852 & 83.8845022570322 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 15.7454545454545 & 0.18770397536852 & 83.8845022570322 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 15.7347107438017 & 0.186022269556837 & 84.5850917811432 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 15.7231404958678 & 0.181179789595367 & 86.7819778960036 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 15.7231404958678 & 0.181179789595367 & 86.7819778960036 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 15.7099173553719 & 0.179202414751376 & 87.6657682161691 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 15.6958677685950 & 0.173528431845327 & 90.4512741899578 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 15.6809917355372 & 0.167670451283435 & 93.5226905844586 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 15.6652892561983 & 0.165489135344536 & 94.660529971254 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 15.6818181818182 & 0.163712103683759 & 95.7889968362422 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 15.6644628099174 & 0.161329955956380 & 97.0958103661338 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 15.6826446280992 & 0.159418181498279 & 98.3742536811492 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 15.6636363636364 & 0.15683684561751 & 99.872171631381 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 15.6438016528926 & 0.154183589549857 & 101.462170510916 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 15.6231404958678 & 0.151461022136694 & 103.149577861477 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 15.5586776859504 & 0.143224714216435 & 108.631235684917 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 15.5363636363636 & 0.135344677834711 & 114.791094004725 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 15.5363636363636 & 0.135344677834711 & 114.791094004725 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 15.5123966942149 & 0.132472619177945 & 117.098890249748 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 15.5371900826446 & 0.129834246053251 & 119.669428944595 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 15.5371900826446 & 0.129834246053251 & 119.669428944595 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 15.5107438016529 & 0.120820209145112 & 128.378720012176 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 15.5107438016529 & 0.120820209145112 & 128.378720012176 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 15.5107438016529 & 0.120820209145112 & 128.378720012176 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 15.4818181818182 & 0.111148524463252 & 139.289462065120 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 15.3628099173554 & 0.0980887060681991 & 156.621598277318 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 15.3933884297521 & 0.0948446281807894 & 162.301109983896 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 15.3933884297521 & 0.0882703050036697 & 174.389206303435 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 15.3289256198347 & 0.0817039439563894 & 187.615491707680 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 15.3289256198347 & 0.075024679286925 & 204.318442484914 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 15.7201680672269 & 0.206753170290910 & 76.0335043235755 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 15.7196581196581 & 0.202242946541134 & 77.7266074713805 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 15.7165217391304 & 0.197763739012017 & 79.4712004215062 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 15.7115044247788 & 0.193497126944787 & 81.1976109043826 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 15.7027027027027 & 0.190466729042553 & 82.4432843554239 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 15.6944954128440 & 0.187960940332556 & 83.4987066199818 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 15.6859813084112 & 0.18549712833418 & 84.5618552118626 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 15.6742857142857 & 0.183170233334747 & 85.5722320648062 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 15.6621359223301 & 0.180898809867526 & 86.5795409809473 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 15.6485148514851 & 0.178473249299765 & 87.6798899156129 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 15.6333333333333 & 0.175868431548756 & 88.8922087702778 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 15.6206185567010 & 0.173619605725037 & 89.9703607289577 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 15.6073684210526 & 0.171053269014231 & 91.242736902936 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 15.5946236559140 & 0.168376217752181 & 92.6177334548899 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 15.5824175824176 & 0.166003026044424 & 93.8682742942744 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 15.5696629213483 & 0.163273807753165 & 95.3592198014164 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 15.5574712643678 & 0.160414394066946 & 96.9830129949262 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 15.5458823529412 & 0.157888314080502 & 98.4612600588971 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 15.5349397590361 & 0.155735047563141 & 99.752367897391 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 15.5246913580247 & 0.153513690870099 & 101.129034615951 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 15.5126582278481 & 0.151122244481231 & 102.649734200941 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 15.5012987012987 & 0.14863808140235 & 104.288877756287 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 15.488 & 0.145935441730764 & 106.129119947256 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 15.4753424657534 & 0.143103522122369 & 108.140891546473 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 15.4633802816901 & 0.140124110504032 & 110.354886293785 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 15.4521739130435 & 0.136975126951801 & 112.81007184962 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 15.4447761194030 & 0.134424810841378 & 114.895278801083 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 15.4384615384615 & 0.132445422498584 & 116.564704519151 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 15.4317460317460 & 0.130024720892378 & 118.683169829828 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 15.4262295081967 & 0.127500169063303 & 120.989874927442 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 15.4262295081967 & 0.124766867957738 & 123.640432437737 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 15.4105263157895 & 0.121387245930022 & 126.953422476307 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 15.4036363636364 & 0.118689920442175 & 129.780492785323 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 15.3962264150943 & 0.115301153738135 & 133.530549486619 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 15.3882352941176 & 0.111025418704979 & 138.601011134287 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 15.3816326530612 & 0.107486491375089 & 143.102937460158 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 15.3829787234043 & 0.105462250588218 & 145.862416529189 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 15.3822222222222 & 0.103391424965775 & 148.776576271331 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 15.3813953488372 & 0.101879122671189 & 150.97691210475 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 15.3853658536585 & 0.101004767794358 & 152.323164436976 \tabularnewline
Median & 15.5 &  &  \tabularnewline
Midrange & 15.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15.4580645161290 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15.4580645161290 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15.4580645161290 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15.4580645161290 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15.4580645161290 &  &  \tabularnewline
Midmean - Closest Observation & 15.3815384615385 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15.4580645161290 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15.4580645161290 &  &  \tabularnewline
Number of observations & 121 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115042&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]15.7173553719008[/C][C]0.211793072012634[/C][C]74.2109041742557[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]15.5481040815154[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.3809402533699[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]15.8876686939565[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]15.7206611570248[/C][C]0.210825863135024[/C][C]74.5670427871387[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]15.7256198347107[/C][C]0.209927604357078[/C][C]74.9097284412495[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]15.7305785123967[/C][C]0.208192546287051[/C][C]75.5578371701539[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]15.7438016528926[/C][C]0.202824044581956[/C][C]77.6229548392173[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]15.7396694214876[/C][C]0.199518978497724[/C][C]78.8880814246306[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]15.7396694214876[/C][C]0.198022174158505[/C][C]79.4843783953655[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]15.7570247933884[/C][C]0.195820047423237[/C][C]80.4668623092092[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]15.7570247933884[/C][C]0.193925756313646[/C][C]81.2528727122962[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]15.7644628099174[/C][C]0.193057391316106[/C][C]81.6568726141397[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]15.7727272727273[/C][C]0.192120973138175[/C][C]82.0978939211568[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]15.7454545454545[/C][C]0.18770397536852[/C][C]83.8845022570322[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]15.7454545454545[/C][C]0.18770397536852[/C][C]83.8845022570322[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]15.7347107438017[/C][C]0.186022269556837[/C][C]84.5850917811432[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]15.7231404958678[/C][C]0.181179789595367[/C][C]86.7819778960036[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]15.7231404958678[/C][C]0.181179789595367[/C][C]86.7819778960036[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]15.7099173553719[/C][C]0.179202414751376[/C][C]87.6657682161691[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]15.6958677685950[/C][C]0.173528431845327[/C][C]90.4512741899578[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]15.6809917355372[/C][C]0.167670451283435[/C][C]93.5226905844586[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]15.6652892561983[/C][C]0.165489135344536[/C][C]94.660529971254[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]15.6818181818182[/C][C]0.163712103683759[/C][C]95.7889968362422[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]15.6644628099174[/C][C]0.161329955956380[/C][C]97.0958103661338[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]15.6826446280992[/C][C]0.159418181498279[/C][C]98.3742536811492[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]15.6636363636364[/C][C]0.15683684561751[/C][C]99.872171631381[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]15.6438016528926[/C][C]0.154183589549857[/C][C]101.462170510916[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]15.6231404958678[/C][C]0.151461022136694[/C][C]103.149577861477[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]15.5586776859504[/C][C]0.143224714216435[/C][C]108.631235684917[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]15.5363636363636[/C][C]0.135344677834711[/C][C]114.791094004725[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]15.5363636363636[/C][C]0.135344677834711[/C][C]114.791094004725[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]15.5123966942149[/C][C]0.132472619177945[/C][C]117.098890249748[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]15.5371900826446[/C][C]0.129834246053251[/C][C]119.669428944595[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]15.5371900826446[/C][C]0.129834246053251[/C][C]119.669428944595[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]15.5107438016529[/C][C]0.120820209145112[/C][C]128.378720012176[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]15.5107438016529[/C][C]0.120820209145112[/C][C]128.378720012176[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]15.5107438016529[/C][C]0.120820209145112[/C][C]128.378720012176[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]15.4818181818182[/C][C]0.111148524463252[/C][C]139.289462065120[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]15.3628099173554[/C][C]0.0980887060681991[/C][C]156.621598277318[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]15.3933884297521[/C][C]0.0948446281807894[/C][C]162.301109983896[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]15.3933884297521[/C][C]0.0882703050036697[/C][C]174.389206303435[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]15.3289256198347[/C][C]0.0817039439563894[/C][C]187.615491707680[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]15.3289256198347[/C][C]0.075024679286925[/C][C]204.318442484914[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]15.7201680672269[/C][C]0.206753170290910[/C][C]76.0335043235755[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]15.7196581196581[/C][C]0.202242946541134[/C][C]77.7266074713805[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]15.7165217391304[/C][C]0.197763739012017[/C][C]79.4712004215062[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]15.7115044247788[/C][C]0.193497126944787[/C][C]81.1976109043826[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]15.7027027027027[/C][C]0.190466729042553[/C][C]82.4432843554239[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]15.6944954128440[/C][C]0.187960940332556[/C][C]83.4987066199818[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]15.6859813084112[/C][C]0.18549712833418[/C][C]84.5618552118626[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]15.6742857142857[/C][C]0.183170233334747[/C][C]85.5722320648062[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]15.6621359223301[/C][C]0.180898809867526[/C][C]86.5795409809473[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]15.6485148514851[/C][C]0.178473249299765[/C][C]87.6798899156129[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]15.6333333333333[/C][C]0.175868431548756[/C][C]88.8922087702778[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]15.6206185567010[/C][C]0.173619605725037[/C][C]89.9703607289577[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]15.6073684210526[/C][C]0.171053269014231[/C][C]91.242736902936[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]15.5946236559140[/C][C]0.168376217752181[/C][C]92.6177334548899[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]15.5824175824176[/C][C]0.166003026044424[/C][C]93.8682742942744[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]15.5696629213483[/C][C]0.163273807753165[/C][C]95.3592198014164[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]15.5574712643678[/C][C]0.160414394066946[/C][C]96.9830129949262[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]15.5458823529412[/C][C]0.157888314080502[/C][C]98.4612600588971[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]15.5349397590361[/C][C]0.155735047563141[/C][C]99.752367897391[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]15.5246913580247[/C][C]0.153513690870099[/C][C]101.129034615951[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]15.5126582278481[/C][C]0.151122244481231[/C][C]102.649734200941[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]15.5012987012987[/C][C]0.14863808140235[/C][C]104.288877756287[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]15.488[/C][C]0.145935441730764[/C][C]106.129119947256[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]15.4753424657534[/C][C]0.143103522122369[/C][C]108.140891546473[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]15.4633802816901[/C][C]0.140124110504032[/C][C]110.354886293785[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]15.4521739130435[/C][C]0.136975126951801[/C][C]112.81007184962[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]15.4447761194030[/C][C]0.134424810841378[/C][C]114.895278801083[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]15.4384615384615[/C][C]0.132445422498584[/C][C]116.564704519151[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]15.4317460317460[/C][C]0.130024720892378[/C][C]118.683169829828[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]15.4262295081967[/C][C]0.127500169063303[/C][C]120.989874927442[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]15.4262295081967[/C][C]0.124766867957738[/C][C]123.640432437737[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]15.4105263157895[/C][C]0.121387245930022[/C][C]126.953422476307[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]15.4036363636364[/C][C]0.118689920442175[/C][C]129.780492785323[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]15.3962264150943[/C][C]0.115301153738135[/C][C]133.530549486619[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]15.3882352941176[/C][C]0.111025418704979[/C][C]138.601011134287[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]15.3816326530612[/C][C]0.107486491375089[/C][C]143.102937460158[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]15.3829787234043[/C][C]0.105462250588218[/C][C]145.862416529189[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]15.3822222222222[/C][C]0.103391424965775[/C][C]148.776576271331[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]15.3813953488372[/C][C]0.101879122671189[/C][C]150.97691210475[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]15.3853658536585[/C][C]0.101004767794358[/C][C]152.323164436976[/C][/ROW]
[ROW][C]Median[/C][C]15.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15.4580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15.4580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15.4580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15.4580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15.4580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15.3815384615385[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15.4580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15.4580645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]121[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115042&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115042&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 Mean15.71735537190080.21179307201263474.2109041742557
Geometric Mean15.5481040815154
Harmonic Mean15.3809402533699
Quadratic Mean15.8876686939565
Winsorized Mean ( 1 / 40 )15.72066115702480.21082586313502474.5670427871387
Winsorized Mean ( 2 / 40 )15.72561983471070.20992760435707874.9097284412495
Winsorized Mean ( 3 / 40 )15.73057851239670.20819254628705175.5578371701539
Winsorized Mean ( 4 / 40 )15.74380165289260.20282404458195677.6229548392173
Winsorized Mean ( 5 / 40 )15.73966942148760.19951897849772478.8880814246306
Winsorized Mean ( 6 / 40 )15.73966942148760.19802217415850579.4843783953655
Winsorized Mean ( 7 / 40 )15.75702479338840.19582004742323780.4668623092092
Winsorized Mean ( 8 / 40 )15.75702479338840.19392575631364681.2528727122962
Winsorized Mean ( 9 / 40 )15.76446280991740.19305739131610681.6568726141397
Winsorized Mean ( 10 / 40 )15.77272727272730.19212097313817582.0978939211568
Winsorized Mean ( 11 / 40 )15.74545454545450.1877039753685283.8845022570322
Winsorized Mean ( 12 / 40 )15.74545454545450.1877039753685283.8845022570322
Winsorized Mean ( 13 / 40 )15.73471074380170.18602226955683784.5850917811432
Winsorized Mean ( 14 / 40 )15.72314049586780.18117978959536786.7819778960036
Winsorized Mean ( 15 / 40 )15.72314049586780.18117978959536786.7819778960036
Winsorized Mean ( 16 / 40 )15.70991735537190.17920241475137687.6657682161691
Winsorized Mean ( 17 / 40 )15.69586776859500.17352843184532790.4512741899578
Winsorized Mean ( 18 / 40 )15.68099173553720.16767045128343593.5226905844586
Winsorized Mean ( 19 / 40 )15.66528925619830.16548913534453694.660529971254
Winsorized Mean ( 20 / 40 )15.68181818181820.16371210368375995.7889968362422
Winsorized Mean ( 21 / 40 )15.66446280991740.16132995595638097.0958103661338
Winsorized Mean ( 22 / 40 )15.68264462809920.15941818149827998.3742536811492
Winsorized Mean ( 23 / 40 )15.66363636363640.1568368456175199.872171631381
Winsorized Mean ( 24 / 40 )15.64380165289260.154183589549857101.462170510916
Winsorized Mean ( 25 / 40 )15.62314049586780.151461022136694103.149577861477
Winsorized Mean ( 26 / 40 )15.55867768595040.143224714216435108.631235684917
Winsorized Mean ( 27 / 40 )15.53636363636360.135344677834711114.791094004725
Winsorized Mean ( 28 / 40 )15.53636363636360.135344677834711114.791094004725
Winsorized Mean ( 29 / 40 )15.51239669421490.132472619177945117.098890249748
Winsorized Mean ( 30 / 40 )15.53719008264460.129834246053251119.669428944595
Winsorized Mean ( 31 / 40 )15.53719008264460.129834246053251119.669428944595
Winsorized Mean ( 32 / 40 )15.51074380165290.120820209145112128.378720012176
Winsorized Mean ( 33 / 40 )15.51074380165290.120820209145112128.378720012176
Winsorized Mean ( 34 / 40 )15.51074380165290.120820209145112128.378720012176
Winsorized Mean ( 35 / 40 )15.48181818181820.111148524463252139.289462065120
Winsorized Mean ( 36 / 40 )15.36280991735540.0980887060681991156.621598277318
Winsorized Mean ( 37 / 40 )15.39338842975210.0948446281807894162.301109983896
Winsorized Mean ( 38 / 40 )15.39338842975210.0882703050036697174.389206303435
Winsorized Mean ( 39 / 40 )15.32892561983470.0817039439563894187.615491707680
Winsorized Mean ( 40 / 40 )15.32892561983470.075024679286925204.318442484914
Trimmed Mean ( 1 / 40 )15.72016806722690.20675317029091076.0335043235755
Trimmed Mean ( 2 / 40 )15.71965811965810.20224294654113477.7266074713805
Trimmed Mean ( 3 / 40 )15.71652173913040.19776373901201779.4712004215062
Trimmed Mean ( 4 / 40 )15.71150442477880.19349712694478781.1976109043826
Trimmed Mean ( 5 / 40 )15.70270270270270.19046672904255382.4432843554239
Trimmed Mean ( 6 / 40 )15.69449541284400.18796094033255683.4987066199818
Trimmed Mean ( 7 / 40 )15.68598130841120.1854971283341884.5618552118626
Trimmed Mean ( 8 / 40 )15.67428571428570.18317023333474785.5722320648062
Trimmed Mean ( 9 / 40 )15.66213592233010.18089880986752686.5795409809473
Trimmed Mean ( 10 / 40 )15.64851485148510.17847324929976587.6798899156129
Trimmed Mean ( 11 / 40 )15.63333333333330.17586843154875688.8922087702778
Trimmed Mean ( 12 / 40 )15.62061855670100.17361960572503789.9703607289577
Trimmed Mean ( 13 / 40 )15.60736842105260.17105326901423191.242736902936
Trimmed Mean ( 14 / 40 )15.59462365591400.16837621775218192.6177334548899
Trimmed Mean ( 15 / 40 )15.58241758241760.16600302604442493.8682742942744
Trimmed Mean ( 16 / 40 )15.56966292134830.16327380775316595.3592198014164
Trimmed Mean ( 17 / 40 )15.55747126436780.16041439406694696.9830129949262
Trimmed Mean ( 18 / 40 )15.54588235294120.15788831408050298.4612600588971
Trimmed Mean ( 19 / 40 )15.53493975903610.15573504756314199.752367897391
Trimmed Mean ( 20 / 40 )15.52469135802470.153513690870099101.129034615951
Trimmed Mean ( 21 / 40 )15.51265822784810.151122244481231102.649734200941
Trimmed Mean ( 22 / 40 )15.50129870129870.14863808140235104.288877756287
Trimmed Mean ( 23 / 40 )15.4880.145935441730764106.129119947256
Trimmed Mean ( 24 / 40 )15.47534246575340.143103522122369108.140891546473
Trimmed Mean ( 25 / 40 )15.46338028169010.140124110504032110.354886293785
Trimmed Mean ( 26 / 40 )15.45217391304350.136975126951801112.81007184962
Trimmed Mean ( 27 / 40 )15.44477611940300.134424810841378114.895278801083
Trimmed Mean ( 28 / 40 )15.43846153846150.132445422498584116.564704519151
Trimmed Mean ( 29 / 40 )15.43174603174600.130024720892378118.683169829828
Trimmed Mean ( 30 / 40 )15.42622950819670.127500169063303120.989874927442
Trimmed Mean ( 31 / 40 )15.42622950819670.124766867957738123.640432437737
Trimmed Mean ( 32 / 40 )15.41052631578950.121387245930022126.953422476307
Trimmed Mean ( 33 / 40 )15.40363636363640.118689920442175129.780492785323
Trimmed Mean ( 34 / 40 )15.39622641509430.115301153738135133.530549486619
Trimmed Mean ( 35 / 40 )15.38823529411760.111025418704979138.601011134287
Trimmed Mean ( 36 / 40 )15.38163265306120.107486491375089143.102937460158
Trimmed Mean ( 37 / 40 )15.38297872340430.105462250588218145.862416529189
Trimmed Mean ( 38 / 40 )15.38222222222220.103391424965775148.776576271331
Trimmed Mean ( 39 / 40 )15.38139534883720.101879122671189150.97691210475
Trimmed Mean ( 40 / 40 )15.38536585365850.101004767794358152.323164436976
Median15.5
Midrange15.55
Midmean - Weighted Average at Xnp15.4580645161290
Midmean - Weighted Average at X(n+1)p15.4580645161290
Midmean - Empirical Distribution Function15.4580645161290
Midmean - Empirical Distribution Function - Averaging15.4580645161290
Midmean - Empirical Distribution Function - Interpolation15.4580645161290
Midmean - Closest Observation15.3815384615385
Midmean - True Basic - Statistics Graphics Toolkit15.4580645161290
Midmean - MS Excel (old versions)15.4580645161290
Number of observations121



Parameters (Session):
Parameters (R input):
par1 = ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')