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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 computationSun, 18 Oct 2009 08:35:02 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/18/t1255876610t851yorcee9zxu1.htm/, Retrieved Mon, 29 Apr 2024 13:50:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47328, Retrieved Mon, 29 Apr 2024 13:50:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsworkshop 3 deel 2
Estimated Impact113
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  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Percentiles] [Percentielen] [2009-10-18 13:47:08] [03557919bc1ce1475f4920f6a43c36b0]
- RM D          [Central Tendency] [central tendency] [2009-10-18 14:35:02] [e7a989b306049c061a54f626f1127c12] [Current]
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Post a new message
Dataseries X:
128.7
115.1
108.8
109.6
105.5
106.5
108.3
107.5
107.2
113.2
108.8
109.8
111.3
116.4
111.2
112.1
113.2
108.5
113.2
116.4
123.7
125.6
128.7
137.5
134.8
140.6
132.2
138
157.6
168.4
172.9
174.1
179.1
178.5
167.8
171
183.5
176.4
183.4
210
213.1
213
241.6
255.8
285.4
306.5
316.9
310
327.4
308.2
279.3
268.4
211.2
193.2
188.2
204.3
194.4
198.9
198.2
213.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47328&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47328&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47328&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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean172.388.3181622807452820.7233273627063
Geometric Mean161.881010008928
Harmonic Mean152.914970695342
Quadratic Mean183.840098999103
Winsorized Mean ( 1 / 20 )172.2216666666678.2622896279676520.8443027806361
Winsorized Mean ( 2 / 20 )172.0158.1921851368474420.9974502683414
Winsorized Mean ( 3 / 20 )171.948.1646001766894721.0592063639443
Winsorized Mean ( 4 / 20 )171.888.1255545834198721.1530177091813
Winsorized Mean ( 5 / 20 )170.1383333333337.6512892055255222.2365576261926
Winsorized Mean ( 6 / 20 )169.5583333333337.493576266620222.6271578883668
Winsorized Mean ( 7 / 20 )168.2866666666677.1854393992085623.4205115814076
Winsorized Mean ( 8 / 20 )166.7133333333336.7847142363774824.5719020028094
Winsorized Mean ( 9 / 20 )164.6133333333336.3229665973605426.0341930956981
Winsorized Mean ( 10 / 20 )160.1966666666675.4115595915416129.6026799588528
Winsorized Mean ( 11 / 20 )160.1055.3903646119457929.7020724062311
Winsorized Mean ( 12 / 20 )160.2455.362580343253929.8820697766491
Winsorized Mean ( 13 / 20 )160.0933333333335.2618259954151230.4254328198671
Winsorized Mean ( 14 / 20 )159.8133333333335.2159465758127330.6393731244135
Winsorized Mean ( 15 / 20 )158.3883333333334.988494724256631.7507268401365
Winsorized Mean ( 16 / 20 )157.4554.6905436935650633.5686031911422
Winsorized Mean ( 17 / 20 )157.6254.6047473813801834.2309766302001
Winsorized Mean ( 18 / 20 )156.4854.4370161150991735.2680711407564
Winsorized Mean ( 19 / 20 )158.4166666666674.0358514574767639.2523531492186
Winsorized Mean ( 20 / 20 )157.3833333333333.7042067753130342.4877289200556
Trimmed Mean ( 1 / 20 )170.8603448275868.0886830413452621.1233823793360
Trimmed Mean ( 2 / 20 )169.4017857142867.8688934233636721.5280315287168
Trimmed Mean ( 3 / 20 )167.957.6378840581730321.9890742934599
Trimmed Mean ( 4 / 20 )166.4153846153857.3563300045513622.6220662358028
Trimmed Mean ( 5 / 20 )164.7767.0095873470205223.5072325719772
Trimmed Mean ( 6 / 20 )163.4354166666676.7429918239191824.2378191957638
Trimmed Mean ( 7 / 20 )162.1043478260876.4487777042969225.1372206112911
Trimmed Mean ( 8 / 20 )160.96.1637537641534926.1042225495355
Trimmed Mean ( 9 / 20 )159.8619047619055.9125272549908727.0378296568464
Trimmed Mean ( 10 / 20 )159.075.7168915258161727.8245615264303
Trimmed Mean ( 11 / 20 )158.8921052631585.7016922216401827.8675345996579
Trimmed Mean ( 12 / 20 )158.7083333333335.6697013932736327.9923619119731
Trimmed Mean ( 13 / 20 )158.4823529411765.6155571888887228.2220174437470
Trimmed Mean ( 14 / 20 )158.255.5494768715967428.5162013756564
Trimmed Mean ( 15 / 20 )158.0266666666675.4500088227985828.9956717144395
Trimmed Mean ( 16 / 20 )157.9755.3564148976302829.4926743015911
Trimmed Mean ( 17 / 20 )158.055.2881965807752529.8873155688985
Trimmed Mean ( 18 / 20 )158.11255.1833111252378530.5041499882461
Trimmed Mean ( 19 / 20 )158.3590909090915.0479032511898131.3712611016792
Trimmed Mean ( 20 / 20 )158.354.9622867182060531.910691379245
Median168.1
Midrange216.45
Midmean - Weighted Average at Xnp155.225
Midmean - Weighted Average at X(n+1)p155.225
Midmean - Empirical Distribution Function155.225
Midmean - Empirical Distribution Function - Averaging155.225
Midmean - Empirical Distribution Function - Interpolation155.225
Midmean - Closest Observation155.225
Midmean - True Basic - Statistics Graphics Toolkit155.225
Midmean - MS Excel (old versions)156.884848484848
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 172.38 & 8.31816228074528 & 20.7233273627063 \tabularnewline
Geometric Mean & 161.881010008928 &  &  \tabularnewline
Harmonic Mean & 152.914970695342 &  &  \tabularnewline
Quadratic Mean & 183.840098999103 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 172.221666666667 & 8.26228962796765 & 20.8443027806361 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 172.015 & 8.19218513684744 & 20.9974502683414 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 171.94 & 8.16460017668947 & 21.0592063639443 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 171.88 & 8.12555458341987 & 21.1530177091813 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 170.138333333333 & 7.65128920552552 & 22.2365576261926 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 169.558333333333 & 7.4935762666202 & 22.6271578883668 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 168.286666666667 & 7.18543939920856 & 23.4205115814076 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 166.713333333333 & 6.78471423637748 & 24.5719020028094 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 164.613333333333 & 6.32296659736054 & 26.0341930956981 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 160.196666666667 & 5.41155959154161 & 29.6026799588528 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 160.105 & 5.39036461194579 & 29.7020724062311 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 160.245 & 5.3625803432539 & 29.8820697766491 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 160.093333333333 & 5.26182599541512 & 30.4254328198671 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 159.813333333333 & 5.21594657581273 & 30.6393731244135 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 158.388333333333 & 4.9884947242566 & 31.7507268401365 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 157.455 & 4.69054369356506 & 33.5686031911422 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 157.625 & 4.60474738138018 & 34.2309766302001 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 156.485 & 4.43701611509917 & 35.2680711407564 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 158.416666666667 & 4.03585145747676 & 39.2523531492186 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 157.383333333333 & 3.70420677531303 & 42.4877289200556 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 170.860344827586 & 8.08868304134526 & 21.1233823793360 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 169.401785714286 & 7.86889342336367 & 21.5280315287168 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 167.95 & 7.63788405817303 & 21.9890742934599 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 166.415384615385 & 7.35633000455136 & 22.6220662358028 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 164.776 & 7.00958734702052 & 23.5072325719772 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 163.435416666667 & 6.74299182391918 & 24.2378191957638 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 162.104347826087 & 6.44877770429692 & 25.1372206112911 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 160.9 & 6.16375376415349 & 26.1042225495355 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 159.861904761905 & 5.91252725499087 & 27.0378296568464 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 159.07 & 5.71689152581617 & 27.8245615264303 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 158.892105263158 & 5.70169222164018 & 27.8675345996579 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 158.708333333333 & 5.66970139327363 & 27.9923619119731 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 158.482352941176 & 5.61555718888872 & 28.2220174437470 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 158.25 & 5.54947687159674 & 28.5162013756564 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 158.026666666667 & 5.45000882279858 & 28.9956717144395 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 157.975 & 5.35641489763028 & 29.4926743015911 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 158.05 & 5.28819658077525 & 29.8873155688985 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 158.1125 & 5.18331112523785 & 30.5041499882461 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 158.359090909091 & 5.04790325118981 & 31.3712611016792 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 158.35 & 4.96228671820605 & 31.910691379245 \tabularnewline
Median & 168.1 &  &  \tabularnewline
Midrange & 216.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 155.225 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 155.225 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 155.225 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 155.225 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 155.225 &  &  \tabularnewline
Midmean - Closest Observation & 155.225 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 155.225 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 156.884848484848 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47328&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]172.38[/C][C]8.31816228074528[/C][C]20.7233273627063[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]161.881010008928[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]152.914970695342[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]183.840098999103[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]172.221666666667[/C][C]8.26228962796765[/C][C]20.8443027806361[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]172.015[/C][C]8.19218513684744[/C][C]20.9974502683414[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]171.94[/C][C]8.16460017668947[/C][C]21.0592063639443[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]171.88[/C][C]8.12555458341987[/C][C]21.1530177091813[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]170.138333333333[/C][C]7.65128920552552[/C][C]22.2365576261926[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]169.558333333333[/C][C]7.4935762666202[/C][C]22.6271578883668[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]168.286666666667[/C][C]7.18543939920856[/C][C]23.4205115814076[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]166.713333333333[/C][C]6.78471423637748[/C][C]24.5719020028094[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]164.613333333333[/C][C]6.32296659736054[/C][C]26.0341930956981[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]160.196666666667[/C][C]5.41155959154161[/C][C]29.6026799588528[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]160.105[/C][C]5.39036461194579[/C][C]29.7020724062311[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]160.245[/C][C]5.3625803432539[/C][C]29.8820697766491[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]160.093333333333[/C][C]5.26182599541512[/C][C]30.4254328198671[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]159.813333333333[/C][C]5.21594657581273[/C][C]30.6393731244135[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]158.388333333333[/C][C]4.9884947242566[/C][C]31.7507268401365[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]157.455[/C][C]4.69054369356506[/C][C]33.5686031911422[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]157.625[/C][C]4.60474738138018[/C][C]34.2309766302001[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]156.485[/C][C]4.43701611509917[/C][C]35.2680711407564[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]158.416666666667[/C][C]4.03585145747676[/C][C]39.2523531492186[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]157.383333333333[/C][C]3.70420677531303[/C][C]42.4877289200556[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]170.860344827586[/C][C]8.08868304134526[/C][C]21.1233823793360[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]169.401785714286[/C][C]7.86889342336367[/C][C]21.5280315287168[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]167.95[/C][C]7.63788405817303[/C][C]21.9890742934599[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]166.415384615385[/C][C]7.35633000455136[/C][C]22.6220662358028[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]164.776[/C][C]7.00958734702052[/C][C]23.5072325719772[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]163.435416666667[/C][C]6.74299182391918[/C][C]24.2378191957638[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]162.104347826087[/C][C]6.44877770429692[/C][C]25.1372206112911[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]160.9[/C][C]6.16375376415349[/C][C]26.1042225495355[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]159.861904761905[/C][C]5.91252725499087[/C][C]27.0378296568464[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]159.07[/C][C]5.71689152581617[/C][C]27.8245615264303[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]158.892105263158[/C][C]5.70169222164018[/C][C]27.8675345996579[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]158.708333333333[/C][C]5.66970139327363[/C][C]27.9923619119731[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]158.482352941176[/C][C]5.61555718888872[/C][C]28.2220174437470[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]158.25[/C][C]5.54947687159674[/C][C]28.5162013756564[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]158.026666666667[/C][C]5.45000882279858[/C][C]28.9956717144395[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]157.975[/C][C]5.35641489763028[/C][C]29.4926743015911[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]158.05[/C][C]5.28819658077525[/C][C]29.8873155688985[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]158.1125[/C][C]5.18331112523785[/C][C]30.5041499882461[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]158.359090909091[/C][C]5.04790325118981[/C][C]31.3712611016792[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]158.35[/C][C]4.96228671820605[/C][C]31.910691379245[/C][/ROW]
[ROW][C]Median[/C][C]168.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]216.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]155.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]155.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]155.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]155.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]155.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]155.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]155.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]156.884848484848[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47328&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47328&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 Mean172.388.3181622807452820.7233273627063
Geometric Mean161.881010008928
Harmonic Mean152.914970695342
Quadratic Mean183.840098999103
Winsorized Mean ( 1 / 20 )172.2216666666678.2622896279676520.8443027806361
Winsorized Mean ( 2 / 20 )172.0158.1921851368474420.9974502683414
Winsorized Mean ( 3 / 20 )171.948.1646001766894721.0592063639443
Winsorized Mean ( 4 / 20 )171.888.1255545834198721.1530177091813
Winsorized Mean ( 5 / 20 )170.1383333333337.6512892055255222.2365576261926
Winsorized Mean ( 6 / 20 )169.5583333333337.493576266620222.6271578883668
Winsorized Mean ( 7 / 20 )168.2866666666677.1854393992085623.4205115814076
Winsorized Mean ( 8 / 20 )166.7133333333336.7847142363774824.5719020028094
Winsorized Mean ( 9 / 20 )164.6133333333336.3229665973605426.0341930956981
Winsorized Mean ( 10 / 20 )160.1966666666675.4115595915416129.6026799588528
Winsorized Mean ( 11 / 20 )160.1055.3903646119457929.7020724062311
Winsorized Mean ( 12 / 20 )160.2455.362580343253929.8820697766491
Winsorized Mean ( 13 / 20 )160.0933333333335.2618259954151230.4254328198671
Winsorized Mean ( 14 / 20 )159.8133333333335.2159465758127330.6393731244135
Winsorized Mean ( 15 / 20 )158.3883333333334.988494724256631.7507268401365
Winsorized Mean ( 16 / 20 )157.4554.6905436935650633.5686031911422
Winsorized Mean ( 17 / 20 )157.6254.6047473813801834.2309766302001
Winsorized Mean ( 18 / 20 )156.4854.4370161150991735.2680711407564
Winsorized Mean ( 19 / 20 )158.4166666666674.0358514574767639.2523531492186
Winsorized Mean ( 20 / 20 )157.3833333333333.7042067753130342.4877289200556
Trimmed Mean ( 1 / 20 )170.8603448275868.0886830413452621.1233823793360
Trimmed Mean ( 2 / 20 )169.4017857142867.8688934233636721.5280315287168
Trimmed Mean ( 3 / 20 )167.957.6378840581730321.9890742934599
Trimmed Mean ( 4 / 20 )166.4153846153857.3563300045513622.6220662358028
Trimmed Mean ( 5 / 20 )164.7767.0095873470205223.5072325719772
Trimmed Mean ( 6 / 20 )163.4354166666676.7429918239191824.2378191957638
Trimmed Mean ( 7 / 20 )162.1043478260876.4487777042969225.1372206112911
Trimmed Mean ( 8 / 20 )160.96.1637537641534926.1042225495355
Trimmed Mean ( 9 / 20 )159.8619047619055.9125272549908727.0378296568464
Trimmed Mean ( 10 / 20 )159.075.7168915258161727.8245615264303
Trimmed Mean ( 11 / 20 )158.8921052631585.7016922216401827.8675345996579
Trimmed Mean ( 12 / 20 )158.7083333333335.6697013932736327.9923619119731
Trimmed Mean ( 13 / 20 )158.4823529411765.6155571888887228.2220174437470
Trimmed Mean ( 14 / 20 )158.255.5494768715967428.5162013756564
Trimmed Mean ( 15 / 20 )158.0266666666675.4500088227985828.9956717144395
Trimmed Mean ( 16 / 20 )157.9755.3564148976302829.4926743015911
Trimmed Mean ( 17 / 20 )158.055.2881965807752529.8873155688985
Trimmed Mean ( 18 / 20 )158.11255.1833111252378530.5041499882461
Trimmed Mean ( 19 / 20 )158.3590909090915.0479032511898131.3712611016792
Trimmed Mean ( 20 / 20 )158.354.9622867182060531.910691379245
Median168.1
Midrange216.45
Midmean - Weighted Average at Xnp155.225
Midmean - Weighted Average at X(n+1)p155.225
Midmean - Empirical Distribution Function155.225
Midmean - Empirical Distribution Function - Averaging155.225
Midmean - Empirical Distribution Function - Interpolation155.225
Midmean - Closest Observation155.225
Midmean - True Basic - Statistics Graphics Toolkit155.225
Midmean - MS Excel (old versions)156.884848484848
Number of observations60



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')