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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Dec 2008 05:16:57 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/21/t12298621639usir8hysj9j20c.htm/, Retrieved Sat, 18 May 2024 09:55:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35529, Retrieved Sat, 18 May 2024 09:55:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2008-12-21 12:16:57] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
111,4
114,1
121,8
127,6
129,9
128
123,5
124
127,4
127,6
128,4
131,4
135,1
134
144,5
147,3
150,9
148,7
141,4
138,9
139,8
145,6
147,9
148,5
151,1
157,5
167,5
172,3
173,5
187,5
205,5
195,1
204,5
204,5
201,7
207
206,6
210,6
211,1
215
223,9
238,2
238,9
229,6
232,2
222,1
221,6
227,3
221
213,6
243,4
253,8
265,3
268,2
268,5
266,9
268,4
250,8
231,2
192
171,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35529&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35529&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35529&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean184.2131147540986.1699193055673129.8566489496673
Geometric Mean177.978126000211
Harmonic Mean171.895510282164
Quadratic Mean190.311707211194
Winsorized Mean ( 1 / 20 )184.2557377049186.160992896255129.9068252159349
Winsorized Mean ( 2 / 20 )184.5016393442626.1139571991309230.1771231520052
Winsorized Mean ( 3 / 20 )184.521311475416.0853187634016530.3223740036691
Winsorized Mean ( 4 / 20 )184.4491803278696.0563436565365130.4555340298095
Winsorized Mean ( 5 / 20 )183.7852459016395.8108922765388331.6277151864719
Winsorized Mean ( 6 / 20 )183.5098360655745.7492939480593131.9186734446789
Winsorized Mean ( 7 / 20 )182.6606557377055.5894882209437132.6793166954497
Winsorized Mean ( 8 / 20 )182.1229508196725.4764056226143733.2559279516496
Winsorized Mean ( 9 / 20 )182.078688524595.4489128181955433.4155995149299
Winsorized Mean ( 10 / 20 )181.3409836065575.2446216932384034.5765613257388
Winsorized Mean ( 11 / 20 )181.4311475409845.1716696424482535.0817357032679
Winsorized Mean ( 12 / 20 )181.6278688524595.0399329572843536.0377549447255
Winsorized Mean ( 13 / 20 )181.3721311475414.9261486586748136.8182415340125
Winsorized Mean ( 14 / 20 )181.4639344262304.6718784516075538.8417499097797
Winsorized Mean ( 15 / 20 )181.2426229508204.5718845339035439.6428697196497
Winsorized Mean ( 16 / 20 )181.5311475409844.4893952402145740.435545953915
Winsorized Mean ( 17 / 20 )182.2278688524594.3374951417415342.0122358406362
Winsorized Mean ( 18 / 20 )180.7819672131154.0330665414608444.8249403660056
Winsorized Mean ( 19 / 20 )180.8754098360663.8951648994869446.435879995707
Winsorized Mean ( 20 / 20 )180.2524590163933.7533559530305148.0243444192537
Trimmed Mean ( 1 / 20 )184.0186440677976.0901149532366730.2159557710807
Trimmed Mean ( 2 / 20 )183.7649122807025.9998895620726330.6280491298278
Trimmed Mean ( 3 / 20 )183.3563636363645.9155008176381130.9959155258088
Trimmed Mean ( 4 / 20 )182.9094339622645.8201374954150931.4269953426967
Trimmed Mean ( 5 / 20 )182.4490196078435.7081780840825331.9627413371368
Trimmed Mean ( 6 / 20 )182.1163265306125.6454419539059632.2590025754511
Trimmed Mean ( 7 / 20 )181.8148936170215.5779266128274632.5954259059100
Trimmed Mean ( 8 / 20 )181.6511111111115.5292469597259432.8527758724155
Trimmed Mean ( 9 / 20 )181.5674418604655.4872001676893933.0892689006680
Trimmed Mean ( 10 / 20 )181.4829268292685.4293240634393733.4264311189969
Trimmed Mean ( 11 / 20 )181.5051282051285.3934382443909333.6529538266040
Trimmed Mean ( 12 / 20 )181.5162162162165.3503424064791733.9260934022472
Trimmed Mean ( 13 / 20 )181.55.3105412849817734.1773070314476
Trimmed Mean ( 14 / 20 )181.5181818181825.2683292133013634.4546011589194
Trimmed Mean ( 15 / 20 )181.5258064516135.2565432194652534.5333042786395
Trimmed Mean ( 16 / 20 )181.5655172413795.2416606905285534.6389299043069
Trimmed Mean ( 17 / 20 )181.5703703703705.2152630885740734.815189049267
Trimmed Mean ( 18 / 20 )181.4765.1904633062312834.9633528440773
Trimmed Mean ( 19 / 20 )181.5782608695655.2134970644640734.8284958492119
Trimmed Mean ( 20 / 20 )181.6857142857145.2446629821103334.6420189258011
Median187.5
Midrange189.95
Midmean - Weighted Average at Xnp180.173333333333
Midmean - Weighted Average at X(n+1)p181.525806451613
Midmean - Empirical Distribution Function181.525806451613
Midmean - Empirical Distribution Function - Averaging181.525806451613
Midmean - Empirical Distribution Function - Interpolation181.525806451613
Midmean - Closest Observation180.19375
Midmean - True Basic - Statistics Graphics Toolkit181.525806451613
Midmean - MS Excel (old versions)181.525806451613
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 184.213114754098 & 6.16991930556731 & 29.8566489496673 \tabularnewline
Geometric Mean & 177.978126000211 &  &  \tabularnewline
Harmonic Mean & 171.895510282164 &  &  \tabularnewline
Quadratic Mean & 190.311707211194 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 184.255737704918 & 6.1609928962551 & 29.9068252159349 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 184.501639344262 & 6.11395719913092 & 30.1771231520052 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 184.52131147541 & 6.08531876340165 & 30.3223740036691 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 184.449180327869 & 6.05634365653651 & 30.4555340298095 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 183.785245901639 & 5.81089227653883 & 31.6277151864719 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 183.509836065574 & 5.74929394805931 & 31.9186734446789 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 182.660655737705 & 5.58948822094371 & 32.6793166954497 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 182.122950819672 & 5.47640562261437 & 33.2559279516496 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 182.07868852459 & 5.44891281819554 & 33.4155995149299 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 181.340983606557 & 5.24462169323840 & 34.5765613257388 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 181.431147540984 & 5.17166964244825 & 35.0817357032679 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 181.627868852459 & 5.03993295728435 & 36.0377549447255 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 181.372131147541 & 4.92614865867481 & 36.8182415340125 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 181.463934426230 & 4.67187845160755 & 38.8417499097797 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 181.242622950820 & 4.57188453390354 & 39.6428697196497 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 181.531147540984 & 4.48939524021457 & 40.435545953915 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 182.227868852459 & 4.33749514174153 & 42.0122358406362 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 180.781967213115 & 4.03306654146084 & 44.8249403660056 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 180.875409836066 & 3.89516489948694 & 46.435879995707 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 180.252459016393 & 3.75335595303051 & 48.0243444192537 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 184.018644067797 & 6.09011495323667 & 30.2159557710807 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 183.764912280702 & 5.99988956207263 & 30.6280491298278 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 183.356363636364 & 5.91550081763811 & 30.9959155258088 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 182.909433962264 & 5.82013749541509 & 31.4269953426967 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 182.449019607843 & 5.70817808408253 & 31.9627413371368 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 182.116326530612 & 5.64544195390596 & 32.2590025754511 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 181.814893617021 & 5.57792661282746 & 32.5954259059100 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 181.651111111111 & 5.52924695972594 & 32.8527758724155 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 181.567441860465 & 5.48720016768939 & 33.0892689006680 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 181.482926829268 & 5.42932406343937 & 33.4264311189969 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 181.505128205128 & 5.39343824439093 & 33.6529538266040 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 181.516216216216 & 5.35034240647917 & 33.9260934022472 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 181.5 & 5.31054128498177 & 34.1773070314476 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 181.518181818182 & 5.26832921330136 & 34.4546011589194 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 181.525806451613 & 5.25654321946525 & 34.5333042786395 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 181.565517241379 & 5.24166069052855 & 34.6389299043069 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 181.570370370370 & 5.21526308857407 & 34.815189049267 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 181.476 & 5.19046330623128 & 34.9633528440773 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 181.578260869565 & 5.21349706446407 & 34.8284958492119 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 181.685714285714 & 5.24466298211033 & 34.6420189258011 \tabularnewline
Median & 187.5 &  &  \tabularnewline
Midrange & 189.95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 180.173333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 181.525806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 181.525806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 181.525806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 181.525806451613 &  &  \tabularnewline
Midmean - Closest Observation & 180.19375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 181.525806451613 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 181.525806451613 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35529&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]184.213114754098[/C][C]6.16991930556731[/C][C]29.8566489496673[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]177.978126000211[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]171.895510282164[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]190.311707211194[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]184.255737704918[/C][C]6.1609928962551[/C][C]29.9068252159349[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]184.501639344262[/C][C]6.11395719913092[/C][C]30.1771231520052[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]184.52131147541[/C][C]6.08531876340165[/C][C]30.3223740036691[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]184.449180327869[/C][C]6.05634365653651[/C][C]30.4555340298095[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]183.785245901639[/C][C]5.81089227653883[/C][C]31.6277151864719[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]183.509836065574[/C][C]5.74929394805931[/C][C]31.9186734446789[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]182.660655737705[/C][C]5.58948822094371[/C][C]32.6793166954497[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]182.122950819672[/C][C]5.47640562261437[/C][C]33.2559279516496[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]182.07868852459[/C][C]5.44891281819554[/C][C]33.4155995149299[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]181.340983606557[/C][C]5.24462169323840[/C][C]34.5765613257388[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]181.431147540984[/C][C]5.17166964244825[/C][C]35.0817357032679[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]181.627868852459[/C][C]5.03993295728435[/C][C]36.0377549447255[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]181.372131147541[/C][C]4.92614865867481[/C][C]36.8182415340125[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]181.463934426230[/C][C]4.67187845160755[/C][C]38.8417499097797[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]181.242622950820[/C][C]4.57188453390354[/C][C]39.6428697196497[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]181.531147540984[/C][C]4.48939524021457[/C][C]40.435545953915[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]182.227868852459[/C][C]4.33749514174153[/C][C]42.0122358406362[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]180.781967213115[/C][C]4.03306654146084[/C][C]44.8249403660056[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]180.875409836066[/C][C]3.89516489948694[/C][C]46.435879995707[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]180.252459016393[/C][C]3.75335595303051[/C][C]48.0243444192537[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]184.018644067797[/C][C]6.09011495323667[/C][C]30.2159557710807[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]183.764912280702[/C][C]5.99988956207263[/C][C]30.6280491298278[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]183.356363636364[/C][C]5.91550081763811[/C][C]30.9959155258088[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]182.909433962264[/C][C]5.82013749541509[/C][C]31.4269953426967[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]182.449019607843[/C][C]5.70817808408253[/C][C]31.9627413371368[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]182.116326530612[/C][C]5.64544195390596[/C][C]32.2590025754511[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]181.814893617021[/C][C]5.57792661282746[/C][C]32.5954259059100[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]181.651111111111[/C][C]5.52924695972594[/C][C]32.8527758724155[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]181.567441860465[/C][C]5.48720016768939[/C][C]33.0892689006680[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]181.482926829268[/C][C]5.42932406343937[/C][C]33.4264311189969[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]181.505128205128[/C][C]5.39343824439093[/C][C]33.6529538266040[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]181.516216216216[/C][C]5.35034240647917[/C][C]33.9260934022472[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]181.5[/C][C]5.31054128498177[/C][C]34.1773070314476[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]181.518181818182[/C][C]5.26832921330136[/C][C]34.4546011589194[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]181.525806451613[/C][C]5.25654321946525[/C][C]34.5333042786395[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]181.565517241379[/C][C]5.24166069052855[/C][C]34.6389299043069[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]181.570370370370[/C][C]5.21526308857407[/C][C]34.815189049267[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]181.476[/C][C]5.19046330623128[/C][C]34.9633528440773[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]181.578260869565[/C][C]5.21349706446407[/C][C]34.8284958492119[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]181.685714285714[/C][C]5.24466298211033[/C][C]34.6420189258011[/C][/ROW]
[ROW][C]Median[/C][C]187.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]189.95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]180.173333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]181.525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]181.525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]181.525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]181.525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]180.19375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]181.525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]181.525806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35529&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35529&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 Mean184.2131147540986.1699193055673129.8566489496673
Geometric Mean177.978126000211
Harmonic Mean171.895510282164
Quadratic Mean190.311707211194
Winsorized Mean ( 1 / 20 )184.2557377049186.160992896255129.9068252159349
Winsorized Mean ( 2 / 20 )184.5016393442626.1139571991309230.1771231520052
Winsorized Mean ( 3 / 20 )184.521311475416.0853187634016530.3223740036691
Winsorized Mean ( 4 / 20 )184.4491803278696.0563436565365130.4555340298095
Winsorized Mean ( 5 / 20 )183.7852459016395.8108922765388331.6277151864719
Winsorized Mean ( 6 / 20 )183.5098360655745.7492939480593131.9186734446789
Winsorized Mean ( 7 / 20 )182.6606557377055.5894882209437132.6793166954497
Winsorized Mean ( 8 / 20 )182.1229508196725.4764056226143733.2559279516496
Winsorized Mean ( 9 / 20 )182.078688524595.4489128181955433.4155995149299
Winsorized Mean ( 10 / 20 )181.3409836065575.2446216932384034.5765613257388
Winsorized Mean ( 11 / 20 )181.4311475409845.1716696424482535.0817357032679
Winsorized Mean ( 12 / 20 )181.6278688524595.0399329572843536.0377549447255
Winsorized Mean ( 13 / 20 )181.3721311475414.9261486586748136.8182415340125
Winsorized Mean ( 14 / 20 )181.4639344262304.6718784516075538.8417499097797
Winsorized Mean ( 15 / 20 )181.2426229508204.5718845339035439.6428697196497
Winsorized Mean ( 16 / 20 )181.5311475409844.4893952402145740.435545953915
Winsorized Mean ( 17 / 20 )182.2278688524594.3374951417415342.0122358406362
Winsorized Mean ( 18 / 20 )180.7819672131154.0330665414608444.8249403660056
Winsorized Mean ( 19 / 20 )180.8754098360663.8951648994869446.435879995707
Winsorized Mean ( 20 / 20 )180.2524590163933.7533559530305148.0243444192537
Trimmed Mean ( 1 / 20 )184.0186440677976.0901149532366730.2159557710807
Trimmed Mean ( 2 / 20 )183.7649122807025.9998895620726330.6280491298278
Trimmed Mean ( 3 / 20 )183.3563636363645.9155008176381130.9959155258088
Trimmed Mean ( 4 / 20 )182.9094339622645.8201374954150931.4269953426967
Trimmed Mean ( 5 / 20 )182.4490196078435.7081780840825331.9627413371368
Trimmed Mean ( 6 / 20 )182.1163265306125.6454419539059632.2590025754511
Trimmed Mean ( 7 / 20 )181.8148936170215.5779266128274632.5954259059100
Trimmed Mean ( 8 / 20 )181.6511111111115.5292469597259432.8527758724155
Trimmed Mean ( 9 / 20 )181.5674418604655.4872001676893933.0892689006680
Trimmed Mean ( 10 / 20 )181.4829268292685.4293240634393733.4264311189969
Trimmed Mean ( 11 / 20 )181.5051282051285.3934382443909333.6529538266040
Trimmed Mean ( 12 / 20 )181.5162162162165.3503424064791733.9260934022472
Trimmed Mean ( 13 / 20 )181.55.3105412849817734.1773070314476
Trimmed Mean ( 14 / 20 )181.5181818181825.2683292133013634.4546011589194
Trimmed Mean ( 15 / 20 )181.5258064516135.2565432194652534.5333042786395
Trimmed Mean ( 16 / 20 )181.5655172413795.2416606905285534.6389299043069
Trimmed Mean ( 17 / 20 )181.5703703703705.2152630885740734.815189049267
Trimmed Mean ( 18 / 20 )181.4765.1904633062312834.9633528440773
Trimmed Mean ( 19 / 20 )181.5782608695655.2134970644640734.8284958492119
Trimmed Mean ( 20 / 20 )181.6857142857145.2446629821103334.6420189258011
Median187.5
Midrange189.95
Midmean - Weighted Average at Xnp180.173333333333
Midmean - Weighted Average at X(n+1)p181.525806451613
Midmean - Empirical Distribution Function181.525806451613
Midmean - Empirical Distribution Function - Averaging181.525806451613
Midmean - Empirical Distribution Function - Interpolation181.525806451613
Midmean - Closest Observation180.19375
Midmean - True Basic - Statistics Graphics Toolkit181.525806451613
Midmean - MS Excel (old versions)181.525806451613
Number of observations61



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')