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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 17 Dec 2007 07:48:31 -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/2007/Dec/17/t1197901961olrj3rrnyqnjoky.htm/, Retrieved Fri, 03 May 2024 22:38:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4374, Retrieved Fri, 03 May 2024 22:38:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordscentral tendency Tinne Van der Eycken
Estimated Impact186
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper: Afzetprijz...] [2007-12-17 14:48:31] [c8635c97647ba59406cb570a9fab7b02] [Current]
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Dataseries X:
98,5
99,3
98
98,1
98
96,5
96,1
96,3
96,1
95,4
95,3
93,9
94
93,6
93,5
93,5
93,5
93
93,1
93,3
93,2
93,1
93,1
93,2
93
93,1
93,2
93,1
93,1
93,1
92,3
92,3
92,3
92,3
92,1
92,1
92,1
92
92
92,3
93,3
92,4
92,6
92,7
92,4
92,2
92,7
92,7
92,8
92,8
92,8
92,7
92,8
93,6
93,4
93,8
93,8
93,9
94
93,9
93,9




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4374&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4374&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4374&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean93.72459016393440.224687466457493417.133147841451
Geometric Mean93.7087537052995
Harmonic Mean93.693233826106
Quadratic Mean93.7407481773666
Winsorized Mean ( 1 / 20 )93.7114754098360.21958851683295426.759453369441
Winsorized Mean ( 2 / 20 )93.70163934426230.21454605532142436.743706165485
Winsorized Mean ( 3 / 20 )93.69672131147540.212877337279953440.144181192268
Winsorized Mean ( 4 / 20 )93.69672131147540.212877337279953440.144181192268
Winsorized Mean ( 5 / 20 )93.58196721311480.173528287747993539.289405938353
Winsorized Mean ( 6 / 20 )93.5721311475410.166810830779213560.94757582852
Winsorized Mean ( 7 / 20 )93.54918032786890.160644585316046582.336342951267
Winsorized Mean ( 8 / 20 )93.54918032786890.160644585316046582.336342951267
Winsorized Mean ( 9 / 20 )93.44590163934430.134358906239027695.494658709876
Winsorized Mean ( 10 / 20 )93.42950819672130.130412214518432716.416852069607
Winsorized Mean ( 11 / 20 )93.21311475409840.07772290031951221199.30051980700
Winsorized Mean ( 12 / 20 )93.21311475409840.07772290031951221199.30051980700
Winsorized Mean ( 13 / 20 )93.23442622950820.06705699581689571390.37583019812
Winsorized Mean ( 14 / 20 )93.25737704918030.06356696982256751467.07287305792
Winsorized Mean ( 15 / 20 )93.25737704918030.06356696982256751467.07287305792
Winsorized Mean ( 16 / 20 )93.25737704918030.06356696982256751467.07287305792
Winsorized Mean ( 17 / 20 )93.22950819672130.05896855985008261581.00364726121
Winsorized Mean ( 18 / 20 )93.25901639344260.05469123710692551705.19120295477
Winsorized Mean ( 19 / 20 )93.19672131147540.04484138488540772078.36402799869
Winsorized Mean ( 20 / 20 )93.19672131147540.04484138488540772078.36402799869
Trimmed Mean ( 1 / 20 )93.65932203389830.209688180230810446.659997386619
Trimmed Mean ( 2 / 20 )93.60350877192980.197175622903601474.721506611863
Trimmed Mean ( 3 / 20 )93.5490909090910.184826294412385506.14600701978
Trimmed Mean ( 4 / 20 )93.49245283018870.169710097229434550.895051953183
Trimmed Mean ( 5 / 20 )93.43137254901960.149416911032774625.306545980768
Trimmed Mean ( 6 / 20 )93.39387755102040.139740045441080668.340111499385
Trimmed Mean ( 7 / 20 )93.35531914893620.129426562443859721.299533775615
Trimmed Mean ( 8 / 20 )93.31777777777780.117863509868295791.744432878799
Trimmed Mean ( 9 / 20 )93.27674418604650.101638689175657917.728720653225
Trimmed Mean ( 10 / 20 )93.24878048780490.08958726167205081040.87097593358
Trimmed Mean ( 11 / 20 )93.22051282051280.07358007996098271266.92595156114
Trimmed Mean ( 12 / 20 )93.22162162162160.07114835989777411310.24273441528
Trimmed Mean ( 13 / 20 )93.22285714285710.06774714658454751376.04108575283
Trimmed Mean ( 14 / 20 )93.22121212121210.06610906618439171410.11237189766
Trimmed Mean ( 15 / 20 )93.2161290322580.06460746223313031442.80746852269
Trimmed Mean ( 16 / 20 )93.21034482758620.06225342050194751497.27266511678
Trimmed Mean ( 17 / 20 )93.20370370370370.0585877191903581590.84028174701
Trimmed Mean ( 18 / 20 )93.20.05477225575051671701.59141198271
Trimmed Mean ( 19 / 20 )93.1913043478260.05026138927750791854.1330768493
Trimmed Mean ( 20 / 20 )93.19047619047620.04776169111664721951.15528809228
Median93.1
Midrange95.65
Midmean - Weighted Average at Xnp93.2411764705882
Midmean - Weighted Average at X(n+1)p93.2411764705882
Midmean - Empirical Distribution Function93.2411764705882
Midmean - Empirical Distribution Function - Averaging93.2411764705882
Midmean - Empirical Distribution Function - Interpolation93.2411764705882
Midmean - Closest Observation93.2411764705882
Midmean - True Basic - Statistics Graphics Toolkit93.2411764705882
Midmean - MS Excel (old versions)93.2411764705882
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 93.7245901639344 & 0.224687466457493 & 417.133147841451 \tabularnewline
Geometric Mean & 93.7087537052995 &  &  \tabularnewline
Harmonic Mean & 93.693233826106 &  &  \tabularnewline
Quadratic Mean & 93.7407481773666 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 93.711475409836 & 0.21958851683295 & 426.759453369441 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 93.7016393442623 & 0.21454605532142 & 436.743706165485 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 93.6967213114754 & 0.212877337279953 & 440.144181192268 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 93.6967213114754 & 0.212877337279953 & 440.144181192268 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 93.5819672131148 & 0.173528287747993 & 539.289405938353 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 93.572131147541 & 0.166810830779213 & 560.94757582852 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 93.5491803278689 & 0.160644585316046 & 582.336342951267 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 93.5491803278689 & 0.160644585316046 & 582.336342951267 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 93.4459016393443 & 0.134358906239027 & 695.494658709876 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 93.4295081967213 & 0.130412214518432 & 716.416852069607 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 93.2131147540984 & 0.0777229003195122 & 1199.30051980700 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 93.2131147540984 & 0.0777229003195122 & 1199.30051980700 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 93.2344262295082 & 0.0670569958168957 & 1390.37583019812 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 93.2573770491803 & 0.0635669698225675 & 1467.07287305792 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 93.2573770491803 & 0.0635669698225675 & 1467.07287305792 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 93.2573770491803 & 0.0635669698225675 & 1467.07287305792 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 93.2295081967213 & 0.0589685598500826 & 1581.00364726121 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 93.2590163934426 & 0.0546912371069255 & 1705.19120295477 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 93.1967213114754 & 0.0448413848854077 & 2078.36402799869 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 93.1967213114754 & 0.0448413848854077 & 2078.36402799869 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 93.6593220338983 & 0.209688180230810 & 446.659997386619 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 93.6035087719298 & 0.197175622903601 & 474.721506611863 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 93.549090909091 & 0.184826294412385 & 506.14600701978 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 93.4924528301887 & 0.169710097229434 & 550.895051953183 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 93.4313725490196 & 0.149416911032774 & 625.306545980768 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 93.3938775510204 & 0.139740045441080 & 668.340111499385 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 93.3553191489362 & 0.129426562443859 & 721.299533775615 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 93.3177777777778 & 0.117863509868295 & 791.744432878799 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 93.2767441860465 & 0.101638689175657 & 917.728720653225 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 93.2487804878049 & 0.0895872616720508 & 1040.87097593358 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 93.2205128205128 & 0.0735800799609827 & 1266.92595156114 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 93.2216216216216 & 0.0711483598977741 & 1310.24273441528 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 93.2228571428571 & 0.0677471465845475 & 1376.04108575283 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 93.2212121212121 & 0.0661090661843917 & 1410.11237189766 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 93.216129032258 & 0.0646074622331303 & 1442.80746852269 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 93.2103448275862 & 0.0622534205019475 & 1497.27266511678 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 93.2037037037037 & 0.058587719190358 & 1590.84028174701 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 93.2 & 0.0547722557505167 & 1701.59141198271 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 93.191304347826 & 0.0502613892775079 & 1854.1330768493 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 93.1904761904762 & 0.0477616911166472 & 1951.15528809228 \tabularnewline
Median & 93.1 &  &  \tabularnewline
Midrange & 95.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 93.2411764705882 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 93.2411764705882 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 93.2411764705882 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 93.2411764705882 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 93.2411764705882 &  &  \tabularnewline
Midmean - Closest Observation & 93.2411764705882 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 93.2411764705882 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 93.2411764705882 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4374&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]93.7245901639344[/C][C]0.224687466457493[/C][C]417.133147841451[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]93.7087537052995[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]93.693233826106[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]93.7407481773666[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]93.711475409836[/C][C]0.21958851683295[/C][C]426.759453369441[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]93.7016393442623[/C][C]0.21454605532142[/C][C]436.743706165485[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]93.6967213114754[/C][C]0.212877337279953[/C][C]440.144181192268[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]93.6967213114754[/C][C]0.212877337279953[/C][C]440.144181192268[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]93.5819672131148[/C][C]0.173528287747993[/C][C]539.289405938353[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]93.572131147541[/C][C]0.166810830779213[/C][C]560.94757582852[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]93.5491803278689[/C][C]0.160644585316046[/C][C]582.336342951267[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]93.5491803278689[/C][C]0.160644585316046[/C][C]582.336342951267[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]93.4459016393443[/C][C]0.134358906239027[/C][C]695.494658709876[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]93.4295081967213[/C][C]0.130412214518432[/C][C]716.416852069607[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]93.2131147540984[/C][C]0.0777229003195122[/C][C]1199.30051980700[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]93.2131147540984[/C][C]0.0777229003195122[/C][C]1199.30051980700[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]93.2344262295082[/C][C]0.0670569958168957[/C][C]1390.37583019812[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]93.2573770491803[/C][C]0.0635669698225675[/C][C]1467.07287305792[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]93.2573770491803[/C][C]0.0635669698225675[/C][C]1467.07287305792[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]93.2573770491803[/C][C]0.0635669698225675[/C][C]1467.07287305792[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]93.2295081967213[/C][C]0.0589685598500826[/C][C]1581.00364726121[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]93.2590163934426[/C][C]0.0546912371069255[/C][C]1705.19120295477[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]93.1967213114754[/C][C]0.0448413848854077[/C][C]2078.36402799869[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]93.1967213114754[/C][C]0.0448413848854077[/C][C]2078.36402799869[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]93.6593220338983[/C][C]0.209688180230810[/C][C]446.659997386619[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]93.6035087719298[/C][C]0.197175622903601[/C][C]474.721506611863[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]93.549090909091[/C][C]0.184826294412385[/C][C]506.14600701978[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]93.4924528301887[/C][C]0.169710097229434[/C][C]550.895051953183[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]93.4313725490196[/C][C]0.149416911032774[/C][C]625.306545980768[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]93.3938775510204[/C][C]0.139740045441080[/C][C]668.340111499385[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]93.3553191489362[/C][C]0.129426562443859[/C][C]721.299533775615[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]93.3177777777778[/C][C]0.117863509868295[/C][C]791.744432878799[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]93.2767441860465[/C][C]0.101638689175657[/C][C]917.728720653225[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]93.2487804878049[/C][C]0.0895872616720508[/C][C]1040.87097593358[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]93.2205128205128[/C][C]0.0735800799609827[/C][C]1266.92595156114[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]93.2216216216216[/C][C]0.0711483598977741[/C][C]1310.24273441528[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]93.2228571428571[/C][C]0.0677471465845475[/C][C]1376.04108575283[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]93.2212121212121[/C][C]0.0661090661843917[/C][C]1410.11237189766[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]93.216129032258[/C][C]0.0646074622331303[/C][C]1442.80746852269[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]93.2103448275862[/C][C]0.0622534205019475[/C][C]1497.27266511678[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]93.2037037037037[/C][C]0.058587719190358[/C][C]1590.84028174701[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]93.2[/C][C]0.0547722557505167[/C][C]1701.59141198271[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]93.191304347826[/C][C]0.0502613892775079[/C][C]1854.1330768493[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]93.1904761904762[/C][C]0.0477616911166472[/C][C]1951.15528809228[/C][/ROW]
[ROW][C]Median[/C][C]93.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]93.2411764705882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]93.2411764705882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]93.2411764705882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]93.2411764705882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]93.2411764705882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]93.2411764705882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]93.2411764705882[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]93.2411764705882[/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=4374&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4374&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 Mean93.72459016393440.224687466457493417.133147841451
Geometric Mean93.7087537052995
Harmonic Mean93.693233826106
Quadratic Mean93.7407481773666
Winsorized Mean ( 1 / 20 )93.7114754098360.21958851683295426.759453369441
Winsorized Mean ( 2 / 20 )93.70163934426230.21454605532142436.743706165485
Winsorized Mean ( 3 / 20 )93.69672131147540.212877337279953440.144181192268
Winsorized Mean ( 4 / 20 )93.69672131147540.212877337279953440.144181192268
Winsorized Mean ( 5 / 20 )93.58196721311480.173528287747993539.289405938353
Winsorized Mean ( 6 / 20 )93.5721311475410.166810830779213560.94757582852
Winsorized Mean ( 7 / 20 )93.54918032786890.160644585316046582.336342951267
Winsorized Mean ( 8 / 20 )93.54918032786890.160644585316046582.336342951267
Winsorized Mean ( 9 / 20 )93.44590163934430.134358906239027695.494658709876
Winsorized Mean ( 10 / 20 )93.42950819672130.130412214518432716.416852069607
Winsorized Mean ( 11 / 20 )93.21311475409840.07772290031951221199.30051980700
Winsorized Mean ( 12 / 20 )93.21311475409840.07772290031951221199.30051980700
Winsorized Mean ( 13 / 20 )93.23442622950820.06705699581689571390.37583019812
Winsorized Mean ( 14 / 20 )93.25737704918030.06356696982256751467.07287305792
Winsorized Mean ( 15 / 20 )93.25737704918030.06356696982256751467.07287305792
Winsorized Mean ( 16 / 20 )93.25737704918030.06356696982256751467.07287305792
Winsorized Mean ( 17 / 20 )93.22950819672130.05896855985008261581.00364726121
Winsorized Mean ( 18 / 20 )93.25901639344260.05469123710692551705.19120295477
Winsorized Mean ( 19 / 20 )93.19672131147540.04484138488540772078.36402799869
Winsorized Mean ( 20 / 20 )93.19672131147540.04484138488540772078.36402799869
Trimmed Mean ( 1 / 20 )93.65932203389830.209688180230810446.659997386619
Trimmed Mean ( 2 / 20 )93.60350877192980.197175622903601474.721506611863
Trimmed Mean ( 3 / 20 )93.5490909090910.184826294412385506.14600701978
Trimmed Mean ( 4 / 20 )93.49245283018870.169710097229434550.895051953183
Trimmed Mean ( 5 / 20 )93.43137254901960.149416911032774625.306545980768
Trimmed Mean ( 6 / 20 )93.39387755102040.139740045441080668.340111499385
Trimmed Mean ( 7 / 20 )93.35531914893620.129426562443859721.299533775615
Trimmed Mean ( 8 / 20 )93.31777777777780.117863509868295791.744432878799
Trimmed Mean ( 9 / 20 )93.27674418604650.101638689175657917.728720653225
Trimmed Mean ( 10 / 20 )93.24878048780490.08958726167205081040.87097593358
Trimmed Mean ( 11 / 20 )93.22051282051280.07358007996098271266.92595156114
Trimmed Mean ( 12 / 20 )93.22162162162160.07114835989777411310.24273441528
Trimmed Mean ( 13 / 20 )93.22285714285710.06774714658454751376.04108575283
Trimmed Mean ( 14 / 20 )93.22121212121210.06610906618439171410.11237189766
Trimmed Mean ( 15 / 20 )93.2161290322580.06460746223313031442.80746852269
Trimmed Mean ( 16 / 20 )93.21034482758620.06225342050194751497.27266511678
Trimmed Mean ( 17 / 20 )93.20370370370370.0585877191903581590.84028174701
Trimmed Mean ( 18 / 20 )93.20.05477225575051671701.59141198271
Trimmed Mean ( 19 / 20 )93.1913043478260.05026138927750791854.1330768493
Trimmed Mean ( 20 / 20 )93.19047619047620.04776169111664721951.15528809228
Median93.1
Midrange95.65
Midmean - Weighted Average at Xnp93.2411764705882
Midmean - Weighted Average at X(n+1)p93.2411764705882
Midmean - Empirical Distribution Function93.2411764705882
Midmean - Empirical Distribution Function - Averaging93.2411764705882
Midmean - Empirical Distribution Function - Interpolation93.2411764705882
Midmean - Closest Observation93.2411764705882
Midmean - True Basic - Statistics Graphics Toolkit93.2411764705882
Midmean - MS Excel (old versions)93.2411764705882
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')