Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Oct 2016 10:06:31 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/11/t1476176815ygbv1gvx613ayv3.htm/, Retrieved Mon, 29 Apr 2024 03:49:45 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Mon, 29 Apr 2024 03:49:45 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
96,07
95
93,27
91,94
91,62
91,01
90,62
97,72
99,09
99,72
100,22
99,15
101,16
101,8
103,31
101,19
99,09
95,91
94,56
95,76
100,36
102,67
103,58
100,89
103,46
104,86
104,88
104,46
103,83
101
99,36
96,71
95,23
95,62
95,8
94,79
95,39
94,9
94,84
94,68
94,17
94,1
93,84
94,2
97,76
98,26
99,63
98,75
100,15
99,63
99,72
98,87
98,4
97,99
98,46
98,73
98,66
98,14
98,39
97,78




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.01916666666670.455429163199978215.22373749181
Geometric Mean97.9566817691393
Harmonic Mean97.8941385943785
Quadratic Mean98.081570958395
Winsorized Mean ( 1 / 20 )98.02533333333330.453597077648461216.10662449925
Winsorized Mean ( 2 / 20 )98.03233333333330.445112971546319220.241465874988
Winsorized Mean ( 3 / 20 )98.01683333333330.433824047989431225.93683726754
Winsorized Mean ( 4 / 20 )98.08883333333330.410652786905918238.860751615466
Winsorized Mean ( 5 / 20 )98.12633333333330.39933765548532245.72271606613
Winsorized Mean ( 6 / 20 )98.13733333333330.391320079853337250.785324816744
Winsorized Mean ( 7 / 20 )98.07083333333330.37371915281252262.418537009077
Winsorized Mean ( 8 / 20 )97.95883333333330.350074495031505279.822822638129
Winsorized Mean ( 9 / 20 )97.92133333333330.324051110799741302.178668950304
Winsorized Mean ( 10 / 20 )97.93633333333330.319711819978985306.326908213062
Winsorized Mean ( 11 / 20 )97.92716666666670.311287384401267314.587649785489
Winsorized Mean ( 12 / 20 )97.91516666666670.305927827579287320.059693299035
Winsorized Mean ( 13 / 20 )97.81333333333330.285527034415828342.57118081114
Winsorized Mean ( 14 / 20 )97.8040.276616890219672353.572046603264
Winsorized Mean ( 15 / 20 )97.8440.264265125389589370.249384423143
Winsorized Mean ( 16 / 20 )97.7720.240739421214212406.132072208489
Winsorized Mean ( 17 / 20 )97.83716666666670.229946946923082425.47712842386
Winsorized Mean ( 18 / 20 )97.85216666666670.219391697753845446.015814037119
Winsorized Mean ( 19 / 20 )97.86483333333330.217348231569706450.26744697459
Winsorized Mean ( 20 / 20 )97.81150.199300163283289490.774811162441
Trimmed Mean ( 1 / 20 )98.02844827586210.437375152126604224.128983549313
Trimmed Mean ( 2 / 20 )98.03178571428570.417358196397513234.886451399448
Trimmed Mean ( 3 / 20 )98.03148148148150.398313040140554246.116676086951
Trimmed Mean ( 4 / 20 )98.03711538461540.380191598174735257.862393212482
Trimmed Mean ( 5 / 20 )98.02160.366936613555185267.134966582609
Trimmed Mean ( 6 / 20 )97.99541666666670.354041503749304276.790759357007
Trimmed Mean ( 7 / 20 )97.96456521739130.340017292331178288.116420625965
Trimmed Mean ( 8 / 20 )97.94386363636360.327361838569972299.191451466108
Trimmed Mean ( 9 / 20 )97.94119047619050.317758409456931308.225329562727
Trimmed Mean ( 10 / 20 )97.94450.312027478655162313.897033755299
Trimmed Mean ( 11 / 20 )97.94578947368420.30510932014182321.018674316987
Trimmed Mean ( 12 / 20 )97.94861111111110.297608764372613329.118704946731
Trimmed Mean ( 13 / 20 )97.95352941176470.288340535190659339.714738154991
Trimmed Mean ( 14 / 20 )97.973750.280687430191916349.049296340102
Trimmed Mean ( 15 / 20 )97.9980.271751830667733360.615785951487
Trimmed Mean ( 16 / 20 )98.020.262119464665663373.951625931427
Trimmed Mean ( 17 / 20 )98.05576923076920.254504147209325385.281616452876
Trimmed Mean ( 18 / 20 )98.08791666666670.245888642144669398.911945713038
Trimmed Mean ( 19 / 20 )98.12363636363640.235162783681449417.258355372058
Trimmed Mean ( 20 / 20 )98.16450.216718924197365452.957674848007
Median98.395
Midrange97.75
Midmean - Weighted Average at Xnp97.9012903225807
Midmean - Weighted Average at X(n+1)p97.998
Midmean - Empirical Distribution Function97.9012903225807
Midmean - Empirical Distribution Function - Averaging97.998
Midmean - Empirical Distribution Function - Interpolation97.998
Midmean - Closest Observation97.9012903225807
Midmean - True Basic - Statistics Graphics Toolkit97.998
Midmean - MS Excel (old versions)97.97375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.0191666666667 & 0.455429163199978 & 215.22373749181 \tabularnewline
Geometric Mean & 97.9566817691393 &  &  \tabularnewline
Harmonic Mean & 97.8941385943785 &  &  \tabularnewline
Quadratic Mean & 98.081570958395 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 98.0253333333333 & 0.453597077648461 & 216.10662449925 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 98.0323333333333 & 0.445112971546319 & 220.241465874988 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 98.0168333333333 & 0.433824047989431 & 225.93683726754 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 98.0888333333333 & 0.410652786905918 & 238.860751615466 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 98.1263333333333 & 0.39933765548532 & 245.72271606613 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 98.1373333333333 & 0.391320079853337 & 250.785324816744 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 98.0708333333333 & 0.37371915281252 & 262.418537009077 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 97.9588333333333 & 0.350074495031505 & 279.822822638129 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 97.9213333333333 & 0.324051110799741 & 302.178668950304 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 97.9363333333333 & 0.319711819978985 & 306.326908213062 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 97.9271666666667 & 0.311287384401267 & 314.587649785489 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 97.9151666666667 & 0.305927827579287 & 320.059693299035 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 97.8133333333333 & 0.285527034415828 & 342.57118081114 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 97.804 & 0.276616890219672 & 353.572046603264 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 97.844 & 0.264265125389589 & 370.249384423143 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 97.772 & 0.240739421214212 & 406.132072208489 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 97.8371666666667 & 0.229946946923082 & 425.47712842386 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 97.8521666666667 & 0.219391697753845 & 446.015814037119 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 97.8648333333333 & 0.217348231569706 & 450.26744697459 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 97.8115 & 0.199300163283289 & 490.774811162441 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 98.0284482758621 & 0.437375152126604 & 224.128983549313 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 98.0317857142857 & 0.417358196397513 & 234.886451399448 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 98.0314814814815 & 0.398313040140554 & 246.116676086951 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 98.0371153846154 & 0.380191598174735 & 257.862393212482 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 98.0216 & 0.366936613555185 & 267.134966582609 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 97.9954166666667 & 0.354041503749304 & 276.790759357007 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 97.9645652173913 & 0.340017292331178 & 288.116420625965 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 97.9438636363636 & 0.327361838569972 & 299.191451466108 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 97.9411904761905 & 0.317758409456931 & 308.225329562727 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 97.9445 & 0.312027478655162 & 313.897033755299 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 97.9457894736842 & 0.30510932014182 & 321.018674316987 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 97.9486111111111 & 0.297608764372613 & 329.118704946731 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 97.9535294117647 & 0.288340535190659 & 339.714738154991 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 97.97375 & 0.280687430191916 & 349.049296340102 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 97.998 & 0.271751830667733 & 360.615785951487 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 98.02 & 0.262119464665663 & 373.951625931427 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 98.0557692307692 & 0.254504147209325 & 385.281616452876 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 98.0879166666667 & 0.245888642144669 & 398.911945713038 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 98.1236363636364 & 0.235162783681449 & 417.258355372058 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 98.1645 & 0.216718924197365 & 452.957674848007 \tabularnewline
Median & 98.395 &  &  \tabularnewline
Midrange & 97.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 97.9012903225807 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 97.998 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 97.9012903225807 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 97.998 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 97.998 &  &  \tabularnewline
Midmean - Closest Observation & 97.9012903225807 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 97.998 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 97.97375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]98.0191666666667[/C][C]0.455429163199978[/C][C]215.22373749181[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.9566817691393[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.8941385943785[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.081570958395[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]98.0253333333333[/C][C]0.453597077648461[/C][C]216.10662449925[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]98.0323333333333[/C][C]0.445112971546319[/C][C]220.241465874988[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]98.0168333333333[/C][C]0.433824047989431[/C][C]225.93683726754[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]98.0888333333333[/C][C]0.410652786905918[/C][C]238.860751615466[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]98.1263333333333[/C][C]0.39933765548532[/C][C]245.72271606613[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]98.1373333333333[/C][C]0.391320079853337[/C][C]250.785324816744[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]98.0708333333333[/C][C]0.37371915281252[/C][C]262.418537009077[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]97.9588333333333[/C][C]0.350074495031505[/C][C]279.822822638129[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]97.9213333333333[/C][C]0.324051110799741[/C][C]302.178668950304[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]97.9363333333333[/C][C]0.319711819978985[/C][C]306.326908213062[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]97.9271666666667[/C][C]0.311287384401267[/C][C]314.587649785489[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]97.9151666666667[/C][C]0.305927827579287[/C][C]320.059693299035[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]97.8133333333333[/C][C]0.285527034415828[/C][C]342.57118081114[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]97.804[/C][C]0.276616890219672[/C][C]353.572046603264[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]97.844[/C][C]0.264265125389589[/C][C]370.249384423143[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]97.772[/C][C]0.240739421214212[/C][C]406.132072208489[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]97.8371666666667[/C][C]0.229946946923082[/C][C]425.47712842386[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]97.8521666666667[/C][C]0.219391697753845[/C][C]446.015814037119[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]97.8648333333333[/C][C]0.217348231569706[/C][C]450.26744697459[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]97.8115[/C][C]0.199300163283289[/C][C]490.774811162441[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]98.0284482758621[/C][C]0.437375152126604[/C][C]224.128983549313[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]98.0317857142857[/C][C]0.417358196397513[/C][C]234.886451399448[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]98.0314814814815[/C][C]0.398313040140554[/C][C]246.116676086951[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]98.0371153846154[/C][C]0.380191598174735[/C][C]257.862393212482[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]98.0216[/C][C]0.366936613555185[/C][C]267.134966582609[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]97.9954166666667[/C][C]0.354041503749304[/C][C]276.790759357007[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]97.9645652173913[/C][C]0.340017292331178[/C][C]288.116420625965[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]97.9438636363636[/C][C]0.327361838569972[/C][C]299.191451466108[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]97.9411904761905[/C][C]0.317758409456931[/C][C]308.225329562727[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]97.9445[/C][C]0.312027478655162[/C][C]313.897033755299[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]97.9457894736842[/C][C]0.30510932014182[/C][C]321.018674316987[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]97.9486111111111[/C][C]0.297608764372613[/C][C]329.118704946731[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]97.9535294117647[/C][C]0.288340535190659[/C][C]339.714738154991[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]97.97375[/C][C]0.280687430191916[/C][C]349.049296340102[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]97.998[/C][C]0.271751830667733[/C][C]360.615785951487[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]98.02[/C][C]0.262119464665663[/C][C]373.951625931427[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]98.0557692307692[/C][C]0.254504147209325[/C][C]385.281616452876[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]98.0879166666667[/C][C]0.245888642144669[/C][C]398.911945713038[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]98.1236363636364[/C][C]0.235162783681449[/C][C]417.258355372058[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]98.1645[/C][C]0.216718924197365[/C][C]452.957674848007[/C][/ROW]
[ROW][C]Median[/C][C]98.395[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]97.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]97.9012903225807[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]97.998[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]97.9012903225807[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]97.998[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]97.998[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]97.9012903225807[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]97.998[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]97.97375[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean98.01916666666670.455429163199978215.22373749181
Geometric Mean97.9566817691393
Harmonic Mean97.8941385943785
Quadratic Mean98.081570958395
Winsorized Mean ( 1 / 20 )98.02533333333330.453597077648461216.10662449925
Winsorized Mean ( 2 / 20 )98.03233333333330.445112971546319220.241465874988
Winsorized Mean ( 3 / 20 )98.01683333333330.433824047989431225.93683726754
Winsorized Mean ( 4 / 20 )98.08883333333330.410652786905918238.860751615466
Winsorized Mean ( 5 / 20 )98.12633333333330.39933765548532245.72271606613
Winsorized Mean ( 6 / 20 )98.13733333333330.391320079853337250.785324816744
Winsorized Mean ( 7 / 20 )98.07083333333330.37371915281252262.418537009077
Winsorized Mean ( 8 / 20 )97.95883333333330.350074495031505279.822822638129
Winsorized Mean ( 9 / 20 )97.92133333333330.324051110799741302.178668950304
Winsorized Mean ( 10 / 20 )97.93633333333330.319711819978985306.326908213062
Winsorized Mean ( 11 / 20 )97.92716666666670.311287384401267314.587649785489
Winsorized Mean ( 12 / 20 )97.91516666666670.305927827579287320.059693299035
Winsorized Mean ( 13 / 20 )97.81333333333330.285527034415828342.57118081114
Winsorized Mean ( 14 / 20 )97.8040.276616890219672353.572046603264
Winsorized Mean ( 15 / 20 )97.8440.264265125389589370.249384423143
Winsorized Mean ( 16 / 20 )97.7720.240739421214212406.132072208489
Winsorized Mean ( 17 / 20 )97.83716666666670.229946946923082425.47712842386
Winsorized Mean ( 18 / 20 )97.85216666666670.219391697753845446.015814037119
Winsorized Mean ( 19 / 20 )97.86483333333330.217348231569706450.26744697459
Winsorized Mean ( 20 / 20 )97.81150.199300163283289490.774811162441
Trimmed Mean ( 1 / 20 )98.02844827586210.437375152126604224.128983549313
Trimmed Mean ( 2 / 20 )98.03178571428570.417358196397513234.886451399448
Trimmed Mean ( 3 / 20 )98.03148148148150.398313040140554246.116676086951
Trimmed Mean ( 4 / 20 )98.03711538461540.380191598174735257.862393212482
Trimmed Mean ( 5 / 20 )98.02160.366936613555185267.134966582609
Trimmed Mean ( 6 / 20 )97.99541666666670.354041503749304276.790759357007
Trimmed Mean ( 7 / 20 )97.96456521739130.340017292331178288.116420625965
Trimmed Mean ( 8 / 20 )97.94386363636360.327361838569972299.191451466108
Trimmed Mean ( 9 / 20 )97.94119047619050.317758409456931308.225329562727
Trimmed Mean ( 10 / 20 )97.94450.312027478655162313.897033755299
Trimmed Mean ( 11 / 20 )97.94578947368420.30510932014182321.018674316987
Trimmed Mean ( 12 / 20 )97.94861111111110.297608764372613329.118704946731
Trimmed Mean ( 13 / 20 )97.95352941176470.288340535190659339.714738154991
Trimmed Mean ( 14 / 20 )97.973750.280687430191916349.049296340102
Trimmed Mean ( 15 / 20 )97.9980.271751830667733360.615785951487
Trimmed Mean ( 16 / 20 )98.020.262119464665663373.951625931427
Trimmed Mean ( 17 / 20 )98.05576923076920.254504147209325385.281616452876
Trimmed Mean ( 18 / 20 )98.08791666666670.245888642144669398.911945713038
Trimmed Mean ( 19 / 20 )98.12363636363640.235162783681449417.258355372058
Trimmed Mean ( 20 / 20 )98.16450.216718924197365452.957674848007
Median98.395
Midrange97.75
Midmean - Weighted Average at Xnp97.9012903225807
Midmean - Weighted Average at X(n+1)p97.998
Midmean - Empirical Distribution Function97.9012903225807
Midmean - Empirical Distribution Function - Averaging97.998
Midmean - Empirical Distribution Function - Interpolation97.998
Midmean - Closest Observation97.9012903225807
Midmean - True Basic - Statistics Graphics Toolkit97.998
Midmean - MS Excel (old versions)97.97375
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')