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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 14 Dec 2007 04:05:04 -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/14/t1197629383axy1k22i322gpi1.htm/, Retrieved Thu, 02 May 2024 15:55:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3839, Retrieved Thu, 02 May 2024 15:55:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency] [2007-12-14 11:05:04] [0cecb02636bfe8ebd97a7fef80b2b9e7] [Current]
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Dataseries X:
101,2
93,1
84,2
85,8
91,8
92,4
80,3
79,7
62,5
57,1
100,8
100,7
86,2
83,2
71,7
77,5
89,8
80,3
78,7
93,8
57,6
60,6
91,0
85,3
77,4
77,3
68,3
69,9
81,7
75,1
69,9
84,0
54,3
60,0
89,9
77,0
85,3
77,6
69,2
75,5
85,7
72,2
79,9
85,3
52,2
61,2
82,4
85,4
78,2
70,2
70,2
69,3
77,5
66,1
69,0
79,2
56,2
64,5
77,4
88,5




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=3839&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=3839&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3839&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 Mean77.47166666666671.5264505774339450.7528169021375
Geometric Mean76.5482778789007
Harmonic Mean75.587509443096
Quadratic Mean78.353890564966
Winsorized Mean ( 1 / 20 )77.51.5152501611441851.1466700267361
Winsorized Mean ( 2 / 20 )77.561.4985081093115051.7581449963829
Winsorized Mean ( 3 / 20 )77.261.4077754218688754.8809126795484
Winsorized Mean ( 4 / 20 )77.24666666666671.3905826658847555.5498558710417
Winsorized Mean ( 5 / 20 )77.38833333333331.3332897415190558.0431476545849
Winsorized Mean ( 6 / 20 )77.38833333333331.3088099819065559.1287768302326
Winsorized Mean ( 7 / 20 )77.3651.2765260613519560.6058915225464
Winsorized Mean ( 8 / 20 )77.39166666666671.2137914909190563.7602646300211
Winsorized Mean ( 9 / 20 )77.67666666666671.1507854519018167.4988257266346
Winsorized Mean ( 10 / 20 )77.72666666666671.0621289426299173.1800665126494
Winsorized Mean ( 11 / 20 )77.70833333333330.92012739128658584.453885482831
Winsorized Mean ( 12 / 20 )77.76833333333330.88379795370634287.9933394360101
Winsorized Mean ( 13 / 20 )77.790.87320987180974389.0851128821744
Winsorized Mean ( 14 / 20 )77.74333333333330.85865604706209990.540716040297
Winsorized Mean ( 15 / 20 )77.86833333333330.83016400144983493.79873518647
Winsorized Mean ( 16 / 20 )77.86833333333330.83016400144983493.79873518647
Winsorized Mean ( 17 / 20 )77.95333333333330.81640823767655595.4832763020416
Winsorized Mean ( 18 / 20 )77.62333333333330.767232780425666101.173118920007
Winsorized Mean ( 19 / 20 )78.0350.681481540759161114.507870474481
Winsorized Mean ( 20 / 20 )77.9350.616087642345509126.499859181225
Trimmed Mean ( 1 / 20 )77.4982758620691.4599565154819053.0825918719149
Trimmed Mean ( 2 / 20 )77.49642857142861.3917100671282855.6843198895144
Trimmed Mean ( 3 / 20 )77.46111111111111.3182464494070658.7607204600873
Trimmed Mean ( 4 / 20 )77.53846153846151.2721140521728860.9524447953541
Trimmed Mean ( 5 / 20 )77.6261.2208354783942563.5843251394532
Trimmed Mean ( 6 / 20 )77.68541666666671.1764646431533166.0329378522117
Trimmed Mean ( 7 / 20 )77.751.1274217090977768.9626599989994
Trimmed Mean ( 8 / 20 )77.8251.0737652085276472.4786008914508
Trimmed Mean ( 9 / 20 )77.9023809523811.0225420266317176.1850162863175
Trimmed Mean ( 10 / 20 )77.940.9737832644658980.038344099854
Trimmed Mean ( 11 / 20 )77.97368421052630.93438110758072883.4495513425068
Trimmed Mean ( 12 / 20 )78.01388888888890.91989606709151784.8072860399865
Trimmed Mean ( 13 / 20 )78.050.9076349749606685.9927197091353
Trimmed Mean ( 14 / 20 )78.08750.89093497011159187.6466887254627
Trimmed Mean ( 15 / 20 )78.13666666666670.86877484528545589.9389146574486
Trimmed Mean ( 16 / 20 )78.1750.84315835125497392.7168661540775
Trimmed Mean ( 17 / 20 )78.21923076923080.80207460291362797.521141406411
Trimmed Mean ( 18 / 20 )78.25833333333330.741715517036391105.509904452348
Trimmed Mean ( 19 / 20 )78.35454545454550.663250792338748118.137130569045
Trimmed Mean ( 20 / 20 )78.4050.578176580202568135.607360596533
Median77.9
Midrange76.7
Midmean - Weighted Average at Xnp77.8516129032258
Midmean - Weighted Average at X(n+1)p78.1366666666667
Midmean - Empirical Distribution Function77.8516129032258
Midmean - Empirical Distribution Function - Averaging78.1366666666667
Midmean - Empirical Distribution Function - Interpolation78.1366666666667
Midmean - Closest Observation77.8516129032258
Midmean - True Basic - Statistics Graphics Toolkit78.1366666666667
Midmean - MS Excel (old versions)78.0875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 77.4716666666667 & 1.52645057743394 & 50.7528169021375 \tabularnewline
Geometric Mean & 76.5482778789007 &  &  \tabularnewline
Harmonic Mean & 75.587509443096 &  &  \tabularnewline
Quadratic Mean & 78.353890564966 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 77.5 & 1.51525016114418 & 51.1466700267361 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 77.56 & 1.49850810931150 & 51.7581449963829 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 77.26 & 1.40777542186887 & 54.8809126795484 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 77.2466666666667 & 1.39058266588475 & 55.5498558710417 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 77.3883333333333 & 1.33328974151905 & 58.0431476545849 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 77.3883333333333 & 1.30880998190655 & 59.1287768302326 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 77.365 & 1.27652606135195 & 60.6058915225464 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 77.3916666666667 & 1.21379149091905 & 63.7602646300211 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 77.6766666666667 & 1.15078545190181 & 67.4988257266346 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 77.7266666666667 & 1.06212894262991 & 73.1800665126494 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 77.7083333333333 & 0.920127391286585 & 84.453885482831 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 77.7683333333333 & 0.883797953706342 & 87.9933394360101 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 77.79 & 0.873209871809743 & 89.0851128821744 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 77.7433333333333 & 0.858656047062099 & 90.540716040297 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 77.8683333333333 & 0.830164001449834 & 93.79873518647 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 77.8683333333333 & 0.830164001449834 & 93.79873518647 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 77.9533333333333 & 0.816408237676555 & 95.4832763020416 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 77.6233333333333 & 0.767232780425666 & 101.173118920007 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 78.035 & 0.681481540759161 & 114.507870474481 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 77.935 & 0.616087642345509 & 126.499859181225 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 77.498275862069 & 1.45995651548190 & 53.0825918719149 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 77.4964285714286 & 1.39171006712828 & 55.6843198895144 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 77.4611111111111 & 1.31824644940706 & 58.7607204600873 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 77.5384615384615 & 1.27211405217288 & 60.9524447953541 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 77.626 & 1.22083547839425 & 63.5843251394532 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 77.6854166666667 & 1.17646464315331 & 66.0329378522117 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 77.75 & 1.12742170909777 & 68.9626599989994 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 77.825 & 1.07376520852764 & 72.4786008914508 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 77.902380952381 & 1.02254202663171 & 76.1850162863175 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 77.94 & 0.97378326446589 & 80.038344099854 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 77.9736842105263 & 0.934381107580728 & 83.4495513425068 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 78.0138888888889 & 0.919896067091517 & 84.8072860399865 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 78.05 & 0.90763497496066 & 85.9927197091353 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 78.0875 & 0.890934970111591 & 87.6466887254627 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 78.1366666666667 & 0.868774845285455 & 89.9389146574486 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 78.175 & 0.843158351254973 & 92.7168661540775 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 78.2192307692308 & 0.802074602913627 & 97.521141406411 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 78.2583333333333 & 0.741715517036391 & 105.509904452348 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 78.3545454545455 & 0.663250792338748 & 118.137130569045 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 78.405 & 0.578176580202568 & 135.607360596533 \tabularnewline
Median & 77.9 &  &  \tabularnewline
Midrange & 76.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 77.8516129032258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 78.1366666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 77.8516129032258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 78.1366666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 78.1366666666667 &  &  \tabularnewline
Midmean - Closest Observation & 77.8516129032258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 78.1366666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 78.0875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3839&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]77.4716666666667[/C][C]1.52645057743394[/C][C]50.7528169021375[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]76.5482778789007[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]75.587509443096[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]78.353890564966[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]77.5[/C][C]1.51525016114418[/C][C]51.1466700267361[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]77.56[/C][C]1.49850810931150[/C][C]51.7581449963829[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]77.26[/C][C]1.40777542186887[/C][C]54.8809126795484[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]77.2466666666667[/C][C]1.39058266588475[/C][C]55.5498558710417[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]77.3883333333333[/C][C]1.33328974151905[/C][C]58.0431476545849[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]77.3883333333333[/C][C]1.30880998190655[/C][C]59.1287768302326[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]77.365[/C][C]1.27652606135195[/C][C]60.6058915225464[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]77.3916666666667[/C][C]1.21379149091905[/C][C]63.7602646300211[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]77.6766666666667[/C][C]1.15078545190181[/C][C]67.4988257266346[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]77.7266666666667[/C][C]1.06212894262991[/C][C]73.1800665126494[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]77.7083333333333[/C][C]0.920127391286585[/C][C]84.453885482831[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]77.7683333333333[/C][C]0.883797953706342[/C][C]87.9933394360101[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]77.79[/C][C]0.873209871809743[/C][C]89.0851128821744[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]77.7433333333333[/C][C]0.858656047062099[/C][C]90.540716040297[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]77.8683333333333[/C][C]0.830164001449834[/C][C]93.79873518647[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]77.8683333333333[/C][C]0.830164001449834[/C][C]93.79873518647[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]77.9533333333333[/C][C]0.816408237676555[/C][C]95.4832763020416[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]77.6233333333333[/C][C]0.767232780425666[/C][C]101.173118920007[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]78.035[/C][C]0.681481540759161[/C][C]114.507870474481[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]77.935[/C][C]0.616087642345509[/C][C]126.499859181225[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]77.498275862069[/C][C]1.45995651548190[/C][C]53.0825918719149[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]77.4964285714286[/C][C]1.39171006712828[/C][C]55.6843198895144[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]77.4611111111111[/C][C]1.31824644940706[/C][C]58.7607204600873[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]77.5384615384615[/C][C]1.27211405217288[/C][C]60.9524447953541[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]77.626[/C][C]1.22083547839425[/C][C]63.5843251394532[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]77.6854166666667[/C][C]1.17646464315331[/C][C]66.0329378522117[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]77.75[/C][C]1.12742170909777[/C][C]68.9626599989994[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]77.825[/C][C]1.07376520852764[/C][C]72.4786008914508[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]77.902380952381[/C][C]1.02254202663171[/C][C]76.1850162863175[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]77.94[/C][C]0.97378326446589[/C][C]80.038344099854[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]77.9736842105263[/C][C]0.934381107580728[/C][C]83.4495513425068[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]78.0138888888889[/C][C]0.919896067091517[/C][C]84.8072860399865[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]78.05[/C][C]0.90763497496066[/C][C]85.9927197091353[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]78.0875[/C][C]0.890934970111591[/C][C]87.6466887254627[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]78.1366666666667[/C][C]0.868774845285455[/C][C]89.9389146574486[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]78.175[/C][C]0.843158351254973[/C][C]92.7168661540775[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]78.2192307692308[/C][C]0.802074602913627[/C][C]97.521141406411[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]78.2583333333333[/C][C]0.741715517036391[/C][C]105.509904452348[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]78.3545454545455[/C][C]0.663250792338748[/C][C]118.137130569045[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]78.405[/C][C]0.578176580202568[/C][C]135.607360596533[/C][/ROW]
[ROW][C]Median[/C][C]77.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]76.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]77.8516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]78.1366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]77.8516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]78.1366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]78.1366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]77.8516129032258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]78.1366666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]78.0875[/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=3839&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3839&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 Mean77.47166666666671.5264505774339450.7528169021375
Geometric Mean76.5482778789007
Harmonic Mean75.587509443096
Quadratic Mean78.353890564966
Winsorized Mean ( 1 / 20 )77.51.5152501611441851.1466700267361
Winsorized Mean ( 2 / 20 )77.561.4985081093115051.7581449963829
Winsorized Mean ( 3 / 20 )77.261.4077754218688754.8809126795484
Winsorized Mean ( 4 / 20 )77.24666666666671.3905826658847555.5498558710417
Winsorized Mean ( 5 / 20 )77.38833333333331.3332897415190558.0431476545849
Winsorized Mean ( 6 / 20 )77.38833333333331.3088099819065559.1287768302326
Winsorized Mean ( 7 / 20 )77.3651.2765260613519560.6058915225464
Winsorized Mean ( 8 / 20 )77.39166666666671.2137914909190563.7602646300211
Winsorized Mean ( 9 / 20 )77.67666666666671.1507854519018167.4988257266346
Winsorized Mean ( 10 / 20 )77.72666666666671.0621289426299173.1800665126494
Winsorized Mean ( 11 / 20 )77.70833333333330.92012739128658584.453885482831
Winsorized Mean ( 12 / 20 )77.76833333333330.88379795370634287.9933394360101
Winsorized Mean ( 13 / 20 )77.790.87320987180974389.0851128821744
Winsorized Mean ( 14 / 20 )77.74333333333330.85865604706209990.540716040297
Winsorized Mean ( 15 / 20 )77.86833333333330.83016400144983493.79873518647
Winsorized Mean ( 16 / 20 )77.86833333333330.83016400144983493.79873518647
Winsorized Mean ( 17 / 20 )77.95333333333330.81640823767655595.4832763020416
Winsorized Mean ( 18 / 20 )77.62333333333330.767232780425666101.173118920007
Winsorized Mean ( 19 / 20 )78.0350.681481540759161114.507870474481
Winsorized Mean ( 20 / 20 )77.9350.616087642345509126.499859181225
Trimmed Mean ( 1 / 20 )77.4982758620691.4599565154819053.0825918719149
Trimmed Mean ( 2 / 20 )77.49642857142861.3917100671282855.6843198895144
Trimmed Mean ( 3 / 20 )77.46111111111111.3182464494070658.7607204600873
Trimmed Mean ( 4 / 20 )77.53846153846151.2721140521728860.9524447953541
Trimmed Mean ( 5 / 20 )77.6261.2208354783942563.5843251394532
Trimmed Mean ( 6 / 20 )77.68541666666671.1764646431533166.0329378522117
Trimmed Mean ( 7 / 20 )77.751.1274217090977768.9626599989994
Trimmed Mean ( 8 / 20 )77.8251.0737652085276472.4786008914508
Trimmed Mean ( 9 / 20 )77.9023809523811.0225420266317176.1850162863175
Trimmed Mean ( 10 / 20 )77.940.9737832644658980.038344099854
Trimmed Mean ( 11 / 20 )77.97368421052630.93438110758072883.4495513425068
Trimmed Mean ( 12 / 20 )78.01388888888890.91989606709151784.8072860399865
Trimmed Mean ( 13 / 20 )78.050.9076349749606685.9927197091353
Trimmed Mean ( 14 / 20 )78.08750.89093497011159187.6466887254627
Trimmed Mean ( 15 / 20 )78.13666666666670.86877484528545589.9389146574486
Trimmed Mean ( 16 / 20 )78.1750.84315835125497392.7168661540775
Trimmed Mean ( 17 / 20 )78.21923076923080.80207460291362797.521141406411
Trimmed Mean ( 18 / 20 )78.25833333333330.741715517036391105.509904452348
Trimmed Mean ( 19 / 20 )78.35454545454550.663250792338748118.137130569045
Trimmed Mean ( 20 / 20 )78.4050.578176580202568135.607360596533
Median77.9
Midrange76.7
Midmean - Weighted Average at Xnp77.8516129032258
Midmean - Weighted Average at X(n+1)p78.1366666666667
Midmean - Empirical Distribution Function77.8516129032258
Midmean - Empirical Distribution Function - Averaging78.1366666666667
Midmean - Empirical Distribution Function - Interpolation78.1366666666667
Midmean - Closest Observation77.8516129032258
Midmean - True Basic - Statistics Graphics Toolkit78.1366666666667
Midmean - MS Excel (old versions)78.0875
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')