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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 30 Oct 2009 05:43:37 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/30/t12569031126nngw7f6fyjf3m6.htm/, Retrieved Mon, 29 Apr 2024 07:44:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=52078, Retrieved Mon, 29 Apr 2024 07:44:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-30 11:43:37] [b09192cb0933771cf15268b9510cc455] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
96.8
114.1
110.3
103.9
101.6
94.6
95.9
104.7
102.8
98.1
113.9
80.9
95.7
113.2
105.9
108.8
102.3
99
100.7
115.5
100.7
109.9
114.6
85.4
100.5
114.8
116.5
112.9
102
106
105.3
118.8
106.1
109.3
117.2
92.5
104.2
112.5
122.4
113.3
100
110.7
112.8
109.8
117.3
109.1
115.9
96
99.8
116.8
115.7
99.4
94.3
91
93.2
103.1
94.1
91.8
102.7
82.6

Tables (Output of Computation)





Summary of computational 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 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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52078&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=52078&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52078&T=0

As an alternative you can also use a QR Code:  
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' @ 72.249.127.135






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean104.6616666666671.2220966786232985.6410695629823
Geometric Mean104.227210673311
Harmonic Mean103.778650089954
Quadratic Mean105.081787987580
Winsorized Mean ( 1 / 20 )104.631.1996169350923987.2195089442798
Winsorized Mean ( 2 / 20 )104.6733333333331.1623395136574490.054009266162
Winsorized Mean ( 3 / 20 )104.9483333333331.0914497994793196.1549797190858
Winsorized Mean ( 4 / 20 )104.9751.0751103609098097.6411388233357
Winsorized Mean ( 5 / 20 )105.0083333333331.0585788673763399.1974585640418
Winsorized Mean ( 6 / 20 )105.0183333333331.03391224443383101.573739839827
Winsorized Mean ( 7 / 20 )105.11.00988616016716104.071136079935
Winsorized Mean ( 8 / 20 )105.11.00026267736471105.072399858902
Winsorized Mean ( 9 / 20 )105.040.97388267138661107.856935015020
Winsorized Mean ( 10 / 20 )105.190.935781796479002112.408683729253
Winsorized Mean ( 11 / 20 )105.1350.914057895408268115.020066593310
Winsorized Mean ( 12 / 20 )105.1150.904017477082195116.275406908359
Winsorized Mean ( 13 / 20 )105.1583333333330.85359092488341123.195233533788
Winsorized Mean ( 14 / 20 )105.4383333333330.801016626877895131.630642605133
Winsorized Mean ( 15 / 20 )105.5883333333330.754557121823234139.934181627231
Winsorized Mean ( 16 / 20 )105.6683333333330.734564291727914143.851715259355
Winsorized Mean ( 17 / 20 )105.6966666666670.704372809394241150.057846153325
Winsorized Mean ( 18 / 20 )105.2166666666670.610233662141434172.420292740718
Winsorized Mean ( 19 / 20 )105.2483333333330.568353214689452185.181205301779
Winsorized Mean ( 20 / 20 )105.1816666666670.53899619856875195.143615012436
Trimmed Mean ( 1 / 20 )104.7655172413791.1545919571705290.7381318488667
Trimmed Mean ( 2 / 20 )104.9107142857141.0986582092959795.4898560790273
Trimmed Mean ( 3 / 20 )105.0425925925931.0545253778594699.6112514672856
Trimmed Mean ( 4 / 20 )105.0788461538461.03439104337132101.585224299091
Trimmed Mean ( 5 / 20 )105.111.01494646485941103.562112524388
Trimmed Mean ( 6 / 20 )105.1354166666670.995337043236853105.627955255000
Trimmed Mean ( 7 / 20 )105.1608695652170.97719147131082107.615418935404
Trimmed Mean ( 8 / 20 )105.1727272727270.959878888349893109.568747213023
Trimmed Mean ( 9 / 20 )105.1857142857140.939008616934876112.017837098304
Trimmed Mean ( 10 / 20 )105.210.91771594957403114.643316430138
Trimmed Mean ( 11 / 20 )105.2131578947370.898561922455507117.090603624979
Trimmed Mean ( 12 / 20 )105.2250.877183217364193119.957835395193
Trimmed Mean ( 13 / 20 )105.2411764705880.849211835981939123.928061305102
Trimmed Mean ( 14 / 20 )105.2531250.823630147859893127.791734279625
Trimmed Mean ( 15 / 20 )105.2266666666670.80129110375081131.321396399018
Trimmed Mean ( 16 / 20 )105.1750.780781473265541134.704784374706
Trimmed Mean ( 17 / 20 )105.1038461538460.75370838615538139.448954110720
Trimmed Mean ( 18 / 20 )105.0166666666670.720096276440168145.836980557408
Trimmed Mean ( 19 / 20 )104.9863636363640.70364836058097149.202882459189
Trimmed Mean ( 20 / 20 )104.9450.688915050908616152.333730931828
Median104.45
Midrange101.65
Midmean - Weighted Average at Xnp104.996774193548
Midmean - Weighted Average at X(n+1)p105.226666666667
Midmean - Empirical Distribution Function104.996774193548
Midmean - Empirical Distribution Function - Averaging105.226666666667
Midmean - Empirical Distribution Function - Interpolation105.226666666667
Midmean - Closest Observation104.996774193548
Midmean - True Basic - Statistics Graphics Toolkit105.226666666667
Midmean - MS Excel (old versions)105.253125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 104.661666666667 & 1.22209667862329 & 85.6410695629823 \tabularnewline
Geometric Mean & 104.227210673311 &  &  \tabularnewline
Harmonic Mean & 103.778650089954 &  &  \tabularnewline
Quadratic Mean & 105.081787987580 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 104.63 & 1.19961693509239 & 87.2195089442798 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 104.673333333333 & 1.16233951365744 & 90.054009266162 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 104.948333333333 & 1.09144979947931 & 96.1549797190858 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 104.975 & 1.07511036090980 & 97.6411388233357 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 105.008333333333 & 1.05857886737633 & 99.1974585640418 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 105.018333333333 & 1.03391224443383 & 101.573739839827 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 105.1 & 1.00988616016716 & 104.071136079935 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 105.1 & 1.00026267736471 & 105.072399858902 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 105.04 & 0.97388267138661 & 107.856935015020 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 105.19 & 0.935781796479002 & 112.408683729253 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 105.135 & 0.914057895408268 & 115.020066593310 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 105.115 & 0.904017477082195 & 116.275406908359 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 105.158333333333 & 0.85359092488341 & 123.195233533788 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 105.438333333333 & 0.801016626877895 & 131.630642605133 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 105.588333333333 & 0.754557121823234 & 139.934181627231 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 105.668333333333 & 0.734564291727914 & 143.851715259355 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 105.696666666667 & 0.704372809394241 & 150.057846153325 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 105.216666666667 & 0.610233662141434 & 172.420292740718 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 105.248333333333 & 0.568353214689452 & 185.181205301779 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 105.181666666667 & 0.53899619856875 & 195.143615012436 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 104.765517241379 & 1.15459195717052 & 90.7381318488667 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 104.910714285714 & 1.09865820929597 & 95.4898560790273 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 105.042592592593 & 1.05452537785946 & 99.6112514672856 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 105.078846153846 & 1.03439104337132 & 101.585224299091 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 105.11 & 1.01494646485941 & 103.562112524388 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 105.135416666667 & 0.995337043236853 & 105.627955255000 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 105.160869565217 & 0.97719147131082 & 107.615418935404 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 105.172727272727 & 0.959878888349893 & 109.568747213023 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 105.185714285714 & 0.939008616934876 & 112.017837098304 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 105.21 & 0.91771594957403 & 114.643316430138 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 105.213157894737 & 0.898561922455507 & 117.090603624979 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 105.225 & 0.877183217364193 & 119.957835395193 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 105.241176470588 & 0.849211835981939 & 123.928061305102 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 105.253125 & 0.823630147859893 & 127.791734279625 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 105.226666666667 & 0.80129110375081 & 131.321396399018 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 105.175 & 0.780781473265541 & 134.704784374706 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 105.103846153846 & 0.75370838615538 & 139.448954110720 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 105.016666666667 & 0.720096276440168 & 145.836980557408 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 104.986363636364 & 0.70364836058097 & 149.202882459189 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 104.945 & 0.688915050908616 & 152.333730931828 \tabularnewline
Median & 104.45 &  &  \tabularnewline
Midrange & 101.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 104.996774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.226666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 104.996774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.226666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.226666666667 &  &  \tabularnewline
Midmean - Closest Observation & 104.996774193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.226666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.253125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52078&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]104.661666666667[/C][C]1.22209667862329[/C][C]85.6410695629823[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]104.227210673311[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.778650089954[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]105.081787987580[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]104.63[/C][C]1.19961693509239[/C][C]87.2195089442798[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]104.673333333333[/C][C]1.16233951365744[/C][C]90.054009266162[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]104.948333333333[/C][C]1.09144979947931[/C][C]96.1549797190858[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]104.975[/C][C]1.07511036090980[/C][C]97.6411388233357[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]105.008333333333[/C][C]1.05857886737633[/C][C]99.1974585640418[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]105.018333333333[/C][C]1.03391224443383[/C][C]101.573739839827[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]105.1[/C][C]1.00988616016716[/C][C]104.071136079935[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]105.1[/C][C]1.00026267736471[/C][C]105.072399858902[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]105.04[/C][C]0.97388267138661[/C][C]107.856935015020[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]105.19[/C][C]0.935781796479002[/C][C]112.408683729253[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]105.135[/C][C]0.914057895408268[/C][C]115.020066593310[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]105.115[/C][C]0.904017477082195[/C][C]116.275406908359[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]105.158333333333[/C][C]0.85359092488341[/C][C]123.195233533788[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]105.438333333333[/C][C]0.801016626877895[/C][C]131.630642605133[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]105.588333333333[/C][C]0.754557121823234[/C][C]139.934181627231[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]105.668333333333[/C][C]0.734564291727914[/C][C]143.851715259355[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]105.696666666667[/C][C]0.704372809394241[/C][C]150.057846153325[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]105.216666666667[/C][C]0.610233662141434[/C][C]172.420292740718[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]105.248333333333[/C][C]0.568353214689452[/C][C]185.181205301779[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]105.181666666667[/C][C]0.53899619856875[/C][C]195.143615012436[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]104.765517241379[/C][C]1.15459195717052[/C][C]90.7381318488667[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]104.910714285714[/C][C]1.09865820929597[/C][C]95.4898560790273[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]105.042592592593[/C][C]1.05452537785946[/C][C]99.6112514672856[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]105.078846153846[/C][C]1.03439104337132[/C][C]101.585224299091[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]105.11[/C][C]1.01494646485941[/C][C]103.562112524388[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]105.135416666667[/C][C]0.995337043236853[/C][C]105.627955255000[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]105.160869565217[/C][C]0.97719147131082[/C][C]107.615418935404[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]105.172727272727[/C][C]0.959878888349893[/C][C]109.568747213023[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]105.185714285714[/C][C]0.939008616934876[/C][C]112.017837098304[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]105.21[/C][C]0.91771594957403[/C][C]114.643316430138[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]105.213157894737[/C][C]0.898561922455507[/C][C]117.090603624979[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]105.225[/C][C]0.877183217364193[/C][C]119.957835395193[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]105.241176470588[/C][C]0.849211835981939[/C][C]123.928061305102[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]105.253125[/C][C]0.823630147859893[/C][C]127.791734279625[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]105.226666666667[/C][C]0.80129110375081[/C][C]131.321396399018[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]105.175[/C][C]0.780781473265541[/C][C]134.704784374706[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]105.103846153846[/C][C]0.75370838615538[/C][C]139.448954110720[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]105.016666666667[/C][C]0.720096276440168[/C][C]145.836980557408[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]104.986363636364[/C][C]0.70364836058097[/C][C]149.202882459189[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]104.945[/C][C]0.688915050908616[/C][C]152.333730931828[/C][/ROW]
[ROW][C]Median[/C][C]104.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]104.996774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.226666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]104.996774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.226666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.226666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]104.996774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.226666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.253125[/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=52078&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52078&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean104.6616666666671.2220966786232985.6410695629823
Geometric Mean104.227210673311
Harmonic Mean103.778650089954
Quadratic Mean105.081787987580
Winsorized Mean ( 1 / 20 )104.631.1996169350923987.2195089442798
Winsorized Mean ( 2 / 20 )104.6733333333331.1623395136574490.054009266162
Winsorized Mean ( 3 / 20 )104.9483333333331.0914497994793196.1549797190858
Winsorized Mean ( 4 / 20 )104.9751.0751103609098097.6411388233357
Winsorized Mean ( 5 / 20 )105.0083333333331.0585788673763399.1974585640418
Winsorized Mean ( 6 / 20 )105.0183333333331.03391224443383101.573739839827
Winsorized Mean ( 7 / 20 )105.11.00988616016716104.071136079935
Winsorized Mean ( 8 / 20 )105.11.00026267736471105.072399858902
Winsorized Mean ( 9 / 20 )105.040.97388267138661107.856935015020
Winsorized Mean ( 10 / 20 )105.190.935781796479002112.408683729253
Winsorized Mean ( 11 / 20 )105.1350.914057895408268115.020066593310
Winsorized Mean ( 12 / 20 )105.1150.904017477082195116.275406908359
Winsorized Mean ( 13 / 20 )105.1583333333330.85359092488341123.195233533788
Winsorized Mean ( 14 / 20 )105.4383333333330.801016626877895131.630642605133
Winsorized Mean ( 15 / 20 )105.5883333333330.754557121823234139.934181627231
Winsorized Mean ( 16 / 20 )105.6683333333330.734564291727914143.851715259355
Winsorized Mean ( 17 / 20 )105.6966666666670.704372809394241150.057846153325
Winsorized Mean ( 18 / 20 )105.2166666666670.610233662141434172.420292740718
Winsorized Mean ( 19 / 20 )105.2483333333330.568353214689452185.181205301779
Winsorized Mean ( 20 / 20 )105.1816666666670.53899619856875195.143615012436
Trimmed Mean ( 1 / 20 )104.7655172413791.1545919571705290.7381318488667
Trimmed Mean ( 2 / 20 )104.9107142857141.0986582092959795.4898560790273
Trimmed Mean ( 3 / 20 )105.0425925925931.0545253778594699.6112514672856
Trimmed Mean ( 4 / 20 )105.0788461538461.03439104337132101.585224299091
Trimmed Mean ( 5 / 20 )105.111.01494646485941103.562112524388
Trimmed Mean ( 6 / 20 )105.1354166666670.995337043236853105.627955255000
Trimmed Mean ( 7 / 20 )105.1608695652170.97719147131082107.615418935404
Trimmed Mean ( 8 / 20 )105.1727272727270.959878888349893109.568747213023
Trimmed Mean ( 9 / 20 )105.1857142857140.939008616934876112.017837098304
Trimmed Mean ( 10 / 20 )105.210.91771594957403114.643316430138
Trimmed Mean ( 11 / 20 )105.2131578947370.898561922455507117.090603624979
Trimmed Mean ( 12 / 20 )105.2250.877183217364193119.957835395193
Trimmed Mean ( 13 / 20 )105.2411764705880.849211835981939123.928061305102
Trimmed Mean ( 14 / 20 )105.2531250.823630147859893127.791734279625
Trimmed Mean ( 15 / 20 )105.2266666666670.80129110375081131.321396399018
Trimmed Mean ( 16 / 20 )105.1750.780781473265541134.704784374706
Trimmed Mean ( 17 / 20 )105.1038461538460.75370838615538139.448954110720
Trimmed Mean ( 18 / 20 )105.0166666666670.720096276440168145.836980557408
Trimmed Mean ( 19 / 20 )104.9863636363640.70364836058097149.202882459189
Trimmed Mean ( 20 / 20 )104.9450.688915050908616152.333730931828
Median104.45
Midrange101.65
Midmean - Weighted Average at Xnp104.996774193548
Midmean - Weighted Average at X(n+1)p105.226666666667
Midmean - Empirical Distribution Function104.996774193548
Midmean - Empirical Distribution Function - Averaging105.226666666667
Midmean - Empirical Distribution Function - Interpolation105.226666666667
Midmean - Closest Observation104.996774193548
Midmean - True Basic - Statistics Graphics Toolkit105.226666666667
Midmean - MS Excel (old versions)105.253125
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')