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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 06 Nov 2007 13:14:14 -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/Nov/06/3u41qbm0xmn2cm81194379883.htm/, Retrieved Fri, 03 May 2024 17:52:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=553, Retrieved Fri, 03 May 2024 17:52:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact254
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2007-11-06 20:14:14] [d9ccf6bb4f7743d5d52b9a9a992ccbd5] [Current]
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Dataseries X:
106.8
113.7
102.5
96.6
92.1
95.6
102.3
98.6
98.2
104.5
84
73.8
103.9
106
97.2
102.6
89
93.8
116.7
106.8
98.5
118.7
90
91.9
113.3
113.1
104.1
108.7
96.7
101
116.9
105.8
99
129.4
83
88.9
115.9
104.2
113.4
112.2
100.8
107.3
126.6
102.9
117.9
128.8
87.5
93.8
122.7
126.2
124.6
116.7
115.2
111.1
129.9
113.3
118.5
133.5
102.1
102.4




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=553&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]2 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=553&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=553&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean106.1866666666671.6661069116520163.7334050558485
Geometric Mean105.404632882537
Harmonic Mean104.609569824186
Quadratic Mean106.955070006054
Winsorized Mean ( 1 / 20 )106.281.6060651287354866.1741532758877
Winsorized Mean ( 2 / 20 )106.2966666666671.5938936560565566.6899364727098
Winsorized Mean ( 3 / 20 )106.4416666666671.5475993650576868.7785670309445
Winsorized Mean ( 4 / 20 )106.3883333333331.4938576529851571.2171826550806
Winsorized Mean ( 5 / 20 )106.3633333333331.4846083519126371.6440354092746
Winsorized Mean ( 6 / 20 )106.3033333333331.4295409690867774.361865544324
Winsorized Mean ( 7 / 20 )106.3033333333331.3408488050077779.2806265227772
Winsorized Mean ( 8 / 20 )105.7966666666671.2330110282786985.8035039754357
Winsorized Mean ( 9 / 20 )106.0216666666671.1812664171977789.7525444921852
Winsorized Mean ( 10 / 20 )105.9216666666671.1635885746251291.0301707807608
Winsorized Mean ( 11 / 20 )106.0683333333331.0755040643656698.6219734984392
Winsorized Mean ( 12 / 20 )106.2283333333331.03640810534684102.496625398142
Winsorized Mean ( 13 / 20 )106.251.03300477736383102.855284242871
Winsorized Mean ( 14 / 20 )106.180.983180012944276107.996499727480
Winsorized Mean ( 15 / 20 )106.2550.916023169099823115.995974320624
Winsorized Mean ( 16 / 20 )105.9350.839527796385537126.184029231775
Winsorized Mean ( 17 / 20 )105.8783333333330.822020700478441128.802514671113
Winsorized Mean ( 18 / 20 )105.9683333333330.799493100943181132.544399955822
Winsorized Mean ( 19 / 20 )106.5383333333330.718630570197125148.251880384255
Winsorized Mean ( 20 / 20 )106.5383333333330.699023094219607152.410319793902
Trimmed Mean ( 1 / 20 )106.2741379310341.5586314136170268.1842653770277
Trimmed Mean ( 2 / 20 )106.2678571428571.5001625607646270.8375611565013
Trimmed Mean ( 3 / 20 )106.2518518518521.4358559556001173.9989630836226
Trimmed Mean ( 4 / 20 )106.1788461538461.3785972731245877.0194807604636
Trimmed Mean ( 5 / 20 )106.1161.3285602457286779.8729303704247
Trimmed Mean ( 6 / 20 )106.0541666666671.2681167919361983.6312296635867
Trimmed Mean ( 7 / 20 )1061.2090839747391587.6696757335394
Trimmed Mean ( 8 / 20 )105.9409090909091.1605400715769991.2858691272524
Trimmed Mean ( 9 / 20 )105.9666666666671.1287226016943693.8819392006475
Trimmed Mean ( 10 / 20 )105.95751.1003314622981096.29598319283
Trimmed Mean ( 11 / 20 )105.9631578947371.0661974352232899.3841800721896
Trimmed Mean ( 12 / 20 )105.9472222222221.04322824749277101.557087317036
Trimmed Mean ( 13 / 20 )105.9058823529411.02039750718255103.788848568791
Trimmed Mean ( 14 / 20 )105.856250.987267096871215107.221490856398
Trimmed Mean ( 15 / 20 )105.810.953533657917543110.966193087596
Trimmed Mean ( 16 / 20 )105.7464285714290.923552523161812114.499636912259
Trimmed Mean ( 17 / 20 )105.7192307692310.902168656085806117.183444643166
Trimmed Mean ( 18 / 20 )105.6958333333330.871602704306606121.266068601082
Trimmed Mean ( 19 / 20 )105.6545454545450.827888548680203127.619285981159
Trimmed Mean ( 20 / 20 )105.5150.78513408174387134.391058105183
Median104.35
Midrange103.65
Midmean - Weighted Average at Xnp105.532258064516
Midmean - Weighted Average at X(n+1)p105.81
Midmean - Empirical Distribution Function105.532258064516
Midmean - Empirical Distribution Function - Averaging105.81
Midmean - Empirical Distribution Function - Interpolation105.81
Midmean - Closest Observation105.532258064516
Midmean - True Basic - Statistics Graphics Toolkit105.81
Midmean - MS Excel (old versions)105.85625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 106.186666666667 & 1.66610691165201 & 63.7334050558485 \tabularnewline
Geometric Mean & 105.404632882537 &  &  \tabularnewline
Harmonic Mean & 104.609569824186 &  &  \tabularnewline
Quadratic Mean & 106.955070006054 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 106.28 & 1.60606512873548 & 66.1741532758877 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 106.296666666667 & 1.59389365605655 & 66.6899364727098 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 106.441666666667 & 1.54759936505768 & 68.7785670309445 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 106.388333333333 & 1.49385765298515 & 71.2171826550806 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 106.363333333333 & 1.48460835191263 & 71.6440354092746 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 106.303333333333 & 1.42954096908677 & 74.361865544324 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 106.303333333333 & 1.34084880500777 & 79.2806265227772 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 105.796666666667 & 1.23301102827869 & 85.8035039754357 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 106.021666666667 & 1.18126641719777 & 89.7525444921852 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 105.921666666667 & 1.16358857462512 & 91.0301707807608 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 106.068333333333 & 1.07550406436566 & 98.6219734984392 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 106.228333333333 & 1.03640810534684 & 102.496625398142 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 106.25 & 1.03300477736383 & 102.855284242871 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 106.18 & 0.983180012944276 & 107.996499727480 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 106.255 & 0.916023169099823 & 115.995974320624 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 105.935 & 0.839527796385537 & 126.184029231775 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 105.878333333333 & 0.822020700478441 & 128.802514671113 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 105.968333333333 & 0.799493100943181 & 132.544399955822 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 106.538333333333 & 0.718630570197125 & 148.251880384255 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 106.538333333333 & 0.699023094219607 & 152.410319793902 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 106.274137931034 & 1.55863141361702 & 68.1842653770277 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 106.267857142857 & 1.50016256076462 & 70.8375611565013 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 106.251851851852 & 1.43585595560011 & 73.9989630836226 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 106.178846153846 & 1.37859727312458 & 77.0194807604636 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 106.116 & 1.32856024572867 & 79.8729303704247 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 106.054166666667 & 1.26811679193619 & 83.6312296635867 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 106 & 1.20908397473915 & 87.6696757335394 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 105.940909090909 & 1.16054007157699 & 91.2858691272524 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 105.966666666667 & 1.12872260169436 & 93.8819392006475 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 105.9575 & 1.10033146229810 & 96.29598319283 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 105.963157894737 & 1.06619743522328 & 99.3841800721896 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 105.947222222222 & 1.04322824749277 & 101.557087317036 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 105.905882352941 & 1.02039750718255 & 103.788848568791 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 105.85625 & 0.987267096871215 & 107.221490856398 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 105.81 & 0.953533657917543 & 110.966193087596 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 105.746428571429 & 0.923552523161812 & 114.499636912259 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 105.719230769231 & 0.902168656085806 & 117.183444643166 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 105.695833333333 & 0.871602704306606 & 121.266068601082 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 105.654545454545 & 0.827888548680203 & 127.619285981159 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 105.515 & 0.78513408174387 & 134.391058105183 \tabularnewline
Median & 104.35 &  &  \tabularnewline
Midrange & 103.65 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 105.532258064516 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.81 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 105.532258064516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.81 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.81 &  &  \tabularnewline
Midmean - Closest Observation & 105.532258064516 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.81 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.85625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=553&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]106.186666666667[/C][C]1.66610691165201[/C][C]63.7334050558485[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.404632882537[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]104.609569824186[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]106.955070006054[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]106.28[/C][C]1.60606512873548[/C][C]66.1741532758877[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]106.296666666667[/C][C]1.59389365605655[/C][C]66.6899364727098[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]106.441666666667[/C][C]1.54759936505768[/C][C]68.7785670309445[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]106.388333333333[/C][C]1.49385765298515[/C][C]71.2171826550806[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]106.363333333333[/C][C]1.48460835191263[/C][C]71.6440354092746[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]106.303333333333[/C][C]1.42954096908677[/C][C]74.361865544324[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]106.303333333333[/C][C]1.34084880500777[/C][C]79.2806265227772[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]105.796666666667[/C][C]1.23301102827869[/C][C]85.8035039754357[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]106.021666666667[/C][C]1.18126641719777[/C][C]89.7525444921852[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]105.921666666667[/C][C]1.16358857462512[/C][C]91.0301707807608[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]106.068333333333[/C][C]1.07550406436566[/C][C]98.6219734984392[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]106.228333333333[/C][C]1.03640810534684[/C][C]102.496625398142[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]106.25[/C][C]1.03300477736383[/C][C]102.855284242871[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]106.18[/C][C]0.983180012944276[/C][C]107.996499727480[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]106.255[/C][C]0.916023169099823[/C][C]115.995974320624[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]105.935[/C][C]0.839527796385537[/C][C]126.184029231775[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]105.878333333333[/C][C]0.822020700478441[/C][C]128.802514671113[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]105.968333333333[/C][C]0.799493100943181[/C][C]132.544399955822[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]106.538333333333[/C][C]0.718630570197125[/C][C]148.251880384255[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]106.538333333333[/C][C]0.699023094219607[/C][C]152.410319793902[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]106.274137931034[/C][C]1.55863141361702[/C][C]68.1842653770277[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]106.267857142857[/C][C]1.50016256076462[/C][C]70.8375611565013[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]106.251851851852[/C][C]1.43585595560011[/C][C]73.9989630836226[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]106.178846153846[/C][C]1.37859727312458[/C][C]77.0194807604636[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]106.116[/C][C]1.32856024572867[/C][C]79.8729303704247[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]106.054166666667[/C][C]1.26811679193619[/C][C]83.6312296635867[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]106[/C][C]1.20908397473915[/C][C]87.6696757335394[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]105.940909090909[/C][C]1.16054007157699[/C][C]91.2858691272524[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]105.966666666667[/C][C]1.12872260169436[/C][C]93.8819392006475[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]105.9575[/C][C]1.10033146229810[/C][C]96.29598319283[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]105.963157894737[/C][C]1.06619743522328[/C][C]99.3841800721896[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]105.947222222222[/C][C]1.04322824749277[/C][C]101.557087317036[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]105.905882352941[/C][C]1.02039750718255[/C][C]103.788848568791[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]105.85625[/C][C]0.987267096871215[/C][C]107.221490856398[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]105.81[/C][C]0.953533657917543[/C][C]110.966193087596[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]105.746428571429[/C][C]0.923552523161812[/C][C]114.499636912259[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]105.719230769231[/C][C]0.902168656085806[/C][C]117.183444643166[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]105.695833333333[/C][C]0.871602704306606[/C][C]121.266068601082[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]105.654545454545[/C][C]0.827888548680203[/C][C]127.619285981159[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]105.515[/C][C]0.78513408174387[/C][C]134.391058105183[/C][/ROW]
[ROW][C]Median[/C][C]104.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]105.532258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]105.532258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]105.532258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.85625[/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=553&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=553&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 Mean106.1866666666671.6661069116520163.7334050558485
Geometric Mean105.404632882537
Harmonic Mean104.609569824186
Quadratic Mean106.955070006054
Winsorized Mean ( 1 / 20 )106.281.6060651287354866.1741532758877
Winsorized Mean ( 2 / 20 )106.2966666666671.5938936560565566.6899364727098
Winsorized Mean ( 3 / 20 )106.4416666666671.5475993650576868.7785670309445
Winsorized Mean ( 4 / 20 )106.3883333333331.4938576529851571.2171826550806
Winsorized Mean ( 5 / 20 )106.3633333333331.4846083519126371.6440354092746
Winsorized Mean ( 6 / 20 )106.3033333333331.4295409690867774.361865544324
Winsorized Mean ( 7 / 20 )106.3033333333331.3408488050077779.2806265227772
Winsorized Mean ( 8 / 20 )105.7966666666671.2330110282786985.8035039754357
Winsorized Mean ( 9 / 20 )106.0216666666671.1812664171977789.7525444921852
Winsorized Mean ( 10 / 20 )105.9216666666671.1635885746251291.0301707807608
Winsorized Mean ( 11 / 20 )106.0683333333331.0755040643656698.6219734984392
Winsorized Mean ( 12 / 20 )106.2283333333331.03640810534684102.496625398142
Winsorized Mean ( 13 / 20 )106.251.03300477736383102.855284242871
Winsorized Mean ( 14 / 20 )106.180.983180012944276107.996499727480
Winsorized Mean ( 15 / 20 )106.2550.916023169099823115.995974320624
Winsorized Mean ( 16 / 20 )105.9350.839527796385537126.184029231775
Winsorized Mean ( 17 / 20 )105.8783333333330.822020700478441128.802514671113
Winsorized Mean ( 18 / 20 )105.9683333333330.799493100943181132.544399955822
Winsorized Mean ( 19 / 20 )106.5383333333330.718630570197125148.251880384255
Winsorized Mean ( 20 / 20 )106.5383333333330.699023094219607152.410319793902
Trimmed Mean ( 1 / 20 )106.2741379310341.5586314136170268.1842653770277
Trimmed Mean ( 2 / 20 )106.2678571428571.5001625607646270.8375611565013
Trimmed Mean ( 3 / 20 )106.2518518518521.4358559556001173.9989630836226
Trimmed Mean ( 4 / 20 )106.1788461538461.3785972731245877.0194807604636
Trimmed Mean ( 5 / 20 )106.1161.3285602457286779.8729303704247
Trimmed Mean ( 6 / 20 )106.0541666666671.2681167919361983.6312296635867
Trimmed Mean ( 7 / 20 )1061.2090839747391587.6696757335394
Trimmed Mean ( 8 / 20 )105.9409090909091.1605400715769991.2858691272524
Trimmed Mean ( 9 / 20 )105.9666666666671.1287226016943693.8819392006475
Trimmed Mean ( 10 / 20 )105.95751.1003314622981096.29598319283
Trimmed Mean ( 11 / 20 )105.9631578947371.0661974352232899.3841800721896
Trimmed Mean ( 12 / 20 )105.9472222222221.04322824749277101.557087317036
Trimmed Mean ( 13 / 20 )105.9058823529411.02039750718255103.788848568791
Trimmed Mean ( 14 / 20 )105.856250.987267096871215107.221490856398
Trimmed Mean ( 15 / 20 )105.810.953533657917543110.966193087596
Trimmed Mean ( 16 / 20 )105.7464285714290.923552523161812114.499636912259
Trimmed Mean ( 17 / 20 )105.7192307692310.902168656085806117.183444643166
Trimmed Mean ( 18 / 20 )105.6958333333330.871602704306606121.266068601082
Trimmed Mean ( 19 / 20 )105.6545454545450.827888548680203127.619285981159
Trimmed Mean ( 20 / 20 )105.5150.78513408174387134.391058105183
Median104.35
Midrange103.65
Midmean - Weighted Average at Xnp105.532258064516
Midmean - Weighted Average at X(n+1)p105.81
Midmean - Empirical Distribution Function105.532258064516
Midmean - Empirical Distribution Function - Averaging105.81
Midmean - Empirical Distribution Function - Interpolation105.81
Midmean - Closest Observation105.532258064516
Midmean - True Basic - Statistics Graphics Toolkit105.81
Midmean - MS Excel (old versions)105.85625
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')