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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Dec 2008 04:29:14 -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/2008/Dec/15/t1229340642hx5tgjoox4js5wz.htm/, Retrieved Wed, 15 May 2024 16:08:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33676, Retrieved Wed, 15 May 2024 16:08:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [paper central ten...] [2008-12-15 11:24:16] [5161246d1ccc1b670cc664d03050f084]
-    D    [Central Tendency] [paper central ten...] [2008-12-15 11:29:14] [366411ff82333cf2a466cacd3525c11d] [Current]
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Dataseries X:
104.5
113.1
95.1
96.9
107.1
135.4
120.3
105.5
128.4
78.2
85.8
128.7
131.2
128.9
112.3
115
116
140.2
121.2
104.1
128.8
76.1
86.9
127.6
108
113.5
117.4
102.4
117.9
132
95
120.8
128.9
88.4
81.1
120.7
131
123.6
139
109.6
108
130.3
111.7
105.9
128.7
89.8
100.7
115.2
129.7
121.7
114.6
114.7
118.9
120.2
128.4
115.2
122.6
92.8
83.4
126.6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33676&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33676&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33676&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean113.2616666666672.076960093443154.5324231429531
Geometric Mean112.049652433290
Harmonic Mean110.745621336941
Quadratic Mean114.379706096259
Winsorized Mean ( 1 / 20 )113.2766666666672.0622944912737954.9274932100994
Winsorized Mean ( 2 / 20 )113.2533333333332.0113540238894356.3070110921255
Winsorized Mean ( 3 / 20 )113.1983333333331.9511035435529358.017594046906
Winsorized Mean ( 4 / 20 )113.3051.9021656183277159.5663168907513
Winsorized Mean ( 5 / 20 )113.381.8773189802674260.394637880798
Winsorized Mean ( 6 / 20 )113.461.8309581943901761.9675535725651
Winsorized Mean ( 7 / 20 )113.5533333333331.7827333591300763.6961959295722
Winsorized Mean ( 8 / 20 )113.8466666666671.6786907507146367.8187251691245
Winsorized Mean ( 9 / 20 )114.1766666666671.6102871391255570.9045386331963
Winsorized Mean ( 10 / 20 )114.1766666666671.6043467908265471.1670739266069
Winsorized Mean ( 11 / 20 )114.4883333333331.5361943800372474.5272439615082
Winsorized Mean ( 12 / 20 )115.2483333333331.3949657097757382.6173235124627
Winsorized Mean ( 13 / 20 )115.5516666666671.3206155294588387.4983400460374
Winsorized Mean ( 14 / 20 )115.9483333333331.2553669904066492.3621014567021
Winsorized Mean ( 15 / 20 )115.8483333333331.2060616479607296.0550677730416
Winsorized Mean ( 16 / 20 )115.8483333333331.12018332757736103.419083717198
Winsorized Mean ( 17 / 20 )115.1116666666670.96956246077723118.725374922612
Winsorized Mean ( 18 / 20 )115.1716666666670.868136818041906132.665340615824
Winsorized Mean ( 19 / 20 )115.1716666666670.782694504504981147.147662343059
Winsorized Mean ( 20 / 20 )115.0050.759387297626587151.444461027252
Trimmed Mean ( 1 / 20 )113.4379310344831.9953254924568656.8518427010151
Trimmed Mean ( 2 / 20 )113.6107142857141.9124891623008959.4046316837846
Trimmed Mean ( 3 / 20 )113.8092592592591.843985195506661.719182744302
Trimmed Mean ( 4 / 20 )114.0442307692311.7874529462771663.8026477881602
Trimmed Mean ( 5 / 20 )114.2661.7354164588692565.8435613054244
Trimmed Mean ( 6 / 20 )114.48751.6773565644567868.2547184218268
Trimmed Mean ( 7 / 20 )114.7108695652171.6173014688572570.9273266450871
Trimmed Mean ( 8 / 20 )114.9363636363641.5536497673098273.9782968174216
Trimmed Mean ( 9 / 20 )115.1309523809521.5011357995460476.6958941461321
Trimmed Mean ( 10 / 20 )115.291.4510199772432479.4544539759107
Trimmed Mean ( 11 / 20 )115.4657894736841.3840139755201683.4281961858716
Trimmed Mean ( 12 / 20 )115.6138888888891.3131094369084688.0458898849178
Trimmed Mean ( 13 / 20 )115.6676470588241.2591180499083191.8640210639872
Trimmed Mean ( 14 / 20 )115.6843751.2050976183103495.9958539808586
Trimmed Mean ( 15 / 20 )115.6466666666671.14706755889718100.819403155166
Trimmed Mean ( 16 / 20 )115.6178571428571.07740199926824107.311715795388
Trimmed Mean ( 17 / 20 )115.5846153846151.00349684461874115.181842378916
Trimmed Mean ( 18 / 20 )115.6541666666670.948300905561058121.959354871901
Trimmed Mean ( 19 / 20 )115.7272727272730.900773640989924128.475420972678
Trimmed Mean ( 20 / 20 )115.8150.8573605456651135.083192929243
Median115.2
Midrange108.15
Midmean - Weighted Average at Xnp115.274193548387
Midmean - Weighted Average at X(n+1)p115.646666666667
Midmean - Empirical Distribution Function115.274193548387
Midmean - Empirical Distribution Function - Averaging115.646666666667
Midmean - Empirical Distribution Function - Interpolation115.646666666667
Midmean - Closest Observation115.274193548387
Midmean - True Basic - Statistics Graphics Toolkit115.646666666667
Midmean - MS Excel (old versions)116.069696969697
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.261666666667 & 2.0769600934431 & 54.5324231429531 \tabularnewline
Geometric Mean & 112.049652433290 &  &  \tabularnewline
Harmonic Mean & 110.745621336941 &  &  \tabularnewline
Quadratic Mean & 114.379706096259 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 113.276666666667 & 2.06229449127379 & 54.9274932100994 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 113.253333333333 & 2.01135402388943 & 56.3070110921255 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 113.198333333333 & 1.95110354355293 & 58.017594046906 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 113.305 & 1.90216561832771 & 59.5663168907513 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 113.38 & 1.87731898026742 & 60.394637880798 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 113.46 & 1.83095819439017 & 61.9675535725651 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 113.553333333333 & 1.78273335913007 & 63.6961959295722 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 113.846666666667 & 1.67869075071463 & 67.8187251691245 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 114.176666666667 & 1.61028713912555 & 70.9045386331963 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 114.176666666667 & 1.60434679082654 & 71.1670739266069 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 114.488333333333 & 1.53619438003724 & 74.5272439615082 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 115.248333333333 & 1.39496570977573 & 82.6173235124627 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 115.551666666667 & 1.32061552945883 & 87.4983400460374 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 115.948333333333 & 1.25536699040664 & 92.3621014567021 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 115.848333333333 & 1.20606164796072 & 96.0550677730416 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 115.848333333333 & 1.12018332757736 & 103.419083717198 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 115.111666666667 & 0.96956246077723 & 118.725374922612 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 115.171666666667 & 0.868136818041906 & 132.665340615824 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 115.171666666667 & 0.782694504504981 & 147.147662343059 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 115.005 & 0.759387297626587 & 151.444461027252 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 113.437931034483 & 1.99532549245686 & 56.8518427010151 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 113.610714285714 & 1.91248916230089 & 59.4046316837846 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 113.809259259259 & 1.8439851955066 & 61.719182744302 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 114.044230769231 & 1.78745294627716 & 63.8026477881602 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 114.266 & 1.73541645886925 & 65.8435613054244 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 114.4875 & 1.67735656445678 & 68.2547184218268 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 114.710869565217 & 1.61730146885725 & 70.9273266450871 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 114.936363636364 & 1.55364976730982 & 73.9782968174216 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 115.130952380952 & 1.50113579954604 & 76.6958941461321 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 115.29 & 1.45101997724324 & 79.4544539759107 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 115.465789473684 & 1.38401397552016 & 83.4281961858716 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 115.613888888889 & 1.31310943690846 & 88.0458898849178 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 115.667647058824 & 1.25911804990831 & 91.8640210639872 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 115.684375 & 1.20509761831034 & 95.9958539808586 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 115.646666666667 & 1.14706755889718 & 100.819403155166 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 115.617857142857 & 1.07740199926824 & 107.311715795388 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 115.584615384615 & 1.00349684461874 & 115.181842378916 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 115.654166666667 & 0.948300905561058 & 121.959354871901 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 115.727272727273 & 0.900773640989924 & 128.475420972678 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 115.815 & 0.8573605456651 & 135.083192929243 \tabularnewline
Median & 115.2 &  &  \tabularnewline
Midrange & 108.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 115.274193548387 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 115.646666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 115.274193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 115.646666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 115.646666666667 &  &  \tabularnewline
Midmean - Closest Observation & 115.274193548387 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 115.646666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.069696969697 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33676&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]113.261666666667[/C][C]2.0769600934431[/C][C]54.5324231429531[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]112.049652433290[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.745621336941[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.379706096259[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]113.276666666667[/C][C]2.06229449127379[/C][C]54.9274932100994[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]113.253333333333[/C][C]2.01135402388943[/C][C]56.3070110921255[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]113.198333333333[/C][C]1.95110354355293[/C][C]58.017594046906[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]113.305[/C][C]1.90216561832771[/C][C]59.5663168907513[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]113.38[/C][C]1.87731898026742[/C][C]60.394637880798[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]113.46[/C][C]1.83095819439017[/C][C]61.9675535725651[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]113.553333333333[/C][C]1.78273335913007[/C][C]63.6961959295722[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]113.846666666667[/C][C]1.67869075071463[/C][C]67.8187251691245[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]114.176666666667[/C][C]1.61028713912555[/C][C]70.9045386331963[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]114.176666666667[/C][C]1.60434679082654[/C][C]71.1670739266069[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]114.488333333333[/C][C]1.53619438003724[/C][C]74.5272439615082[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]115.248333333333[/C][C]1.39496570977573[/C][C]82.6173235124627[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]115.551666666667[/C][C]1.32061552945883[/C][C]87.4983400460374[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]115.948333333333[/C][C]1.25536699040664[/C][C]92.3621014567021[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]115.848333333333[/C][C]1.20606164796072[/C][C]96.0550677730416[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]115.848333333333[/C][C]1.12018332757736[/C][C]103.419083717198[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]115.111666666667[/C][C]0.96956246077723[/C][C]118.725374922612[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]115.171666666667[/C][C]0.868136818041906[/C][C]132.665340615824[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]115.171666666667[/C][C]0.782694504504981[/C][C]147.147662343059[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]115.005[/C][C]0.759387297626587[/C][C]151.444461027252[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]113.437931034483[/C][C]1.99532549245686[/C][C]56.8518427010151[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]113.610714285714[/C][C]1.91248916230089[/C][C]59.4046316837846[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]113.809259259259[/C][C]1.8439851955066[/C][C]61.719182744302[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]114.044230769231[/C][C]1.78745294627716[/C][C]63.8026477881602[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]114.266[/C][C]1.73541645886925[/C][C]65.8435613054244[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]114.4875[/C][C]1.67735656445678[/C][C]68.2547184218268[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]114.710869565217[/C][C]1.61730146885725[/C][C]70.9273266450871[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]114.936363636364[/C][C]1.55364976730982[/C][C]73.9782968174216[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]115.130952380952[/C][C]1.50113579954604[/C][C]76.6958941461321[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]115.29[/C][C]1.45101997724324[/C][C]79.4544539759107[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]115.465789473684[/C][C]1.38401397552016[/C][C]83.4281961858716[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]115.613888888889[/C][C]1.31310943690846[/C][C]88.0458898849178[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]115.667647058824[/C][C]1.25911804990831[/C][C]91.8640210639872[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]115.684375[/C][C]1.20509761831034[/C][C]95.9958539808586[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]115.646666666667[/C][C]1.14706755889718[/C][C]100.819403155166[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]115.617857142857[/C][C]1.07740199926824[/C][C]107.311715795388[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]115.584615384615[/C][C]1.00349684461874[/C][C]115.181842378916[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]115.654166666667[/C][C]0.948300905561058[/C][C]121.959354871901[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]115.727272727273[/C][C]0.900773640989924[/C][C]128.475420972678[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]115.815[/C][C]0.8573605456651[/C][C]135.083192929243[/C][/ROW]
[ROW][C]Median[/C][C]115.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]108.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]115.274193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]115.646666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]115.274193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]115.646666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]115.646666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]115.274193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]115.646666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.069696969697[/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=33676&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33676&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 Mean113.2616666666672.076960093443154.5324231429531
Geometric Mean112.049652433290
Harmonic Mean110.745621336941
Quadratic Mean114.379706096259
Winsorized Mean ( 1 / 20 )113.2766666666672.0622944912737954.9274932100994
Winsorized Mean ( 2 / 20 )113.2533333333332.0113540238894356.3070110921255
Winsorized Mean ( 3 / 20 )113.1983333333331.9511035435529358.017594046906
Winsorized Mean ( 4 / 20 )113.3051.9021656183277159.5663168907513
Winsorized Mean ( 5 / 20 )113.381.8773189802674260.394637880798
Winsorized Mean ( 6 / 20 )113.461.8309581943901761.9675535725651
Winsorized Mean ( 7 / 20 )113.5533333333331.7827333591300763.6961959295722
Winsorized Mean ( 8 / 20 )113.8466666666671.6786907507146367.8187251691245
Winsorized Mean ( 9 / 20 )114.1766666666671.6102871391255570.9045386331963
Winsorized Mean ( 10 / 20 )114.1766666666671.6043467908265471.1670739266069
Winsorized Mean ( 11 / 20 )114.4883333333331.5361943800372474.5272439615082
Winsorized Mean ( 12 / 20 )115.2483333333331.3949657097757382.6173235124627
Winsorized Mean ( 13 / 20 )115.5516666666671.3206155294588387.4983400460374
Winsorized Mean ( 14 / 20 )115.9483333333331.2553669904066492.3621014567021
Winsorized Mean ( 15 / 20 )115.8483333333331.2060616479607296.0550677730416
Winsorized Mean ( 16 / 20 )115.8483333333331.12018332757736103.419083717198
Winsorized Mean ( 17 / 20 )115.1116666666670.96956246077723118.725374922612
Winsorized Mean ( 18 / 20 )115.1716666666670.868136818041906132.665340615824
Winsorized Mean ( 19 / 20 )115.1716666666670.782694504504981147.147662343059
Winsorized Mean ( 20 / 20 )115.0050.759387297626587151.444461027252
Trimmed Mean ( 1 / 20 )113.4379310344831.9953254924568656.8518427010151
Trimmed Mean ( 2 / 20 )113.6107142857141.9124891623008959.4046316837846
Trimmed Mean ( 3 / 20 )113.8092592592591.843985195506661.719182744302
Trimmed Mean ( 4 / 20 )114.0442307692311.7874529462771663.8026477881602
Trimmed Mean ( 5 / 20 )114.2661.7354164588692565.8435613054244
Trimmed Mean ( 6 / 20 )114.48751.6773565644567868.2547184218268
Trimmed Mean ( 7 / 20 )114.7108695652171.6173014688572570.9273266450871
Trimmed Mean ( 8 / 20 )114.9363636363641.5536497673098273.9782968174216
Trimmed Mean ( 9 / 20 )115.1309523809521.5011357995460476.6958941461321
Trimmed Mean ( 10 / 20 )115.291.4510199772432479.4544539759107
Trimmed Mean ( 11 / 20 )115.4657894736841.3840139755201683.4281961858716
Trimmed Mean ( 12 / 20 )115.6138888888891.3131094369084688.0458898849178
Trimmed Mean ( 13 / 20 )115.6676470588241.2591180499083191.8640210639872
Trimmed Mean ( 14 / 20 )115.6843751.2050976183103495.9958539808586
Trimmed Mean ( 15 / 20 )115.6466666666671.14706755889718100.819403155166
Trimmed Mean ( 16 / 20 )115.6178571428571.07740199926824107.311715795388
Trimmed Mean ( 17 / 20 )115.5846153846151.00349684461874115.181842378916
Trimmed Mean ( 18 / 20 )115.6541666666670.948300905561058121.959354871901
Trimmed Mean ( 19 / 20 )115.7272727272730.900773640989924128.475420972678
Trimmed Mean ( 20 / 20 )115.8150.8573605456651135.083192929243
Median115.2
Midrange108.15
Midmean - Weighted Average at Xnp115.274193548387
Midmean - Weighted Average at X(n+1)p115.646666666667
Midmean - Empirical Distribution Function115.274193548387
Midmean - Empirical Distribution Function - Averaging115.646666666667
Midmean - Empirical Distribution Function - Interpolation115.646666666667
Midmean - Closest Observation115.274193548387
Midmean - True Basic - Statistics Graphics Toolkit115.646666666667
Midmean - MS Excel (old versions)116.069696969697
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')