Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Nov 2007 12:58:20 -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/20/t1195588267ecbmnt3py5qd8i7.htm/, Retrieved Sun, 05 May 2024 16:52:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5812, Retrieved Sun, 05 May 2024 16:52:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsNiet-duurzame consumptiegoederen
Estimated Impact244
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency] [2007-11-20 19:58:20] [6dd0685065b0babfa744248f2bd1b94f] [Current]
Feedback Forum

Post a new message
Dataseries X:
125
121,7
134,3
124,3
119,1
137,8
120,5
122,7
127,2
133,2
136,3
134,9
120,9
109,4
129,6
124,7
114,6
137,4
117,9
117,4
122
124,8
123,3
132,8
115,1
104,2
125,5
116,8
116,8
125,5
110,9
114,9
136,4
125,8
126,5
134
116,1
115
130,3
106,5
111,6
125
108,3
105
127,4
116,6
128,6
127,5
108,4
110,8
114,2
101,8
109,8
115,9
106,9
114,6
105,4
108,1
118,4
112,7
98,4
99,6
103,9
101,5
100,8
104,5
98,2
99,9
97,5
105,7
117,7
107,4
98,4
92
107,7
100,2
96,7
106,8
98
98,6




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5812&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5812&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5812&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean115.53251.3233943878134887.300128415146
Geometric Mean114.932164347723
Harmonic Mean114.331813929533
Quadratic Mean116.129742099085
Winsorized Mean ( 1 / 26 )115.586251.3103576472726188.2096962158246
Winsorized Mean ( 2 / 26 )115.581251.3016093905384988.798721675005
Winsorized Mean ( 3 / 26 )115.596251.2975932489479189.0851197736468
Winsorized Mean ( 4 / 26 )115.536251.2821168262568390.1136679855538
Winsorized Mean ( 5 / 26 )115.511251.2728953760813890.7468533318128
Winsorized Mean ( 6 / 26 )115.488751.2687155791302791.0280853327033
Winsorized Mean ( 7 / 26 )115.436251.2529891396253192.1286915818913
Winsorized Mean ( 8 / 26 )115.496251.2291430118227393.9648591653523
Winsorized Mean ( 9 / 26 )115.248751.1756939692519798.0261471217097
Winsorized Mean ( 10 / 26 )115.198751.1555212722409299.6941837138088
Winsorized Mean ( 11 / 26 )115.143751.12075901573923102.737295335567
Winsorized Mean ( 12 / 26 )115.083751.07932592030713106.625577904450
Winsorized Mean ( 13 / 26 )115.116251.06923526994764107.662226673122
Winsorized Mean ( 14 / 26 )115.448751.00843749570966114.482801850556
Winsorized Mean ( 15 / 26 )115.373750.981202671599076117.584015351257
Winsorized Mean ( 16 / 26 )115.293750.95275307902342121.011154451662
Winsorized Mean ( 17 / 26 )115.336250.928784157846746124.179820494991
Winsorized Mean ( 18 / 26 )115.426250.916210798373912125.982197770271
Winsorized Mean ( 19 / 26 )115.378750.889980610210488129.641869357931
Winsorized Mean ( 20 / 26 )115.578750.862889416309228133.943872546677
Winsorized Mean ( 21 / 26 )115.6050.84520969609899136.776708234143
Winsorized Mean ( 22 / 26 )115.6050.837805111623993137.985551050068
Winsorized Mean ( 23 / 26 )115.633750.803268528154056143.954040208361
Winsorized Mean ( 24 / 26 )115.423750.751159954796495153.660680741788
Winsorized Mean ( 25 / 26 )115.361250.710224812308742162.429202698499
Winsorized Mean ( 26 / 26 )115.198750.672345916068827171.338513772139
Trimmed Mean ( 1 / 26 )115.5487179487181.2915769331808489.4632870719901
Trimmed Mean ( 2 / 26 )115.5092105263161.2694910952080690.988594533926
Trimmed Mean ( 3 / 26 )115.4702702702701.2488643189373692.4602204733673
Trimmed Mean ( 4 / 26 )115.4236111111111.2261855000362194.1322590323428
Trimmed Mean ( 5 / 26 )115.3914285714291.2047176810024295.7829625903838
Trimmed Mean ( 6 / 26 )115.3632352941181.1818515413954897.6122899140965
Trimmed Mean ( 7 / 26 )115.3378787878791.1555657655315999.8107439906899
Trimmed Mean ( 8 / 26 )115.32031251.12790009726140102.243374905281
Trimmed Mean ( 9 / 26 )115.2919354838711.10004879077193104.806201734896
Trimmed Mean ( 10 / 26 )115.2983333333331.07809072620813106.946781500349
Trimmed Mean ( 11 / 26 )115.3120689655171.05532979562458109.266382360854
Trimmed Mean ( 12 / 26 )115.3339285714291.03427707604737111.511635752571
Trimmed Mean ( 13 / 26 )115.3648148148151.01617305062419113.528709252771
Trimmed Mean ( 14 / 26 )115.3942307692310.995167105356305115.954627266258
Trimmed Mean ( 15 / 26 )115.3880.980406579549775117.694028586578
Trimmed Mean ( 16 / 26 )115.3895833333330.966248868428197119.420148476902
Trimmed Mean ( 17 / 26 )115.40.952829500997431121.112958697436
Trimmed Mean ( 18 / 26 )115.4068181818180.939262213990742122.869648605875
Trimmed Mean ( 19 / 26 )115.4047619047620.923036902866225125.027245981613
Trimmed Mean ( 20 / 26 )115.40750.906135691287812127.36227157765
Trimmed Mean ( 21 / 26 )115.3894736842110.888329497146462129.894902797746
Trimmed Mean ( 22 / 26 )115.3666666666670.86701458218088133.061968088789
Trimmed Mean ( 23 / 26 )115.3411764705880.838225755957867137.601565748578
Trimmed Mean ( 24 / 26 )115.3093750.806342791296985143.002921641461
Trimmed Mean ( 25 / 26 )115.2966666666670.775508484777366148.672347150098
Trimmed Mean ( 26 / 26 )115.2892857142860.742356809019223155.301715177371
Median115.5
Midrange114.9
Midmean - Weighted Average at Xnp115.404761904762
Midmean - Weighted Average at X(n+1)p115.641463414634
Midmean - Empirical Distribution Function115.404761904762
Midmean - Empirical Distribution Function - Averaging115.641463414634
Midmean - Empirical Distribution Function - Interpolation115.641463414634
Midmean - Closest Observation115.404761904762
Midmean - True Basic - Statistics Graphics Toolkit115.641463414634
Midmean - MS Excel (old versions)115.404761904762
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 115.5325 & 1.32339438781348 & 87.300128415146 \tabularnewline
Geometric Mean & 114.932164347723 &  &  \tabularnewline
Harmonic Mean & 114.331813929533 &  &  \tabularnewline
Quadratic Mean & 116.129742099085 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 115.58625 & 1.31035764727261 & 88.2096962158246 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 115.58125 & 1.30160939053849 & 88.798721675005 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 115.59625 & 1.29759324894791 & 89.0851197736468 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 115.53625 & 1.28211682625683 & 90.1136679855538 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 115.51125 & 1.27289537608138 & 90.7468533318128 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 115.48875 & 1.26871557913027 & 91.0280853327033 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 115.43625 & 1.25298913962531 & 92.1286915818913 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 115.49625 & 1.22914301182273 & 93.9648591653523 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 115.24875 & 1.17569396925197 & 98.0261471217097 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 115.19875 & 1.15552127224092 & 99.6941837138088 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 115.14375 & 1.12075901573923 & 102.737295335567 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 115.08375 & 1.07932592030713 & 106.625577904450 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 115.11625 & 1.06923526994764 & 107.662226673122 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 115.44875 & 1.00843749570966 & 114.482801850556 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 115.37375 & 0.981202671599076 & 117.584015351257 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 115.29375 & 0.95275307902342 & 121.011154451662 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 115.33625 & 0.928784157846746 & 124.179820494991 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 115.42625 & 0.916210798373912 & 125.982197770271 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 115.37875 & 0.889980610210488 & 129.641869357931 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 115.57875 & 0.862889416309228 & 133.943872546677 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 115.605 & 0.84520969609899 & 136.776708234143 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 115.605 & 0.837805111623993 & 137.985551050068 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 115.63375 & 0.803268528154056 & 143.954040208361 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 115.42375 & 0.751159954796495 & 153.660680741788 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 115.36125 & 0.710224812308742 & 162.429202698499 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 115.19875 & 0.672345916068827 & 171.338513772139 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 115.548717948718 & 1.29157693318084 & 89.4632870719901 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 115.509210526316 & 1.26949109520806 & 90.988594533926 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 115.470270270270 & 1.24886431893736 & 92.4602204733673 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 115.423611111111 & 1.22618550003621 & 94.1322590323428 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 115.391428571429 & 1.20471768100242 & 95.7829625903838 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 115.363235294118 & 1.18185154139548 & 97.6122899140965 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 115.337878787879 & 1.15556576553159 & 99.8107439906899 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 115.3203125 & 1.12790009726140 & 102.243374905281 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 115.291935483871 & 1.10004879077193 & 104.806201734896 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 115.298333333333 & 1.07809072620813 & 106.946781500349 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 115.312068965517 & 1.05532979562458 & 109.266382360854 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 115.333928571429 & 1.03427707604737 & 111.511635752571 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 115.364814814815 & 1.01617305062419 & 113.528709252771 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 115.394230769231 & 0.995167105356305 & 115.954627266258 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 115.388 & 0.980406579549775 & 117.694028586578 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 115.389583333333 & 0.966248868428197 & 119.420148476902 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 115.4 & 0.952829500997431 & 121.112958697436 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 115.406818181818 & 0.939262213990742 & 122.869648605875 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 115.404761904762 & 0.923036902866225 & 125.027245981613 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 115.4075 & 0.906135691287812 & 127.36227157765 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 115.389473684211 & 0.888329497146462 & 129.894902797746 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 115.366666666667 & 0.86701458218088 & 133.061968088789 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 115.341176470588 & 0.838225755957867 & 137.601565748578 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 115.309375 & 0.806342791296985 & 143.002921641461 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 115.296666666667 & 0.775508484777366 & 148.672347150098 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 115.289285714286 & 0.742356809019223 & 155.301715177371 \tabularnewline
Median & 115.5 &  &  \tabularnewline
Midrange & 114.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 115.404761904762 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 115.641463414634 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 115.404761904762 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 115.641463414634 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 115.641463414634 &  &  \tabularnewline
Midmean - Closest Observation & 115.404761904762 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 115.641463414634 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 115.404761904762 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5812&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]115.5325[/C][C]1.32339438781348[/C][C]87.300128415146[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]114.932164347723[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]114.331813929533[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]116.129742099085[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]115.58625[/C][C]1.31035764727261[/C][C]88.2096962158246[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]115.58125[/C][C]1.30160939053849[/C][C]88.798721675005[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]115.59625[/C][C]1.29759324894791[/C][C]89.0851197736468[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]115.53625[/C][C]1.28211682625683[/C][C]90.1136679855538[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]115.51125[/C][C]1.27289537608138[/C][C]90.7468533318128[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]115.48875[/C][C]1.26871557913027[/C][C]91.0280853327033[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]115.43625[/C][C]1.25298913962531[/C][C]92.1286915818913[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]115.49625[/C][C]1.22914301182273[/C][C]93.9648591653523[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]115.24875[/C][C]1.17569396925197[/C][C]98.0261471217097[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]115.19875[/C][C]1.15552127224092[/C][C]99.6941837138088[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]115.14375[/C][C]1.12075901573923[/C][C]102.737295335567[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]115.08375[/C][C]1.07932592030713[/C][C]106.625577904450[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]115.11625[/C][C]1.06923526994764[/C][C]107.662226673122[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]115.44875[/C][C]1.00843749570966[/C][C]114.482801850556[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]115.37375[/C][C]0.981202671599076[/C][C]117.584015351257[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]115.29375[/C][C]0.95275307902342[/C][C]121.011154451662[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]115.33625[/C][C]0.928784157846746[/C][C]124.179820494991[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]115.42625[/C][C]0.916210798373912[/C][C]125.982197770271[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]115.37875[/C][C]0.889980610210488[/C][C]129.641869357931[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]115.57875[/C][C]0.862889416309228[/C][C]133.943872546677[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]115.605[/C][C]0.84520969609899[/C][C]136.776708234143[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]115.605[/C][C]0.837805111623993[/C][C]137.985551050068[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]115.63375[/C][C]0.803268528154056[/C][C]143.954040208361[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]115.42375[/C][C]0.751159954796495[/C][C]153.660680741788[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]115.36125[/C][C]0.710224812308742[/C][C]162.429202698499[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]115.19875[/C][C]0.672345916068827[/C][C]171.338513772139[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]115.548717948718[/C][C]1.29157693318084[/C][C]89.4632870719901[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]115.509210526316[/C][C]1.26949109520806[/C][C]90.988594533926[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]115.470270270270[/C][C]1.24886431893736[/C][C]92.4602204733673[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]115.423611111111[/C][C]1.22618550003621[/C][C]94.1322590323428[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]115.391428571429[/C][C]1.20471768100242[/C][C]95.7829625903838[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]115.363235294118[/C][C]1.18185154139548[/C][C]97.6122899140965[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]115.337878787879[/C][C]1.15556576553159[/C][C]99.8107439906899[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]115.3203125[/C][C]1.12790009726140[/C][C]102.243374905281[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]115.291935483871[/C][C]1.10004879077193[/C][C]104.806201734896[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]115.298333333333[/C][C]1.07809072620813[/C][C]106.946781500349[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]115.312068965517[/C][C]1.05532979562458[/C][C]109.266382360854[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]115.333928571429[/C][C]1.03427707604737[/C][C]111.511635752571[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]115.364814814815[/C][C]1.01617305062419[/C][C]113.528709252771[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]115.394230769231[/C][C]0.995167105356305[/C][C]115.954627266258[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]115.388[/C][C]0.980406579549775[/C][C]117.694028586578[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]115.389583333333[/C][C]0.966248868428197[/C][C]119.420148476902[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]115.4[/C][C]0.952829500997431[/C][C]121.112958697436[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]115.406818181818[/C][C]0.939262213990742[/C][C]122.869648605875[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]115.404761904762[/C][C]0.923036902866225[/C][C]125.027245981613[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]115.4075[/C][C]0.906135691287812[/C][C]127.36227157765[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]115.389473684211[/C][C]0.888329497146462[/C][C]129.894902797746[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]115.366666666667[/C][C]0.86701458218088[/C][C]133.061968088789[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]115.341176470588[/C][C]0.838225755957867[/C][C]137.601565748578[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]115.309375[/C][C]0.806342791296985[/C][C]143.002921641461[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]115.296666666667[/C][C]0.775508484777366[/C][C]148.672347150098[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]115.289285714286[/C][C]0.742356809019223[/C][C]155.301715177371[/C][/ROW]
[ROW][C]Median[/C][C]115.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]114.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]115.404761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]115.641463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]115.404761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]115.641463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]115.641463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]115.404761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]115.641463414634[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]115.404761904762[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5812&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5812&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 Mean115.53251.3233943878134887.300128415146
Geometric Mean114.932164347723
Harmonic Mean114.331813929533
Quadratic Mean116.129742099085
Winsorized Mean ( 1 / 26 )115.586251.3103576472726188.2096962158246
Winsorized Mean ( 2 / 26 )115.581251.3016093905384988.798721675005
Winsorized Mean ( 3 / 26 )115.596251.2975932489479189.0851197736468
Winsorized Mean ( 4 / 26 )115.536251.2821168262568390.1136679855538
Winsorized Mean ( 5 / 26 )115.511251.2728953760813890.7468533318128
Winsorized Mean ( 6 / 26 )115.488751.2687155791302791.0280853327033
Winsorized Mean ( 7 / 26 )115.436251.2529891396253192.1286915818913
Winsorized Mean ( 8 / 26 )115.496251.2291430118227393.9648591653523
Winsorized Mean ( 9 / 26 )115.248751.1756939692519798.0261471217097
Winsorized Mean ( 10 / 26 )115.198751.1555212722409299.6941837138088
Winsorized Mean ( 11 / 26 )115.143751.12075901573923102.737295335567
Winsorized Mean ( 12 / 26 )115.083751.07932592030713106.625577904450
Winsorized Mean ( 13 / 26 )115.116251.06923526994764107.662226673122
Winsorized Mean ( 14 / 26 )115.448751.00843749570966114.482801850556
Winsorized Mean ( 15 / 26 )115.373750.981202671599076117.584015351257
Winsorized Mean ( 16 / 26 )115.293750.95275307902342121.011154451662
Winsorized Mean ( 17 / 26 )115.336250.928784157846746124.179820494991
Winsorized Mean ( 18 / 26 )115.426250.916210798373912125.982197770271
Winsorized Mean ( 19 / 26 )115.378750.889980610210488129.641869357931
Winsorized Mean ( 20 / 26 )115.578750.862889416309228133.943872546677
Winsorized Mean ( 21 / 26 )115.6050.84520969609899136.776708234143
Winsorized Mean ( 22 / 26 )115.6050.837805111623993137.985551050068
Winsorized Mean ( 23 / 26 )115.633750.803268528154056143.954040208361
Winsorized Mean ( 24 / 26 )115.423750.751159954796495153.660680741788
Winsorized Mean ( 25 / 26 )115.361250.710224812308742162.429202698499
Winsorized Mean ( 26 / 26 )115.198750.672345916068827171.338513772139
Trimmed Mean ( 1 / 26 )115.5487179487181.2915769331808489.4632870719901
Trimmed Mean ( 2 / 26 )115.5092105263161.2694910952080690.988594533926
Trimmed Mean ( 3 / 26 )115.4702702702701.2488643189373692.4602204733673
Trimmed Mean ( 4 / 26 )115.4236111111111.2261855000362194.1322590323428
Trimmed Mean ( 5 / 26 )115.3914285714291.2047176810024295.7829625903838
Trimmed Mean ( 6 / 26 )115.3632352941181.1818515413954897.6122899140965
Trimmed Mean ( 7 / 26 )115.3378787878791.1555657655315999.8107439906899
Trimmed Mean ( 8 / 26 )115.32031251.12790009726140102.243374905281
Trimmed Mean ( 9 / 26 )115.2919354838711.10004879077193104.806201734896
Trimmed Mean ( 10 / 26 )115.2983333333331.07809072620813106.946781500349
Trimmed Mean ( 11 / 26 )115.3120689655171.05532979562458109.266382360854
Trimmed Mean ( 12 / 26 )115.3339285714291.03427707604737111.511635752571
Trimmed Mean ( 13 / 26 )115.3648148148151.01617305062419113.528709252771
Trimmed Mean ( 14 / 26 )115.3942307692310.995167105356305115.954627266258
Trimmed Mean ( 15 / 26 )115.3880.980406579549775117.694028586578
Trimmed Mean ( 16 / 26 )115.3895833333330.966248868428197119.420148476902
Trimmed Mean ( 17 / 26 )115.40.952829500997431121.112958697436
Trimmed Mean ( 18 / 26 )115.4068181818180.939262213990742122.869648605875
Trimmed Mean ( 19 / 26 )115.4047619047620.923036902866225125.027245981613
Trimmed Mean ( 20 / 26 )115.40750.906135691287812127.36227157765
Trimmed Mean ( 21 / 26 )115.3894736842110.888329497146462129.894902797746
Trimmed Mean ( 22 / 26 )115.3666666666670.86701458218088133.061968088789
Trimmed Mean ( 23 / 26 )115.3411764705880.838225755957867137.601565748578
Trimmed Mean ( 24 / 26 )115.3093750.806342791296985143.002921641461
Trimmed Mean ( 25 / 26 )115.2966666666670.775508484777366148.672347150098
Trimmed Mean ( 26 / 26 )115.2892857142860.742356809019223155.301715177371
Median115.5
Midrange114.9
Midmean - Weighted Average at Xnp115.404761904762
Midmean - Weighted Average at X(n+1)p115.641463414634
Midmean - Empirical Distribution Function115.404761904762
Midmean - Empirical Distribution Function - Averaging115.641463414634
Midmean - Empirical Distribution Function - Interpolation115.641463414634
Midmean - Closest Observation115.404761904762
Midmean - True Basic - Statistics Graphics Toolkit115.641463414634
Midmean - MS Excel (old versions)115.404761904762
Number of observations80



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')