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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 10 Oct 2014 13:31:41 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/10/t1412944403d201uv7u3g0vmr1.htm/, Retrieved Mon, 13 May 2024 04:53:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240281, Retrieved Mon, 13 May 2024 04:53:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact70
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-10 12:31:41] [c53b0bb515ebe5f6f1384250cc1174dd] [Current]
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Dataseries X:
246,78
247,91
247,99
248,6
248,68
248,75
248,75
249,03
249,05
249,57
249,35
249,46
249,46
250,82
254,19
255,18
256,68
256,73
256,73
257,39
257,78
258,67
258,71
258,91
258,91
261,38
262,42
262,77
263,24
262,83
262,83
263,09
263,6
265,68
266,08
266,28
266,28
269,14
270,96
272,97
273,13
274,73
274,73
274,59
275,15
275,16
275,38
275,4
275,4
275,71
275,21
279,04
279,1
279,11
279,11
279,02
279,3
279,34
279,36
279,39
279,39
280,21
283
284,33
285,15
284,21
284,21
284,17
286,28
286,95
287,12
287,34




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240281&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240281&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240281&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean267.268751.50710316002487177.339386638662
Geometric Mean266.965600825149
Harmonic Mean266.661281555025
Quadratic Mean267.570273539391
Winsorized Mean ( 1 / 24 )267.2813888888891.50360611530501177.760243303261
Winsorized Mean ( 2 / 24 )267.2788888888891.50232936708721177.909648006883
Winsorized Mean ( 3 / 24 )267.2763888888891.49271432647635179.05394498344
Winsorized Mean ( 4 / 24 )267.2180555555561.48094845258211180.437107780252
Winsorized Mean ( 5 / 24 )267.1659722222221.47055432869223181.677049946066
Winsorized Mean ( 6 / 24 )267.1559722222221.46891476580195181.873025203316
Winsorized Mean ( 7 / 24 )267.1831944444441.46413571137177182.485265791459
Winsorized Mean ( 8 / 24 )267.1809722222221.46302030403026182.622873712829
Winsorized Mean ( 9 / 24 )267.0722222222221.43306939133059186.363775430475
Winsorized Mean ( 10 / 24 )266.71.3731353838834194.227024611178
Winsorized Mean ( 11 / 24 )266.5747222222221.35611594946627196.572219600499
Winsorized Mean ( 12 / 24 )266.5930555555561.35286198455434197.058575523043
Winsorized Mean ( 13 / 24 )266.8133333333331.3127641548026203.245443865318
Winsorized Mean ( 14 / 24 )267.4647222222221.20494374787081221.972787273136
Winsorized Mean ( 15 / 24 )267.6626388888891.17230815744144228.321058068096
Winsorized Mean ( 16 / 24 )267.953751.11768474432445239.740008406356
Winsorized Mean ( 17 / 24 )267.9655555555561.11600915911442240.110534368906
Winsorized Mean ( 18 / 24 )267.9630555555561.11565760306667240.183955022571
Winsorized Mean ( 19 / 24 )268.1213888888891.08898736370452246.211662159965
Winsorized Mean ( 20 / 24 )268.2241666666671.07325871183027249.915666847236
Winsorized Mean ( 21 / 24 )267.5183333333330.907286018090682294.85556704192
Winsorized Mean ( 22 / 24 )267.4358333333330.893638002273841299.266406143035
Winsorized Mean ( 23 / 24 )267.4997222222220.884877160343502302.301533151089
Winsorized Mean ( 24 / 24 )267.4930555555560.884039151063913302.580553399288
Trimmed Mean ( 1 / 24 )267.2747142857141.49454117434023178.833958457988
Trimmed Mean ( 2 / 24 )267.2676470588241.4829817908508180.223148192191
Trimmed Mean ( 3 / 24 )267.2615151515151.46924091595309181.904487037882
Trimmed Mean ( 4 / 24 )267.25593751.4562683120783183.521082813776
Trimmed Mean ( 5 / 24 )267.2669354838711.44395218613681185.094034310738
Trimmed Mean ( 6 / 24 )267.2911666666671.43122974841551186.756296089136
Trimmed Mean ( 7 / 24 )267.3191379310351.41521148602619188.889887179794
Trimmed Mean ( 8 / 24 )267.3441071428571.39590146306839191.520758603689
Trimmed Mean ( 9 / 24 )267.3712962962961.37152852664164194.94402858028
Trimmed Mean ( 10 / 24 )267.4173076923081.34738272394303198.4716761914
Trimmed Mean ( 11 / 24 )267.52061.32909299777506201.280572877773
Trimmed Mean ( 12 / 24 )267.6495833333331.30805428965121204.616570925891
Trimmed Mean ( 13 / 24 )267.7873913043481.28055831855694209.117685171978
Trimmed Mean ( 14 / 24 )267.911.25331868122274213.760477693213
Trimmed Mean ( 15 / 24 )267.9645238095241.24122004544145215.888008571614
Trimmed Mean ( 16 / 24 )268.000751.23022055493397217.847725698571
Trimmed Mean ( 17 / 24 )268.0063157894741.22485940906895218.805777875514
Trimmed Mean ( 18 / 24 )268.0111111111111.21464167933225220.650349540491
Trimmed Mean ( 19 / 24 )268.0167647058821.19741199838067223.83003099045
Trimmed Mean ( 20 / 24 )268.0043751.17701174192316227.698981627913
Trimmed Mean ( 21 / 24 )267.9781.14889806276305233.247847381276
Trimmed Mean ( 22 / 24 )268.0342857142861.15117818972121232.834749743824
Trimmed Mean ( 23 / 24 )268.1096153846151.1505958965509233.018052809261
Trimmed Mean ( 24 / 24 )268.1891666666671.1441261326829234.405245195983
Median266.28
Midrange267.06
Midmean - Weighted Average at Xnp267.706216216216
Midmean - Weighted Average at X(n+1)p267.706216216216
Midmean - Empirical Distribution Function267.706216216216
Midmean - Empirical Distribution Function - Averaging267.706216216216
Midmean - Empirical Distribution Function - Interpolation267.706216216216
Midmean - Closest Observation267.706216216216
Midmean - True Basic - Statistics Graphics Toolkit267.706216216216
Midmean - MS Excel (old versions)268.291025641026
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 267.26875 & 1.50710316002487 & 177.339386638662 \tabularnewline
Geometric Mean & 266.965600825149 &  &  \tabularnewline
Harmonic Mean & 266.661281555025 &  &  \tabularnewline
Quadratic Mean & 267.570273539391 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 267.281388888889 & 1.50360611530501 & 177.760243303261 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 267.278888888889 & 1.50232936708721 & 177.909648006883 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 267.276388888889 & 1.49271432647635 & 179.05394498344 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 267.218055555556 & 1.48094845258211 & 180.437107780252 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 267.165972222222 & 1.47055432869223 & 181.677049946066 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 267.155972222222 & 1.46891476580195 & 181.873025203316 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 267.183194444444 & 1.46413571137177 & 182.485265791459 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 267.180972222222 & 1.46302030403026 & 182.622873712829 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 267.072222222222 & 1.43306939133059 & 186.363775430475 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 266.7 & 1.3731353838834 & 194.227024611178 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 266.574722222222 & 1.35611594946627 & 196.572219600499 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 266.593055555556 & 1.35286198455434 & 197.058575523043 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 266.813333333333 & 1.3127641548026 & 203.245443865318 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 267.464722222222 & 1.20494374787081 & 221.972787273136 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 267.662638888889 & 1.17230815744144 & 228.321058068096 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 267.95375 & 1.11768474432445 & 239.740008406356 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 267.965555555556 & 1.11600915911442 & 240.110534368906 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 267.963055555556 & 1.11565760306667 & 240.183955022571 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 268.121388888889 & 1.08898736370452 & 246.211662159965 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 268.224166666667 & 1.07325871183027 & 249.915666847236 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 267.518333333333 & 0.907286018090682 & 294.85556704192 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 267.435833333333 & 0.893638002273841 & 299.266406143035 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 267.499722222222 & 0.884877160343502 & 302.301533151089 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 267.493055555556 & 0.884039151063913 & 302.580553399288 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 267.274714285714 & 1.49454117434023 & 178.833958457988 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 267.267647058824 & 1.4829817908508 & 180.223148192191 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 267.261515151515 & 1.46924091595309 & 181.904487037882 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 267.2559375 & 1.4562683120783 & 183.521082813776 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 267.266935483871 & 1.44395218613681 & 185.094034310738 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 267.291166666667 & 1.43122974841551 & 186.756296089136 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 267.319137931035 & 1.41521148602619 & 188.889887179794 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 267.344107142857 & 1.39590146306839 & 191.520758603689 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 267.371296296296 & 1.37152852664164 & 194.94402858028 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 267.417307692308 & 1.34738272394303 & 198.4716761914 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 267.5206 & 1.32909299777506 & 201.280572877773 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 267.649583333333 & 1.30805428965121 & 204.616570925891 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 267.787391304348 & 1.28055831855694 & 209.117685171978 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 267.91 & 1.25331868122274 & 213.760477693213 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 267.964523809524 & 1.24122004544145 & 215.888008571614 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 268.00075 & 1.23022055493397 & 217.847725698571 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 268.006315789474 & 1.22485940906895 & 218.805777875514 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 268.011111111111 & 1.21464167933225 & 220.650349540491 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 268.016764705882 & 1.19741199838067 & 223.83003099045 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 268.004375 & 1.17701174192316 & 227.698981627913 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 267.978 & 1.14889806276305 & 233.247847381276 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 268.034285714286 & 1.15117818972121 & 232.834749743824 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 268.109615384615 & 1.1505958965509 & 233.018052809261 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 268.189166666667 & 1.1441261326829 & 234.405245195983 \tabularnewline
Median & 266.28 &  &  \tabularnewline
Midrange & 267.06 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 267.706216216216 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 267.706216216216 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 267.706216216216 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 267.706216216216 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 267.706216216216 &  &  \tabularnewline
Midmean - Closest Observation & 267.706216216216 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 267.706216216216 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 268.291025641026 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240281&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]267.26875[/C][C]1.50710316002487[/C][C]177.339386638662[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]266.965600825149[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]266.661281555025[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]267.570273539391[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]267.281388888889[/C][C]1.50360611530501[/C][C]177.760243303261[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]267.278888888889[/C][C]1.50232936708721[/C][C]177.909648006883[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]267.276388888889[/C][C]1.49271432647635[/C][C]179.05394498344[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]267.218055555556[/C][C]1.48094845258211[/C][C]180.437107780252[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]267.165972222222[/C][C]1.47055432869223[/C][C]181.677049946066[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]267.155972222222[/C][C]1.46891476580195[/C][C]181.873025203316[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]267.183194444444[/C][C]1.46413571137177[/C][C]182.485265791459[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]267.180972222222[/C][C]1.46302030403026[/C][C]182.622873712829[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]267.072222222222[/C][C]1.43306939133059[/C][C]186.363775430475[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]266.7[/C][C]1.3731353838834[/C][C]194.227024611178[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]266.574722222222[/C][C]1.35611594946627[/C][C]196.572219600499[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]266.593055555556[/C][C]1.35286198455434[/C][C]197.058575523043[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]266.813333333333[/C][C]1.3127641548026[/C][C]203.245443865318[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]267.464722222222[/C][C]1.20494374787081[/C][C]221.972787273136[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]267.662638888889[/C][C]1.17230815744144[/C][C]228.321058068096[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]267.95375[/C][C]1.11768474432445[/C][C]239.740008406356[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]267.965555555556[/C][C]1.11600915911442[/C][C]240.110534368906[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]267.963055555556[/C][C]1.11565760306667[/C][C]240.183955022571[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]268.121388888889[/C][C]1.08898736370452[/C][C]246.211662159965[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]268.224166666667[/C][C]1.07325871183027[/C][C]249.915666847236[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]267.518333333333[/C][C]0.907286018090682[/C][C]294.85556704192[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]267.435833333333[/C][C]0.893638002273841[/C][C]299.266406143035[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]267.499722222222[/C][C]0.884877160343502[/C][C]302.301533151089[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]267.493055555556[/C][C]0.884039151063913[/C][C]302.580553399288[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]267.274714285714[/C][C]1.49454117434023[/C][C]178.833958457988[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]267.267647058824[/C][C]1.4829817908508[/C][C]180.223148192191[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]267.261515151515[/C][C]1.46924091595309[/C][C]181.904487037882[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]267.2559375[/C][C]1.4562683120783[/C][C]183.521082813776[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]267.266935483871[/C][C]1.44395218613681[/C][C]185.094034310738[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]267.291166666667[/C][C]1.43122974841551[/C][C]186.756296089136[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]267.319137931035[/C][C]1.41521148602619[/C][C]188.889887179794[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]267.344107142857[/C][C]1.39590146306839[/C][C]191.520758603689[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]267.371296296296[/C][C]1.37152852664164[/C][C]194.94402858028[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]267.417307692308[/C][C]1.34738272394303[/C][C]198.4716761914[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]267.5206[/C][C]1.32909299777506[/C][C]201.280572877773[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]267.649583333333[/C][C]1.30805428965121[/C][C]204.616570925891[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]267.787391304348[/C][C]1.28055831855694[/C][C]209.117685171978[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]267.91[/C][C]1.25331868122274[/C][C]213.760477693213[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]267.964523809524[/C][C]1.24122004544145[/C][C]215.888008571614[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]268.00075[/C][C]1.23022055493397[/C][C]217.847725698571[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]268.006315789474[/C][C]1.22485940906895[/C][C]218.805777875514[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]268.011111111111[/C][C]1.21464167933225[/C][C]220.650349540491[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]268.016764705882[/C][C]1.19741199838067[/C][C]223.83003099045[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]268.004375[/C][C]1.17701174192316[/C][C]227.698981627913[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]267.978[/C][C]1.14889806276305[/C][C]233.247847381276[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]268.034285714286[/C][C]1.15117818972121[/C][C]232.834749743824[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]268.109615384615[/C][C]1.1505958965509[/C][C]233.018052809261[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]268.189166666667[/C][C]1.1441261326829[/C][C]234.405245195983[/C][/ROW]
[ROW][C]Median[/C][C]266.28[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]267.06[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]267.706216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]267.706216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]267.706216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]267.706216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]267.706216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]267.706216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]267.706216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]268.291025641026[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240281&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240281&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 Mean267.268751.50710316002487177.339386638662
Geometric Mean266.965600825149
Harmonic Mean266.661281555025
Quadratic Mean267.570273539391
Winsorized Mean ( 1 / 24 )267.2813888888891.50360611530501177.760243303261
Winsorized Mean ( 2 / 24 )267.2788888888891.50232936708721177.909648006883
Winsorized Mean ( 3 / 24 )267.2763888888891.49271432647635179.05394498344
Winsorized Mean ( 4 / 24 )267.2180555555561.48094845258211180.437107780252
Winsorized Mean ( 5 / 24 )267.1659722222221.47055432869223181.677049946066
Winsorized Mean ( 6 / 24 )267.1559722222221.46891476580195181.873025203316
Winsorized Mean ( 7 / 24 )267.1831944444441.46413571137177182.485265791459
Winsorized Mean ( 8 / 24 )267.1809722222221.46302030403026182.622873712829
Winsorized Mean ( 9 / 24 )267.0722222222221.43306939133059186.363775430475
Winsorized Mean ( 10 / 24 )266.71.3731353838834194.227024611178
Winsorized Mean ( 11 / 24 )266.5747222222221.35611594946627196.572219600499
Winsorized Mean ( 12 / 24 )266.5930555555561.35286198455434197.058575523043
Winsorized Mean ( 13 / 24 )266.8133333333331.3127641548026203.245443865318
Winsorized Mean ( 14 / 24 )267.4647222222221.20494374787081221.972787273136
Winsorized Mean ( 15 / 24 )267.6626388888891.17230815744144228.321058068096
Winsorized Mean ( 16 / 24 )267.953751.11768474432445239.740008406356
Winsorized Mean ( 17 / 24 )267.9655555555561.11600915911442240.110534368906
Winsorized Mean ( 18 / 24 )267.9630555555561.11565760306667240.183955022571
Winsorized Mean ( 19 / 24 )268.1213888888891.08898736370452246.211662159965
Winsorized Mean ( 20 / 24 )268.2241666666671.07325871183027249.915666847236
Winsorized Mean ( 21 / 24 )267.5183333333330.907286018090682294.85556704192
Winsorized Mean ( 22 / 24 )267.4358333333330.893638002273841299.266406143035
Winsorized Mean ( 23 / 24 )267.4997222222220.884877160343502302.301533151089
Winsorized Mean ( 24 / 24 )267.4930555555560.884039151063913302.580553399288
Trimmed Mean ( 1 / 24 )267.2747142857141.49454117434023178.833958457988
Trimmed Mean ( 2 / 24 )267.2676470588241.4829817908508180.223148192191
Trimmed Mean ( 3 / 24 )267.2615151515151.46924091595309181.904487037882
Trimmed Mean ( 4 / 24 )267.25593751.4562683120783183.521082813776
Trimmed Mean ( 5 / 24 )267.2669354838711.44395218613681185.094034310738
Trimmed Mean ( 6 / 24 )267.2911666666671.43122974841551186.756296089136
Trimmed Mean ( 7 / 24 )267.3191379310351.41521148602619188.889887179794
Trimmed Mean ( 8 / 24 )267.3441071428571.39590146306839191.520758603689
Trimmed Mean ( 9 / 24 )267.3712962962961.37152852664164194.94402858028
Trimmed Mean ( 10 / 24 )267.4173076923081.34738272394303198.4716761914
Trimmed Mean ( 11 / 24 )267.52061.32909299777506201.280572877773
Trimmed Mean ( 12 / 24 )267.6495833333331.30805428965121204.616570925891
Trimmed Mean ( 13 / 24 )267.7873913043481.28055831855694209.117685171978
Trimmed Mean ( 14 / 24 )267.911.25331868122274213.760477693213
Trimmed Mean ( 15 / 24 )267.9645238095241.24122004544145215.888008571614
Trimmed Mean ( 16 / 24 )268.000751.23022055493397217.847725698571
Trimmed Mean ( 17 / 24 )268.0063157894741.22485940906895218.805777875514
Trimmed Mean ( 18 / 24 )268.0111111111111.21464167933225220.650349540491
Trimmed Mean ( 19 / 24 )268.0167647058821.19741199838067223.83003099045
Trimmed Mean ( 20 / 24 )268.0043751.17701174192316227.698981627913
Trimmed Mean ( 21 / 24 )267.9781.14889806276305233.247847381276
Trimmed Mean ( 22 / 24 )268.0342857142861.15117818972121232.834749743824
Trimmed Mean ( 23 / 24 )268.1096153846151.1505958965509233.018052809261
Trimmed Mean ( 24 / 24 )268.1891666666671.1441261326829234.405245195983
Median266.28
Midrange267.06
Midmean - Weighted Average at Xnp267.706216216216
Midmean - Weighted Average at X(n+1)p267.706216216216
Midmean - Empirical Distribution Function267.706216216216
Midmean - Empirical Distribution Function - Averaging267.706216216216
Midmean - Empirical Distribution Function - Interpolation267.706216216216
Midmean - Closest Observation267.706216216216
Midmean - True Basic - Statistics Graphics Toolkit267.706216216216
Midmean - MS Excel (old versions)268.291025641026
Number of observations72



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')