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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 14 Mar 2010 03:17:07 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Mar/14/t1268558280igvvqx1mnoygven.htm/, Retrieved Fri, 27 May 2022 00:51:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=74374, Retrieved Fri, 27 May 2022 00:51:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-03-14 09:17:07] [676a4f18bfa59791b951d67c8b4b8fd1] [Current]
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Dataseries X:
77
70
67
76
85
106
108
120
108
111
109
104
104
117
111
110
116
118
115
111
112
97
106
93
95
97
81
71
75
70
72
80
78
80
81
99
87
100
95
128
112
104
102
108
103
99
96
85
78
74
106
100
109
87
107
106
109
83
84
83
65
68
61
75
66
78
68
68
174
64
48
45




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74374&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=74374&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74374&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean92.43055555555562.4761638629321637.3281255490513
Geometric Mean90.0472883555268
Harmonic Mean87.5715615902422
Quadratic Mean94.756192996084
Winsorized Mean ( 1 / 24 )91.83333333333332.2401759097035840.9938045202372
Winsorized Mean ( 2 / 24 )91.97222222222222.1064187824222943.6628380784082
Winsorized Mean ( 3 / 24 )92.01388888888892.0663384806393744.5299208000122
Winsorized Mean ( 4 / 24 )92.01388888888892.0461702322984844.9688336954882
Winsorized Mean ( 5 / 24 )92.01388888888892.0216447168898145.5143716005884
Winsorized Mean ( 6 / 24 )92.01388888888891.9929936997266446.1686802630183
Winsorized Mean ( 7 / 24 )91.81944444444441.9307581996976947.5561592636618
Winsorized Mean ( 8 / 24 )91.81944444444441.9307581996976947.5561592636618
Winsorized Mean ( 9 / 24 )91.69444444444441.9126707569385647.9405271983201
Winsorized Mean ( 10 / 24 )91.97222222222221.8653806164895449.304802145583
Winsorized Mean ( 11 / 24 )91.97222222222221.8653806164895449.304802145583
Winsorized Mean ( 12 / 24 )91.97222222222221.8143460025984150.6916663582934
Winsorized Mean ( 13 / 24 )91.97222222222221.7602785806856252.2486742901793
Winsorized Mean ( 14 / 24 )92.36111111111111.6995932445762554.343067911016
Winsorized Mean ( 15 / 24 )92.56944444444441.6682886929731555.4876651950875
Winsorized Mean ( 16 / 24 )92.34722222222221.6379163117738656.3809161422968
Winsorized Mean ( 17 / 24 )92.58333333333331.6031012101011857.7526439066752
Winsorized Mean ( 18 / 24 )92.83333333333331.5670961353215059.2390800034024
Winsorized Mean ( 19 / 24 )92.83333333333331.4942508499257862.1270072143138
Winsorized Mean ( 20 / 24 )92.55555555555561.4576559646040963.4961594526141
Winsorized Mean ( 21 / 24 )92.55555555555561.4576559646040963.4961594526141
Winsorized Mean ( 22 / 24 )93.16666666666671.3733718486782067.8379033007955
Winsorized Mean ( 23 / 24 )93.16666666666671.3733718486782067.8379033007955
Winsorized Mean ( 24 / 24 )92.83333333333331.2423474675174274.7241297306638
Trimmed Mean ( 1 / 24 )91.94285714285712.1546699933499242.671433410511
Trimmed Mean ( 2 / 24 )92.05882352941182.0524169731058744.8538599786093
Trimmed Mean ( 3 / 24 )92.10606060606062.0166126816113745.6736494052311
Trimmed Mean ( 4 / 24 )92.1406251.9911594277745546.2748606237836
Trimmed Mean ( 5 / 24 )92.17741935483871.9668759093296746.8648880784012
Trimmed Mean ( 6 / 24 )92.21666666666671.9440030437926247.4364826542444
Trimmed Mean ( 7 / 24 )92.25862068965521.9228244036133547.9807831210608
Trimmed Mean ( 8 / 24 )92.33928571428571.9107142857142948.3271028037383
Trimmed Mean ( 9 / 24 )92.4259259259261.8938647960518648.8028111186216
Trimmed Mean ( 10 / 24 )92.53846153846151.8749482724813549.3552077658089
Trimmed Mean ( 11 / 24 )92.621.8597542080301149.8022801078132
Trimmed Mean ( 12 / 24 )92.70833333333331.8383132718824650.4311940469203
Trimmed Mean ( 13 / 24 )92.8043478260871.8195448720141151.0041545297858
Trimmed Mean ( 14 / 24 )92.90909090909091.8040412063548951.5005370064778
Trimmed Mean ( 15 / 24 )92.97619047619051.7938105273897651.8316673118669
Trimmed Mean ( 16 / 24 )93.0251.7832869033016552.1649095430297
Trimmed Mean ( 17 / 24 )93.10526315789471.7713499419665852.5617558405924
Trimmed Mean ( 18 / 24 )93.16666666666671.7586520812420952.9761785519654
Trimmed Mean ( 19 / 24 )93.20588235294121.7447550184615953.4206128463377
Trimmed Mean ( 20 / 24 )93.251.7372809678605053.6758312127481
Trimmed Mean ( 21 / 24 )93.33333333333331.7282861973864854.0034014473252
Trimmed Mean ( 22 / 24 )93.42857142857141.7069950789461854.7327713951289
Trimmed Mean ( 23 / 24 )93.46153846153851.6936358424596255.1839634698607
Trimmed Mean ( 24 / 24 )93.51.6626763827104756.2346352978067
Median95.5
Midrange109.5
Midmean - Weighted Average at Xnp93.4871794871795
Midmean - Weighted Average at X(n+1)p93.9473684210526
Midmean - Empirical Distribution Function93.4871794871795
Midmean - Empirical Distribution Function - Averaging93.9473684210526
Midmean - Empirical Distribution Function - Interpolation93.9473684210526
Midmean - Closest Observation93.4871794871795
Midmean - True Basic - Statistics Graphics Toolkit93.9473684210526
Midmean - MS Excel (old versions)93.4871794871795
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 92.4305555555556 & 2.47616386293216 & 37.3281255490513 \tabularnewline
Geometric Mean & 90.0472883555268 &  &  \tabularnewline
Harmonic Mean & 87.5715615902422 &  &  \tabularnewline
Quadratic Mean & 94.756192996084 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 91.8333333333333 & 2.24017590970358 & 40.9938045202372 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 91.9722222222222 & 2.10641878242229 & 43.6628380784082 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 92.0138888888889 & 2.06633848063937 & 44.5299208000122 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 92.0138888888889 & 2.04617023229848 & 44.9688336954882 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 92.0138888888889 & 2.02164471688981 & 45.5143716005884 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 92.0138888888889 & 1.99299369972664 & 46.1686802630183 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 91.8194444444444 & 1.93075819969769 & 47.5561592636618 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 91.8194444444444 & 1.93075819969769 & 47.5561592636618 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 91.6944444444444 & 1.91267075693856 & 47.9405271983201 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 91.9722222222222 & 1.86538061648954 & 49.304802145583 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 91.9722222222222 & 1.86538061648954 & 49.304802145583 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 91.9722222222222 & 1.81434600259841 & 50.6916663582934 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 91.9722222222222 & 1.76027858068562 & 52.2486742901793 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 92.3611111111111 & 1.69959324457625 & 54.343067911016 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 92.5694444444444 & 1.66828869297315 & 55.4876651950875 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 92.3472222222222 & 1.63791631177386 & 56.3809161422968 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 92.5833333333333 & 1.60310121010118 & 57.7526439066752 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 92.8333333333333 & 1.56709613532150 & 59.2390800034024 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 92.8333333333333 & 1.49425084992578 & 62.1270072143138 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 92.5555555555556 & 1.45765596460409 & 63.4961594526141 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 92.5555555555556 & 1.45765596460409 & 63.4961594526141 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 93.1666666666667 & 1.37337184867820 & 67.8379033007955 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 93.1666666666667 & 1.37337184867820 & 67.8379033007955 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 92.8333333333333 & 1.24234746751742 & 74.7241297306638 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 91.9428571428571 & 2.15466999334992 & 42.671433410511 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 92.0588235294118 & 2.05241697310587 & 44.8538599786093 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 92.1060606060606 & 2.01661268161137 & 45.6736494052311 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 92.140625 & 1.99115942777455 & 46.2748606237836 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 92.1774193548387 & 1.96687590932967 & 46.8648880784012 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 92.2166666666667 & 1.94400304379262 & 47.4364826542444 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 92.2586206896552 & 1.92282440361335 & 47.9807831210608 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 92.3392857142857 & 1.91071428571429 & 48.3271028037383 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 92.425925925926 & 1.89386479605186 & 48.8028111186216 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 92.5384615384615 & 1.87494827248135 & 49.3552077658089 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 92.62 & 1.85975420803011 & 49.8022801078132 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 92.7083333333333 & 1.83831327188246 & 50.4311940469203 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 92.804347826087 & 1.81954487201411 & 51.0041545297858 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 92.9090909090909 & 1.80404120635489 & 51.5005370064778 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 92.9761904761905 & 1.79381052738976 & 51.8316673118669 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 93.025 & 1.78328690330165 & 52.1649095430297 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 93.1052631578947 & 1.77134994196658 & 52.5617558405924 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 93.1666666666667 & 1.75865208124209 & 52.9761785519654 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 93.2058823529412 & 1.74475501846159 & 53.4206128463377 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 93.25 & 1.73728096786050 & 53.6758312127481 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 93.3333333333333 & 1.72828619738648 & 54.0034014473252 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 93.4285714285714 & 1.70699507894618 & 54.7327713951289 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 93.4615384615385 & 1.69363584245962 & 55.1839634698607 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 93.5 & 1.66267638271047 & 56.2346352978067 \tabularnewline
Median & 95.5 &  &  \tabularnewline
Midrange & 109.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 93.4871794871795 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 93.9473684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 93.4871794871795 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 93.9473684210526 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 93.9473684210526 &  &  \tabularnewline
Midmean - Closest Observation & 93.4871794871795 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 93.9473684210526 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 93.4871794871795 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=74374&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]92.4305555555556[/C][C]2.47616386293216[/C][C]37.3281255490513[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]90.0472883555268[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]87.5715615902422[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]94.756192996084[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]91.8333333333333[/C][C]2.24017590970358[/C][C]40.9938045202372[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]91.9722222222222[/C][C]2.10641878242229[/C][C]43.6628380784082[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]92.0138888888889[/C][C]2.06633848063937[/C][C]44.5299208000122[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]92.0138888888889[/C][C]2.04617023229848[/C][C]44.9688336954882[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]92.0138888888889[/C][C]2.02164471688981[/C][C]45.5143716005884[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]92.0138888888889[/C][C]1.99299369972664[/C][C]46.1686802630183[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]91.8194444444444[/C][C]1.93075819969769[/C][C]47.5561592636618[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]91.8194444444444[/C][C]1.93075819969769[/C][C]47.5561592636618[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]91.6944444444444[/C][C]1.91267075693856[/C][C]47.9405271983201[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]91.9722222222222[/C][C]1.86538061648954[/C][C]49.304802145583[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]91.9722222222222[/C][C]1.86538061648954[/C][C]49.304802145583[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]91.9722222222222[/C][C]1.81434600259841[/C][C]50.6916663582934[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]91.9722222222222[/C][C]1.76027858068562[/C][C]52.2486742901793[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]92.3611111111111[/C][C]1.69959324457625[/C][C]54.343067911016[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]92.5694444444444[/C][C]1.66828869297315[/C][C]55.4876651950875[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]92.3472222222222[/C][C]1.63791631177386[/C][C]56.3809161422968[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]92.5833333333333[/C][C]1.60310121010118[/C][C]57.7526439066752[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]92.8333333333333[/C][C]1.56709613532150[/C][C]59.2390800034024[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]92.8333333333333[/C][C]1.49425084992578[/C][C]62.1270072143138[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]92.5555555555556[/C][C]1.45765596460409[/C][C]63.4961594526141[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]92.5555555555556[/C][C]1.45765596460409[/C][C]63.4961594526141[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]93.1666666666667[/C][C]1.37337184867820[/C][C]67.8379033007955[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]93.1666666666667[/C][C]1.37337184867820[/C][C]67.8379033007955[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]92.8333333333333[/C][C]1.24234746751742[/C][C]74.7241297306638[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]91.9428571428571[/C][C]2.15466999334992[/C][C]42.671433410511[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]92.0588235294118[/C][C]2.05241697310587[/C][C]44.8538599786093[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]92.1060606060606[/C][C]2.01661268161137[/C][C]45.6736494052311[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]92.140625[/C][C]1.99115942777455[/C][C]46.2748606237836[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]92.1774193548387[/C][C]1.96687590932967[/C][C]46.8648880784012[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]92.2166666666667[/C][C]1.94400304379262[/C][C]47.4364826542444[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]92.2586206896552[/C][C]1.92282440361335[/C][C]47.9807831210608[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]92.3392857142857[/C][C]1.91071428571429[/C][C]48.3271028037383[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]92.425925925926[/C][C]1.89386479605186[/C][C]48.8028111186216[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]92.5384615384615[/C][C]1.87494827248135[/C][C]49.3552077658089[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]92.62[/C][C]1.85975420803011[/C][C]49.8022801078132[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]92.7083333333333[/C][C]1.83831327188246[/C][C]50.4311940469203[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]92.804347826087[/C][C]1.81954487201411[/C][C]51.0041545297858[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]92.9090909090909[/C][C]1.80404120635489[/C][C]51.5005370064778[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]92.9761904761905[/C][C]1.79381052738976[/C][C]51.8316673118669[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]93.025[/C][C]1.78328690330165[/C][C]52.1649095430297[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]93.1052631578947[/C][C]1.77134994196658[/C][C]52.5617558405924[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]93.1666666666667[/C][C]1.75865208124209[/C][C]52.9761785519654[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]93.2058823529412[/C][C]1.74475501846159[/C][C]53.4206128463377[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]93.25[/C][C]1.73728096786050[/C][C]53.6758312127481[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]93.3333333333333[/C][C]1.72828619738648[/C][C]54.0034014473252[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]93.4285714285714[/C][C]1.70699507894618[/C][C]54.7327713951289[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]93.4615384615385[/C][C]1.69363584245962[/C][C]55.1839634698607[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]93.5[/C][C]1.66267638271047[/C][C]56.2346352978067[/C][/ROW]
[ROW][C]Median[/C][C]95.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]93.4871794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]93.9473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]93.4871794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]93.9473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]93.9473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]93.4871794871795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]93.9473684210526[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]93.4871794871795[/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=74374&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=74374&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 Mean92.43055555555562.4761638629321637.3281255490513
Geometric Mean90.0472883555268
Harmonic Mean87.5715615902422
Quadratic Mean94.756192996084
Winsorized Mean ( 1 / 24 )91.83333333333332.2401759097035840.9938045202372
Winsorized Mean ( 2 / 24 )91.97222222222222.1064187824222943.6628380784082
Winsorized Mean ( 3 / 24 )92.01388888888892.0663384806393744.5299208000122
Winsorized Mean ( 4 / 24 )92.01388888888892.0461702322984844.9688336954882
Winsorized Mean ( 5 / 24 )92.01388888888892.0216447168898145.5143716005884
Winsorized Mean ( 6 / 24 )92.01388888888891.9929936997266446.1686802630183
Winsorized Mean ( 7 / 24 )91.81944444444441.9307581996976947.5561592636618
Winsorized Mean ( 8 / 24 )91.81944444444441.9307581996976947.5561592636618
Winsorized Mean ( 9 / 24 )91.69444444444441.9126707569385647.9405271983201
Winsorized Mean ( 10 / 24 )91.97222222222221.8653806164895449.304802145583
Winsorized Mean ( 11 / 24 )91.97222222222221.8653806164895449.304802145583
Winsorized Mean ( 12 / 24 )91.97222222222221.8143460025984150.6916663582934
Winsorized Mean ( 13 / 24 )91.97222222222221.7602785806856252.2486742901793
Winsorized Mean ( 14 / 24 )92.36111111111111.6995932445762554.343067911016
Winsorized Mean ( 15 / 24 )92.56944444444441.6682886929731555.4876651950875
Winsorized Mean ( 16 / 24 )92.34722222222221.6379163117738656.3809161422968
Winsorized Mean ( 17 / 24 )92.58333333333331.6031012101011857.7526439066752
Winsorized Mean ( 18 / 24 )92.83333333333331.5670961353215059.2390800034024
Winsorized Mean ( 19 / 24 )92.83333333333331.4942508499257862.1270072143138
Winsorized Mean ( 20 / 24 )92.55555555555561.4576559646040963.4961594526141
Winsorized Mean ( 21 / 24 )92.55555555555561.4576559646040963.4961594526141
Winsorized Mean ( 22 / 24 )93.16666666666671.3733718486782067.8379033007955
Winsorized Mean ( 23 / 24 )93.16666666666671.3733718486782067.8379033007955
Winsorized Mean ( 24 / 24 )92.83333333333331.2423474675174274.7241297306638
Trimmed Mean ( 1 / 24 )91.94285714285712.1546699933499242.671433410511
Trimmed Mean ( 2 / 24 )92.05882352941182.0524169731058744.8538599786093
Trimmed Mean ( 3 / 24 )92.10606060606062.0166126816113745.6736494052311
Trimmed Mean ( 4 / 24 )92.1406251.9911594277745546.2748606237836
Trimmed Mean ( 5 / 24 )92.17741935483871.9668759093296746.8648880784012
Trimmed Mean ( 6 / 24 )92.21666666666671.9440030437926247.4364826542444
Trimmed Mean ( 7 / 24 )92.25862068965521.9228244036133547.9807831210608
Trimmed Mean ( 8 / 24 )92.33928571428571.9107142857142948.3271028037383
Trimmed Mean ( 9 / 24 )92.4259259259261.8938647960518648.8028111186216
Trimmed Mean ( 10 / 24 )92.53846153846151.8749482724813549.3552077658089
Trimmed Mean ( 11 / 24 )92.621.8597542080301149.8022801078132
Trimmed Mean ( 12 / 24 )92.70833333333331.8383132718824650.4311940469203
Trimmed Mean ( 13 / 24 )92.8043478260871.8195448720141151.0041545297858
Trimmed Mean ( 14 / 24 )92.90909090909091.8040412063548951.5005370064778
Trimmed Mean ( 15 / 24 )92.97619047619051.7938105273897651.8316673118669
Trimmed Mean ( 16 / 24 )93.0251.7832869033016552.1649095430297
Trimmed Mean ( 17 / 24 )93.10526315789471.7713499419665852.5617558405924
Trimmed Mean ( 18 / 24 )93.16666666666671.7586520812420952.9761785519654
Trimmed Mean ( 19 / 24 )93.20588235294121.7447550184615953.4206128463377
Trimmed Mean ( 20 / 24 )93.251.7372809678605053.6758312127481
Trimmed Mean ( 21 / 24 )93.33333333333331.7282861973864854.0034014473252
Trimmed Mean ( 22 / 24 )93.42857142857141.7069950789461854.7327713951289
Trimmed Mean ( 23 / 24 )93.46153846153851.6936358424596255.1839634698607
Trimmed Mean ( 24 / 24 )93.51.6626763827104756.2346352978067
Median95.5
Midrange109.5
Midmean - Weighted Average at Xnp93.4871794871795
Midmean - Weighted Average at X(n+1)p93.9473684210526
Midmean - Empirical Distribution Function93.4871794871795
Midmean - Empirical Distribution Function - Averaging93.9473684210526
Midmean - Empirical Distribution Function - Interpolation93.9473684210526
Midmean - Closest Observation93.4871794871795
Midmean - True Basic - Statistics Graphics Toolkit93.9473684210526
Midmean - MS Excel (old versions)93.4871794871795
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')