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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 23 Dec 2012 15:18:00 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/23/t135629427949rfiyg3marnvc3.htm/, Retrieved Tue, 07 Feb 2023 17:35:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204698, Retrieved Tue, 07 Feb 2023 17:35:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact110
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [gemiddelde prijze...] [2012-12-23 20:18:00] [d0e7cd87186a15776b36563906a5538f] [Current]
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Dataseries X:
86,86
86,79
82,52
86,87
81,62
82,66
89,87
92,04
79,74
77,75
79,12
76,37
75,01
77,6
77,81
81,7
76,47
74,72
84,43
86,72
70,99
75,43
74,14
73,3
71,97
69,27
74,13
76,4
72,26
72,1
87,82
91,62
82,69
85,76
86,87
93,09
83,73
84,49
87,37
89,13
83,2
83,77
93,68
93,09
88,59
87,88
87,89
89,38
89,13
89,58
90,22
91,44
91,04
92,1
97,54
99,12
100
99,68
100,08
99,9
99,63
99,45
99,63
99,46
96,91
97,65
102,1
103,57
104,59
104,79
101,31
104,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204698&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204698&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204698&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 time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean87.50597222222221.147173512623276.2796309881018
Geometric Mean86.9679277585231
Harmonic Mean86.4273225444436
Quadratic Mean88.0382398528554
Winsorized Mean ( 1 / 24 )87.52972222222221.1420327190179876.6437955450944
Winsorized Mean ( 2 / 24 )87.55138888888891.1354467540150377.107436856286
Winsorized Mean ( 3 / 24 )87.51430555555561.1256396690634277.7462876982393
Winsorized Mean ( 4 / 24 )87.44152777777781.1081090644594478.9105789152927
Winsorized Mean ( 5 / 24 )87.45888888888891.0844496696011880.6481769882904
Winsorized Mean ( 6 / 24 )87.42555555555551.0540495701983982.9425465626829
Winsorized Mean ( 7 / 24 )87.418751.052564550849583.053101046816
Winsorized Mean ( 8 / 24 )87.47208333333331.0393993340605684.1563780800312
Winsorized Mean ( 9 / 24 )87.48083333333331.0285593901248985.0518056353666
Winsorized Mean ( 10 / 24 )87.53222222222221.0175307499827786.0241542810422
Winsorized Mean ( 11 / 24 )87.67583333333330.99399273002351188.2057088398016
Winsorized Mean ( 12 / 24 )87.65250.98840810249286888.680474976815
Winsorized Mean ( 13 / 24 )87.66333333333330.98608058979855588.900779753957
Winsorized Mean ( 14 / 24 )87.81888888888890.94086410096099293.3385478297996
Winsorized Mean ( 15 / 24 )87.54388888888890.88548253813089198.8657428227548
Winsorized Mean ( 16 / 24 )87.53277777777780.87948248721271299.5275961152903
Winsorized Mean ( 17 / 24 )87.69333333333330.808398767982187108.477816650094
Winsorized Mean ( 18 / 24 )87.04083333333330.662209565180059131.440012210736
Winsorized Mean ( 19 / 24 )87.381250.56583828354573154.4279567873
Winsorized Mean ( 20 / 24 )87.40347222222220.562658538246829155.340168647507
Winsorized Mean ( 21 / 24 )87.35388888888890.488528961262279178.81005184049
Winsorized Mean ( 22 / 24 )87.37833333333330.480079218815008182.008155964367
Winsorized Mean ( 23 / 24 )87.253750.460611981388108189.430048556381
Winsorized Mean ( 24 / 24 )87.363750.429106116677576203.594744061045
Trimmed Mean ( 1 / 24 )87.51942857142861.123417347965977.9046440131038
Trimmed Mean ( 2 / 24 )87.50852941176471.1011485994790179.4702272274313
Trimmed Mean ( 3 / 24 )87.48515151515151.0786138960303481.1088674428597
Trimmed Mean ( 4 / 24 )87.474218751.0559247011216682.8413414868317
Trimmed Mean ( 5 / 24 )87.48370967741941.0348496068629984.5376072979481
Trimmed Mean ( 6 / 24 )87.48966666666671.0165091468227986.0687451166824
Trimmed Mean ( 7 / 24 )87.50293103448281.0022422233201687.3071688644382
Trimmed Mean ( 8 / 24 )87.51839285714290.98463589343900388.884016356006
Trimmed Mean ( 9 / 24 )87.52611111111110.96568986347354890.6358391257035
Trimmed Mean ( 10 / 24 )87.53307692307690.94426212497817192.6999766353019
Trimmed Mean ( 11 / 24 )87.53320.91957960403831695.1882790957952
Trimmed Mean ( 12 / 24 )87.513750.89343982367497497.9514766199148
Trimmed Mean ( 13 / 24 )87.4956521739130.861011126310415101.619653335779
Trimmed Mean ( 14 / 24 )87.47454545454540.819323668805465106.764333541199
Trimmed Mean ( 15 / 24 )87.4323809523810.775976834424676112.673957615249
Trimmed Mean ( 16 / 24 )87.4190.733244353576134119.222193220644
Trimmed Mean ( 17 / 24 )87.40552631578950.676760829325476129.152756082095
Trimmed Mean ( 18 / 24 )87.37166666666670.620374374937719140.837001327526
Trimmed Mean ( 19 / 24 )87.41058823529410.587177444533043148.865711803368
Trimmed Mean ( 20 / 24 )87.41406250.568895693741711153.65569376183
Trimmed Mean ( 21 / 24 )87.41533333333330.542648196471802161.090249450181
Trimmed Mean ( 22 / 24 )87.42285714285710.527390465355457165.76495573149
Trimmed Mean ( 23 / 24 )87.42846153846150.505767867795765172.862823254257
Trimmed Mean ( 24 / 24 )87.451250.478214263004126182.87043437524
Median87.595
Midrange87.035
Midmean - Weighted Average at Xnp87.1486486486486
Midmean - Weighted Average at X(n+1)p87.3716666666666
Midmean - Empirical Distribution Function87.1486486486486
Midmean - Empirical Distribution Function - Averaging87.3716666666666
Midmean - Empirical Distribution Function - Interpolation87.3716666666666
Midmean - Closest Observation87.1486486486486
Midmean - True Basic - Statistics Graphics Toolkit87.3716666666666
Midmean - MS Excel (old versions)87.4055263157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 87.5059722222222 & 1.1471735126232 & 76.2796309881018 \tabularnewline
Geometric Mean & 86.9679277585231 &  &  \tabularnewline
Harmonic Mean & 86.4273225444436 &  &  \tabularnewline
Quadratic Mean & 88.0382398528554 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 87.5297222222222 & 1.14203271901798 & 76.6437955450944 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 87.5513888888889 & 1.13544675401503 & 77.107436856286 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 87.5143055555556 & 1.12563966906342 & 77.7462876982393 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 87.4415277777778 & 1.10810906445944 & 78.9105789152927 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 87.4588888888889 & 1.08444966960118 & 80.6481769882904 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 87.4255555555555 & 1.05404957019839 & 82.9425465626829 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 87.41875 & 1.0525645508495 & 83.053101046816 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 87.4720833333333 & 1.03939933406056 & 84.1563780800312 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 87.4808333333333 & 1.02855939012489 & 85.0518056353666 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 87.5322222222222 & 1.01753074998277 & 86.0241542810422 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 87.6758333333333 & 0.993992730023511 & 88.2057088398016 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 87.6525 & 0.988408102492868 & 88.680474976815 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 87.6633333333333 & 0.986080589798555 & 88.900779753957 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 87.8188888888889 & 0.940864100960992 & 93.3385478297996 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 87.5438888888889 & 0.885482538130891 & 98.8657428227548 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 87.5327777777778 & 0.879482487212712 & 99.5275961152903 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 87.6933333333333 & 0.808398767982187 & 108.477816650094 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 87.0408333333333 & 0.662209565180059 & 131.440012210736 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 87.38125 & 0.56583828354573 & 154.4279567873 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 87.4034722222222 & 0.562658538246829 & 155.340168647507 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 87.3538888888889 & 0.488528961262279 & 178.81005184049 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 87.3783333333333 & 0.480079218815008 & 182.008155964367 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 87.25375 & 0.460611981388108 & 189.430048556381 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 87.36375 & 0.429106116677576 & 203.594744061045 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 87.5194285714286 & 1.1234173479659 & 77.9046440131038 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 87.5085294117647 & 1.10114859947901 & 79.4702272274313 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 87.4851515151515 & 1.07861389603034 & 81.1088674428597 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 87.47421875 & 1.05592470112166 & 82.8413414868317 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 87.4837096774194 & 1.03484960686299 & 84.5376072979481 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 87.4896666666667 & 1.01650914682279 & 86.0687451166824 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 87.5029310344828 & 1.00224222332016 & 87.3071688644382 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 87.5183928571429 & 0.984635893439003 & 88.884016356006 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 87.5261111111111 & 0.965689863473548 & 90.6358391257035 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 87.5330769230769 & 0.944262124978171 & 92.6999766353019 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 87.5332 & 0.919579604038316 & 95.1882790957952 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 87.51375 & 0.893439823674974 & 97.9514766199148 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 87.495652173913 & 0.861011126310415 & 101.619653335779 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 87.4745454545454 & 0.819323668805465 & 106.764333541199 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 87.432380952381 & 0.775976834424676 & 112.673957615249 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 87.419 & 0.733244353576134 & 119.222193220644 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 87.4055263157895 & 0.676760829325476 & 129.152756082095 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 87.3716666666667 & 0.620374374937719 & 140.837001327526 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 87.4105882352941 & 0.587177444533043 & 148.865711803368 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 87.4140625 & 0.568895693741711 & 153.65569376183 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 87.4153333333333 & 0.542648196471802 & 161.090249450181 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 87.4228571428571 & 0.527390465355457 & 165.76495573149 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 87.4284615384615 & 0.505767867795765 & 172.862823254257 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 87.45125 & 0.478214263004126 & 182.87043437524 \tabularnewline
Median & 87.595 &  &  \tabularnewline
Midrange & 87.035 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 87.1486486486486 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 87.3716666666666 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 87.1486486486486 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 87.3716666666666 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 87.3716666666666 &  &  \tabularnewline
Midmean - Closest Observation & 87.1486486486486 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 87.3716666666666 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 87.4055263157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204698&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]87.5059722222222[/C][C]1.1471735126232[/C][C]76.2796309881018[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]86.9679277585231[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]86.4273225444436[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]88.0382398528554[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]87.5297222222222[/C][C]1.14203271901798[/C][C]76.6437955450944[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]87.5513888888889[/C][C]1.13544675401503[/C][C]77.107436856286[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]87.5143055555556[/C][C]1.12563966906342[/C][C]77.7462876982393[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]87.4415277777778[/C][C]1.10810906445944[/C][C]78.9105789152927[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]87.4588888888889[/C][C]1.08444966960118[/C][C]80.6481769882904[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]87.4255555555555[/C][C]1.05404957019839[/C][C]82.9425465626829[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]87.41875[/C][C]1.0525645508495[/C][C]83.053101046816[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]87.4720833333333[/C][C]1.03939933406056[/C][C]84.1563780800312[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]87.4808333333333[/C][C]1.02855939012489[/C][C]85.0518056353666[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]87.5322222222222[/C][C]1.01753074998277[/C][C]86.0241542810422[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]87.6758333333333[/C][C]0.993992730023511[/C][C]88.2057088398016[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]87.6525[/C][C]0.988408102492868[/C][C]88.680474976815[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]87.6633333333333[/C][C]0.986080589798555[/C][C]88.900779753957[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]87.8188888888889[/C][C]0.940864100960992[/C][C]93.3385478297996[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]87.5438888888889[/C][C]0.885482538130891[/C][C]98.8657428227548[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]87.5327777777778[/C][C]0.879482487212712[/C][C]99.5275961152903[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]87.6933333333333[/C][C]0.808398767982187[/C][C]108.477816650094[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]87.0408333333333[/C][C]0.662209565180059[/C][C]131.440012210736[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]87.38125[/C][C]0.56583828354573[/C][C]154.4279567873[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]87.4034722222222[/C][C]0.562658538246829[/C][C]155.340168647507[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]87.3538888888889[/C][C]0.488528961262279[/C][C]178.81005184049[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]87.3783333333333[/C][C]0.480079218815008[/C][C]182.008155964367[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]87.25375[/C][C]0.460611981388108[/C][C]189.430048556381[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]87.36375[/C][C]0.429106116677576[/C][C]203.594744061045[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]87.5194285714286[/C][C]1.1234173479659[/C][C]77.9046440131038[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]87.5085294117647[/C][C]1.10114859947901[/C][C]79.4702272274313[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]87.4851515151515[/C][C]1.07861389603034[/C][C]81.1088674428597[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]87.47421875[/C][C]1.05592470112166[/C][C]82.8413414868317[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]87.4837096774194[/C][C]1.03484960686299[/C][C]84.5376072979481[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]87.4896666666667[/C][C]1.01650914682279[/C][C]86.0687451166824[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]87.5029310344828[/C][C]1.00224222332016[/C][C]87.3071688644382[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]87.5183928571429[/C][C]0.984635893439003[/C][C]88.884016356006[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]87.5261111111111[/C][C]0.965689863473548[/C][C]90.6358391257035[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]87.5330769230769[/C][C]0.944262124978171[/C][C]92.6999766353019[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]87.5332[/C][C]0.919579604038316[/C][C]95.1882790957952[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]87.51375[/C][C]0.893439823674974[/C][C]97.9514766199148[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]87.495652173913[/C][C]0.861011126310415[/C][C]101.619653335779[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]87.4745454545454[/C][C]0.819323668805465[/C][C]106.764333541199[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]87.432380952381[/C][C]0.775976834424676[/C][C]112.673957615249[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]87.419[/C][C]0.733244353576134[/C][C]119.222193220644[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]87.4055263157895[/C][C]0.676760829325476[/C][C]129.152756082095[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]87.3716666666667[/C][C]0.620374374937719[/C][C]140.837001327526[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]87.4105882352941[/C][C]0.587177444533043[/C][C]148.865711803368[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]87.4140625[/C][C]0.568895693741711[/C][C]153.65569376183[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]87.4153333333333[/C][C]0.542648196471802[/C][C]161.090249450181[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]87.4228571428571[/C][C]0.527390465355457[/C][C]165.76495573149[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]87.4284615384615[/C][C]0.505767867795765[/C][C]172.862823254257[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]87.45125[/C][C]0.478214263004126[/C][C]182.87043437524[/C][/ROW]
[ROW][C]Median[/C][C]87.595[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]87.035[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]87.1486486486486[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]87.3716666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]87.1486486486486[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]87.3716666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]87.3716666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]87.1486486486486[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]87.3716666666666[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]87.4055263157895[/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=204698&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204698&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 Mean87.50597222222221.147173512623276.2796309881018
Geometric Mean86.9679277585231
Harmonic Mean86.4273225444436
Quadratic Mean88.0382398528554
Winsorized Mean ( 1 / 24 )87.52972222222221.1420327190179876.6437955450944
Winsorized Mean ( 2 / 24 )87.55138888888891.1354467540150377.107436856286
Winsorized Mean ( 3 / 24 )87.51430555555561.1256396690634277.7462876982393
Winsorized Mean ( 4 / 24 )87.44152777777781.1081090644594478.9105789152927
Winsorized Mean ( 5 / 24 )87.45888888888891.0844496696011880.6481769882904
Winsorized Mean ( 6 / 24 )87.42555555555551.0540495701983982.9425465626829
Winsorized Mean ( 7 / 24 )87.418751.052564550849583.053101046816
Winsorized Mean ( 8 / 24 )87.47208333333331.0393993340605684.1563780800312
Winsorized Mean ( 9 / 24 )87.48083333333331.0285593901248985.0518056353666
Winsorized Mean ( 10 / 24 )87.53222222222221.0175307499827786.0241542810422
Winsorized Mean ( 11 / 24 )87.67583333333330.99399273002351188.2057088398016
Winsorized Mean ( 12 / 24 )87.65250.98840810249286888.680474976815
Winsorized Mean ( 13 / 24 )87.66333333333330.98608058979855588.900779753957
Winsorized Mean ( 14 / 24 )87.81888888888890.94086410096099293.3385478297996
Winsorized Mean ( 15 / 24 )87.54388888888890.88548253813089198.8657428227548
Winsorized Mean ( 16 / 24 )87.53277777777780.87948248721271299.5275961152903
Winsorized Mean ( 17 / 24 )87.69333333333330.808398767982187108.477816650094
Winsorized Mean ( 18 / 24 )87.04083333333330.662209565180059131.440012210736
Winsorized Mean ( 19 / 24 )87.381250.56583828354573154.4279567873
Winsorized Mean ( 20 / 24 )87.40347222222220.562658538246829155.340168647507
Winsorized Mean ( 21 / 24 )87.35388888888890.488528961262279178.81005184049
Winsorized Mean ( 22 / 24 )87.37833333333330.480079218815008182.008155964367
Winsorized Mean ( 23 / 24 )87.253750.460611981388108189.430048556381
Winsorized Mean ( 24 / 24 )87.363750.429106116677576203.594744061045
Trimmed Mean ( 1 / 24 )87.51942857142861.123417347965977.9046440131038
Trimmed Mean ( 2 / 24 )87.50852941176471.1011485994790179.4702272274313
Trimmed Mean ( 3 / 24 )87.48515151515151.0786138960303481.1088674428597
Trimmed Mean ( 4 / 24 )87.474218751.0559247011216682.8413414868317
Trimmed Mean ( 5 / 24 )87.48370967741941.0348496068629984.5376072979481
Trimmed Mean ( 6 / 24 )87.48966666666671.0165091468227986.0687451166824
Trimmed Mean ( 7 / 24 )87.50293103448281.0022422233201687.3071688644382
Trimmed Mean ( 8 / 24 )87.51839285714290.98463589343900388.884016356006
Trimmed Mean ( 9 / 24 )87.52611111111110.96568986347354890.6358391257035
Trimmed Mean ( 10 / 24 )87.53307692307690.94426212497817192.6999766353019
Trimmed Mean ( 11 / 24 )87.53320.91957960403831695.1882790957952
Trimmed Mean ( 12 / 24 )87.513750.89343982367497497.9514766199148
Trimmed Mean ( 13 / 24 )87.4956521739130.861011126310415101.619653335779
Trimmed Mean ( 14 / 24 )87.47454545454540.819323668805465106.764333541199
Trimmed Mean ( 15 / 24 )87.4323809523810.775976834424676112.673957615249
Trimmed Mean ( 16 / 24 )87.4190.733244353576134119.222193220644
Trimmed Mean ( 17 / 24 )87.40552631578950.676760829325476129.152756082095
Trimmed Mean ( 18 / 24 )87.37166666666670.620374374937719140.837001327526
Trimmed Mean ( 19 / 24 )87.41058823529410.587177444533043148.865711803368
Trimmed Mean ( 20 / 24 )87.41406250.568895693741711153.65569376183
Trimmed Mean ( 21 / 24 )87.41533333333330.542648196471802161.090249450181
Trimmed Mean ( 22 / 24 )87.42285714285710.527390465355457165.76495573149
Trimmed Mean ( 23 / 24 )87.42846153846150.505767867795765172.862823254257
Trimmed Mean ( 24 / 24 )87.451250.478214263004126182.87043437524
Median87.595
Midrange87.035
Midmean - Weighted Average at Xnp87.1486486486486
Midmean - Weighted Average at X(n+1)p87.3716666666666
Midmean - Empirical Distribution Function87.1486486486486
Midmean - Empirical Distribution Function - Averaging87.3716666666666
Midmean - Empirical Distribution Function - Interpolation87.3716666666666
Midmean - Closest Observation87.1486486486486
Midmean - True Basic - Statistics Graphics Toolkit87.3716666666666
Midmean - MS Excel (old versions)87.4055263157895
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')