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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 14 Nov 2011 11:50:04 -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/2011/Nov/14/t132128941855tbh5i0mtcumw5.htm/, Retrieved Fri, 19 Apr 2024 15:51:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=142083, Retrieved Fri, 19 Apr 2024 15:51:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
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Dataseries X:
57,8
52,5
58,2
61,1
65,7
62,3
63,3
62,6
61,9
63,9
64,2
64,8
55,1
56,2
63,7
62,6
58,4
55,5
66,6
54,7
58,9
51,3
51
48,9
52,6
51,2
59,6
63
61,4
59,3
58,6
63,6
66,9
68,9
64,2
63,1
63,3
60,1
59,2
55,3
56,6
58,9
60,3
60,1
60,8
60,7
61,8
69,5
62,2
60,7
63,4
69,7
64,2
63,8
64,1
63,2
62,2
65,4
61,2
60,8
59,1
55,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142083&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142083&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean60.58225806451610.579859955892944104.477395703629
Geometric Mean60.4075674964496
Harmonic Mean60.2271218512565
Quadratic Mean60.7513002648583
Winsorized Mean ( 1 / 20 )60.61290322580640.568736359293738106.574693591027
Winsorized Mean ( 2 / 20 )60.60.56213595070554107.803103366615
Winsorized Mean ( 3 / 20 )60.5080645161290.539641156143601112.126482250786
Winsorized Mean ( 4 / 20 )60.56612903225810.515117539062853117.577299236297
Winsorized Mean ( 5 / 20 )60.50161290322580.499870379472892121.034602944516
Winsorized Mean ( 6 / 20 )60.67580645161290.445998042907676136.045006063341
Winsorized Mean ( 7 / 20 )60.65322580645160.424885076333137142.752073878198
Winsorized Mean ( 8 / 20 )60.60161290322580.407560047941885148.693703441381
Winsorized Mean ( 9 / 20 )60.63064516129030.401422567611518151.039453317349
Winsorized Mean ( 10 / 20 )60.69516129032260.388126439920262156.379867609102
Winsorized Mean ( 11 / 20 )60.73064516129030.374840623348239162.017245139595
Winsorized Mean ( 12 / 20 )60.76935483870970.354032363467265171.649151629971
Winsorized Mean ( 13 / 20 )610.304800304800457200.131033464467
Winsorized Mean ( 14 / 20 )61.06774193548390.28619547292568213.377735542805
Winsorized Mean ( 15 / 20 )61.0919354838710.274698030324347222.396700157395
Winsorized Mean ( 16 / 20 )61.0919354838710.258839479577043236.02247842446
Winsorized Mean ( 17 / 20 )61.14677419354840.242079368460519252.589779056371
Winsorized Mean ( 18 / 20 )61.14677419354840.242079368460519252.589779056371
Winsorized Mean ( 19 / 20 )61.17741935483870.228385214523162267.869439282964
Winsorized Mean ( 20 / 20 )61.17741935483870.218927477431705279.441484789972
Trimmed Mean ( 1 / 20 )60.6250.545120237604813111.2139961385
Trimmed Mean ( 2 / 20 )60.63793103448280.516080366672804117.497070127698
Trimmed Mean ( 3 / 20 )60.65892857142860.484552121395412125.185559804677
Trimmed Mean ( 4 / 20 )60.71666666666670.45650626879063133.002919823021
Trimmed Mean ( 5 / 20 )60.76153846153850.43168401037405140.754665452837
Trimmed Mean ( 6 / 20 )60.8260.405571504050715149.976019992751
Trimmed Mean ( 7 / 20 )60.85833333333330.390771574155348155.73889545287
Trimmed Mean ( 8 / 20 )60.89782608695650.377974376485448161.116281619956
Trimmed Mean ( 9 / 20 )60.950.365946021273982166.554618595968
Trimmed Mean ( 10 / 20 )61.0023809523810.351692243763383173.45387063305
Trimmed Mean ( 11 / 20 )61.050.336497799741349181.427635030382
Trimmed Mean ( 12 / 20 )61.09736842105260.31972798809955191.091711376952
Trimmed Mean ( 13 / 20 )61.14444444444440.302855312629657201.893253625088
Trimmed Mean ( 14 / 20 )61.16470588235290.294509542831664207.683273330513
Trimmed Mean ( 15 / 20 )61.1781250.287674714619571212.664241558052
Trimmed Mean ( 16 / 20 )61.190.280613039898219218.058291311744
Trimmed Mean ( 17 / 20 )61.20357142857140.274367099643144223.071831528547
Trimmed Mean ( 18 / 20 )61.21153846153850.26949108294521227.137528234963
Trimmed Mean ( 19 / 20 )61.22083333333330.260641569550557234.885146827886
Trimmed Mean ( 20 / 20 )61.22727272727270.250901562092955244.029061503368
Median61.15
Midrange59.3
Midmean - Weighted Average at Xnp61.1
Midmean - Weighted Average at X(n+1)p61.178125
Midmean - Empirical Distribution Function61.178125
Midmean - Empirical Distribution Function - Averaging61.178125
Midmean - Empirical Distribution Function - Interpolation61.19
Midmean - Closest Observation61.178125
Midmean - True Basic - Statistics Graphics Toolkit61.178125
Midmean - MS Excel (old versions)61.178125
Number of observations62

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 60.5822580645161 & 0.579859955892944 & 104.477395703629 \tabularnewline
Geometric Mean & 60.4075674964496 &  &  \tabularnewline
Harmonic Mean & 60.2271218512565 &  &  \tabularnewline
Quadratic Mean & 60.7513002648583 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 60.6129032258064 & 0.568736359293738 & 106.574693591027 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 60.6 & 0.56213595070554 & 107.803103366615 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 60.508064516129 & 0.539641156143601 & 112.126482250786 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 60.5661290322581 & 0.515117539062853 & 117.577299236297 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 60.5016129032258 & 0.499870379472892 & 121.034602944516 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 60.6758064516129 & 0.445998042907676 & 136.045006063341 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 60.6532258064516 & 0.424885076333137 & 142.752073878198 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 60.6016129032258 & 0.407560047941885 & 148.693703441381 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 60.6306451612903 & 0.401422567611518 & 151.039453317349 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 60.6951612903226 & 0.388126439920262 & 156.379867609102 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 60.7306451612903 & 0.374840623348239 & 162.017245139595 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 60.7693548387097 & 0.354032363467265 & 171.649151629971 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 61 & 0.304800304800457 & 200.131033464467 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 61.0677419354839 & 0.28619547292568 & 213.377735542805 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 61.091935483871 & 0.274698030324347 & 222.396700157395 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 61.091935483871 & 0.258839479577043 & 236.02247842446 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 61.1467741935484 & 0.242079368460519 & 252.589779056371 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 61.1467741935484 & 0.242079368460519 & 252.589779056371 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 61.1774193548387 & 0.228385214523162 & 267.869439282964 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 61.1774193548387 & 0.218927477431705 & 279.441484789972 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 60.625 & 0.545120237604813 & 111.2139961385 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 60.6379310344828 & 0.516080366672804 & 117.497070127698 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 60.6589285714286 & 0.484552121395412 & 125.185559804677 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 60.7166666666667 & 0.45650626879063 & 133.002919823021 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 60.7615384615385 & 0.43168401037405 & 140.754665452837 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 60.826 & 0.405571504050715 & 149.976019992751 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 60.8583333333333 & 0.390771574155348 & 155.73889545287 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 60.8978260869565 & 0.377974376485448 & 161.116281619956 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 60.95 & 0.365946021273982 & 166.554618595968 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 61.002380952381 & 0.351692243763383 & 173.45387063305 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 61.05 & 0.336497799741349 & 181.427635030382 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 61.0973684210526 & 0.31972798809955 & 191.091711376952 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 61.1444444444444 & 0.302855312629657 & 201.893253625088 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 61.1647058823529 & 0.294509542831664 & 207.683273330513 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 61.178125 & 0.287674714619571 & 212.664241558052 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 61.19 & 0.280613039898219 & 218.058291311744 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 61.2035714285714 & 0.274367099643144 & 223.071831528547 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 61.2115384615385 & 0.26949108294521 & 227.137528234963 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 61.2208333333333 & 0.260641569550557 & 234.885146827886 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 61.2272727272727 & 0.250901562092955 & 244.029061503368 \tabularnewline
Median & 61.15 &  &  \tabularnewline
Midrange & 59.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 61.1 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 61.178125 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 61.178125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 61.178125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 61.19 &  &  \tabularnewline
Midmean - Closest Observation & 61.178125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 61.178125 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 61.178125 &  &  \tabularnewline
Number of observations & 62 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=142083&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]60.5822580645161[/C][C]0.579859955892944[/C][C]104.477395703629[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]60.4075674964496[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]60.2271218512565[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]60.7513002648583[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]60.6129032258064[/C][C]0.568736359293738[/C][C]106.574693591027[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]60.6[/C][C]0.56213595070554[/C][C]107.803103366615[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]60.508064516129[/C][C]0.539641156143601[/C][C]112.126482250786[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]60.5661290322581[/C][C]0.515117539062853[/C][C]117.577299236297[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]60.5016129032258[/C][C]0.499870379472892[/C][C]121.034602944516[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]60.6758064516129[/C][C]0.445998042907676[/C][C]136.045006063341[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]60.6532258064516[/C][C]0.424885076333137[/C][C]142.752073878198[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]60.6016129032258[/C][C]0.407560047941885[/C][C]148.693703441381[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]60.6306451612903[/C][C]0.401422567611518[/C][C]151.039453317349[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]60.6951612903226[/C][C]0.388126439920262[/C][C]156.379867609102[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]60.7306451612903[/C][C]0.374840623348239[/C][C]162.017245139595[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]60.7693548387097[/C][C]0.354032363467265[/C][C]171.649151629971[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]61[/C][C]0.304800304800457[/C][C]200.131033464467[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]61.0677419354839[/C][C]0.28619547292568[/C][C]213.377735542805[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]61.091935483871[/C][C]0.274698030324347[/C][C]222.396700157395[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]61.091935483871[/C][C]0.258839479577043[/C][C]236.02247842446[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]61.1467741935484[/C][C]0.242079368460519[/C][C]252.589779056371[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]61.1467741935484[/C][C]0.242079368460519[/C][C]252.589779056371[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]61.1774193548387[/C][C]0.228385214523162[/C][C]267.869439282964[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]61.1774193548387[/C][C]0.218927477431705[/C][C]279.441484789972[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]60.625[/C][C]0.545120237604813[/C][C]111.2139961385[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]60.6379310344828[/C][C]0.516080366672804[/C][C]117.497070127698[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]60.6589285714286[/C][C]0.484552121395412[/C][C]125.185559804677[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]60.7166666666667[/C][C]0.45650626879063[/C][C]133.002919823021[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]60.7615384615385[/C][C]0.43168401037405[/C][C]140.754665452837[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]60.826[/C][C]0.405571504050715[/C][C]149.976019992751[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]60.8583333333333[/C][C]0.390771574155348[/C][C]155.73889545287[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]60.8978260869565[/C][C]0.377974376485448[/C][C]161.116281619956[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]60.95[/C][C]0.365946021273982[/C][C]166.554618595968[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]61.002380952381[/C][C]0.351692243763383[/C][C]173.45387063305[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]61.05[/C][C]0.336497799741349[/C][C]181.427635030382[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]61.0973684210526[/C][C]0.31972798809955[/C][C]191.091711376952[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]61.1444444444444[/C][C]0.302855312629657[/C][C]201.893253625088[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]61.1647058823529[/C][C]0.294509542831664[/C][C]207.683273330513[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]61.178125[/C][C]0.287674714619571[/C][C]212.664241558052[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]61.19[/C][C]0.280613039898219[/C][C]218.058291311744[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]61.2035714285714[/C][C]0.274367099643144[/C][C]223.071831528547[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]61.2115384615385[/C][C]0.26949108294521[/C][C]227.137528234963[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]61.2208333333333[/C][C]0.260641569550557[/C][C]234.885146827886[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]61.2272727272727[/C][C]0.250901562092955[/C][C]244.029061503368[/C][/ROW]
[ROW][C]Median[/C][C]61.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]59.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]61.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]61.178125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]61.178125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]61.178125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]61.19[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]61.178125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]61.178125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]61.178125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]62[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=142083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=142083&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 Mean60.58225806451610.579859955892944104.477395703629
Geometric Mean60.4075674964496
Harmonic Mean60.2271218512565
Quadratic Mean60.7513002648583
Winsorized Mean ( 1 / 20 )60.61290322580640.568736359293738106.574693591027
Winsorized Mean ( 2 / 20 )60.60.56213595070554107.803103366615
Winsorized Mean ( 3 / 20 )60.5080645161290.539641156143601112.126482250786
Winsorized Mean ( 4 / 20 )60.56612903225810.515117539062853117.577299236297
Winsorized Mean ( 5 / 20 )60.50161290322580.499870379472892121.034602944516
Winsorized Mean ( 6 / 20 )60.67580645161290.445998042907676136.045006063341
Winsorized Mean ( 7 / 20 )60.65322580645160.424885076333137142.752073878198
Winsorized Mean ( 8 / 20 )60.60161290322580.407560047941885148.693703441381
Winsorized Mean ( 9 / 20 )60.63064516129030.401422567611518151.039453317349
Winsorized Mean ( 10 / 20 )60.69516129032260.388126439920262156.379867609102
Winsorized Mean ( 11 / 20 )60.73064516129030.374840623348239162.017245139595
Winsorized Mean ( 12 / 20 )60.76935483870970.354032363467265171.649151629971
Winsorized Mean ( 13 / 20 )610.304800304800457200.131033464467
Winsorized Mean ( 14 / 20 )61.06774193548390.28619547292568213.377735542805
Winsorized Mean ( 15 / 20 )61.0919354838710.274698030324347222.396700157395
Winsorized Mean ( 16 / 20 )61.0919354838710.258839479577043236.02247842446
Winsorized Mean ( 17 / 20 )61.14677419354840.242079368460519252.589779056371
Winsorized Mean ( 18 / 20 )61.14677419354840.242079368460519252.589779056371
Winsorized Mean ( 19 / 20 )61.17741935483870.228385214523162267.869439282964
Winsorized Mean ( 20 / 20 )61.17741935483870.218927477431705279.441484789972
Trimmed Mean ( 1 / 20 )60.6250.545120237604813111.2139961385
Trimmed Mean ( 2 / 20 )60.63793103448280.516080366672804117.497070127698
Trimmed Mean ( 3 / 20 )60.65892857142860.484552121395412125.185559804677
Trimmed Mean ( 4 / 20 )60.71666666666670.45650626879063133.002919823021
Trimmed Mean ( 5 / 20 )60.76153846153850.43168401037405140.754665452837
Trimmed Mean ( 6 / 20 )60.8260.405571504050715149.976019992751
Trimmed Mean ( 7 / 20 )60.85833333333330.390771574155348155.73889545287
Trimmed Mean ( 8 / 20 )60.89782608695650.377974376485448161.116281619956
Trimmed Mean ( 9 / 20 )60.950.365946021273982166.554618595968
Trimmed Mean ( 10 / 20 )61.0023809523810.351692243763383173.45387063305
Trimmed Mean ( 11 / 20 )61.050.336497799741349181.427635030382
Trimmed Mean ( 12 / 20 )61.09736842105260.31972798809955191.091711376952
Trimmed Mean ( 13 / 20 )61.14444444444440.302855312629657201.893253625088
Trimmed Mean ( 14 / 20 )61.16470588235290.294509542831664207.683273330513
Trimmed Mean ( 15 / 20 )61.1781250.287674714619571212.664241558052
Trimmed Mean ( 16 / 20 )61.190.280613039898219218.058291311744
Trimmed Mean ( 17 / 20 )61.20357142857140.274367099643144223.071831528547
Trimmed Mean ( 18 / 20 )61.21153846153850.26949108294521227.137528234963
Trimmed Mean ( 19 / 20 )61.22083333333330.260641569550557234.885146827886
Trimmed Mean ( 20 / 20 )61.22727272727270.250901562092955244.029061503368
Median61.15
Midrange59.3
Midmean - Weighted Average at Xnp61.1
Midmean - Weighted Average at X(n+1)p61.178125
Midmean - Empirical Distribution Function61.178125
Midmean - Empirical Distribution Function - Averaging61.178125
Midmean - Empirical Distribution Function - Interpolation61.19
Midmean - Closest Observation61.178125
Midmean - True Basic - Statistics Graphics Toolkit61.178125
Midmean - MS Excel (old versions)61.178125
Number of observations62



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')