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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 20 Apr 2008 10:35:23 -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/2008/Apr/20/t12087093639wwghmtyoxzdjc1.htm/, Retrieved Sun, 12 May 2024 13:38:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10371, Retrieved Sun, 12 May 2024 13:38:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact178
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten - Bl...] [2008-04-20 16:35:23] [6461440fa2a8ea0ebac8d11789a457eb] [Current]
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Dataseries X:
48,04
48,06
48,04
48,09
48,12
48,16
48,16
48,16
48,08
48,13
48,16
48,15
48,15
48,15
48,27
48,47
48,51
48,53
48,53
48,53
48,68
48,64
48,67
48,66
48,66
48,67
48,71
48,96
49,01
49,04
49,04
49,04
49,06
49,13
49,19
49,26
49,26
49,26
49,29
49,43
49,43
49,45
49,45
49,46
49,57
49,68
49,71
49,7
49,7
49,8
49,84
50,09
50,2
50,16
50,16
50,29
50,36
51,02
51,03
51,04




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

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10371&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10371&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10371&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean49.07150.105293194365358466.046265342908
Geometric Mean49.0648786941376
Harmonic Mean49.0583008557927
Quadratic Mean49.0781644420408
Winsorized Mean ( 1 / 20 )49.07133333333330.105240501179500466.278027787388
Winsorized Mean ( 2 / 20 )49.07166666666670.105025734448381467.234691805796
Winsorized Mean ( 3 / 20 )49.03966666666670.0957536170539146512.144273767273
Winsorized Mean ( 4 / 20 )49.03566666666670.0945705029999565518.509102850909
Winsorized Mean ( 5 / 20 )49.03066666666670.0925031276510985530.043339200373
Winsorized Mean ( 6 / 20 )49.02766666666670.0914884348427775535.889227429898
Winsorized Mean ( 7 / 20 )49.030.091103405581101538.179661750988
Winsorized Mean ( 8 / 20 )49.02066666666670.0891735015068835549.722348436465
Winsorized Mean ( 9 / 20 )48.98316666666670.0820222829261773597.193407927369
Winsorized Mean ( 10 / 20 )48.97816666666670.080568773186676607.905081950117
Winsorized Mean ( 11 / 20 )48.96166666666670.0777959690859777629.359942962543
Winsorized Mean ( 12 / 20 )48.95966666666670.0774709592633926631.97444735658
Winsorized Mean ( 13 / 20 )48.95966666666670.0774709592633926631.97444735658
Winsorized Mean ( 14 / 20 )48.98066666666670.0723245457965027677.234348688232
Winsorized Mean ( 15 / 20 )49.00316666666670.0598880743562036818.245822619117
Winsorized Mean ( 16 / 20 )48.98450.0537231998617901911.794162038356
Winsorized Mean ( 17 / 20 )48.98733333333330.0524559899832461933.874917792598
Winsorized Mean ( 18 / 20 )48.98733333333330.0524559899832461933.874917792598
Winsorized Mean ( 19 / 20 )48.9810.0515147392653977950.815255953365
Winsorized Mean ( 20 / 20 )49.01766666666670.04624692181948731059.91198415311
Trimmed Mean ( 1 / 20 )49.05534482758620.101847190945668481.656336047162
Trimmed Mean ( 2 / 20 )49.03821428571430.0976111112284379502.38352651217
Trimmed Mean ( 3 / 20 )49.01962962962960.0924149798947239530.429478916418
Trimmed Mean ( 4 / 20 )49.01192307692310.0905830112949405541.071911567822
Trimmed Mean ( 5 / 20 )49.00480.0886967960675755552.497972561091
Trimmed Mean ( 6 / 20 )48.99833333333330.0869628055597762563.44011693198
Trimmed Mean ( 7 / 20 )48.99195652173910.0849999258682357576.376461759331
Trimmed Mean ( 8 / 20 )48.98454545454550.0825085392117683593.690615813966
Trimmed Mean ( 9 / 20 )48.97809523809520.0797784665662981613.926255368585
Trimmed Mean ( 10 / 20 )48.977250.078164838560439626.589281088702
Trimmed Mean ( 11 / 20 )48.97710526315790.0763050588423942641.859216232551
Trimmed Mean ( 12 / 20 )48.97944444444440.0744364482793981658.003512749554
Trimmed Mean ( 13 / 20 )48.98235294117650.0718386720311777681.838229413795
Trimmed Mean ( 14 / 20 )48.9856250.0680872564873027719.453647087912
Trimmed Mean ( 15 / 20 )48.98633333333330.0643669139920366761.048344486328
Trimmed Mean ( 16 / 20 )48.98392857142860.062963286702738777.976041858984
Trimmed Mean ( 17 / 20 )48.98384615384620.0625830572379972782.70139420587
Trimmed Mean ( 18 / 20 )48.98333333333330.0620094273649225789.933650653936
Trimmed Mean ( 19 / 20 )48.98272727272730.0606465232893996807.675767974138
Trimmed Mean ( 20 / 20 )48.9830.0583595930868538839.330732260264
Median49.04
Midrange49.54
Midmean - Weighted Average at Xnp48.9632258064516
Midmean - Weighted Average at X(n+1)p48.9863333333333
Midmean - Empirical Distribution Function48.9632258064516
Midmean - Empirical Distribution Function - Averaging48.9863333333333
Midmean - Empirical Distribution Function - Interpolation48.9863333333333
Midmean - Closest Observation48.9632258064516
Midmean - True Basic - Statistics Graphics Toolkit48.9863333333333
Midmean - MS Excel (old versions)48.985625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 49.0715 & 0.105293194365358 & 466.046265342908 \tabularnewline
Geometric Mean & 49.0648786941376 &  &  \tabularnewline
Harmonic Mean & 49.0583008557927 &  &  \tabularnewline
Quadratic Mean & 49.0781644420408 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 49.0713333333333 & 0.105240501179500 & 466.278027787388 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 49.0716666666667 & 0.105025734448381 & 467.234691805796 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 49.0396666666667 & 0.0957536170539146 & 512.144273767273 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 49.0356666666667 & 0.0945705029999565 & 518.509102850909 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 49.0306666666667 & 0.0925031276510985 & 530.043339200373 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 49.0276666666667 & 0.0914884348427775 & 535.889227429898 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 49.03 & 0.091103405581101 & 538.179661750988 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 49.0206666666667 & 0.0891735015068835 & 549.722348436465 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 48.9831666666667 & 0.0820222829261773 & 597.193407927369 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 48.9781666666667 & 0.080568773186676 & 607.905081950117 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 48.9616666666667 & 0.0777959690859777 & 629.359942962543 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 48.9596666666667 & 0.0774709592633926 & 631.97444735658 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 48.9596666666667 & 0.0774709592633926 & 631.97444735658 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 48.9806666666667 & 0.0723245457965027 & 677.234348688232 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 49.0031666666667 & 0.0598880743562036 & 818.245822619117 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 48.9845 & 0.0537231998617901 & 911.794162038356 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 48.9873333333333 & 0.0524559899832461 & 933.874917792598 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 48.9873333333333 & 0.0524559899832461 & 933.874917792598 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 48.981 & 0.0515147392653977 & 950.815255953365 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 49.0176666666667 & 0.0462469218194873 & 1059.91198415311 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 49.0553448275862 & 0.101847190945668 & 481.656336047162 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 49.0382142857143 & 0.0976111112284379 & 502.38352651217 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 49.0196296296296 & 0.0924149798947239 & 530.429478916418 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 49.0119230769231 & 0.0905830112949405 & 541.071911567822 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 49.0048 & 0.0886967960675755 & 552.497972561091 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 48.9983333333333 & 0.0869628055597762 & 563.44011693198 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 48.9919565217391 & 0.0849999258682357 & 576.376461759331 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 48.9845454545455 & 0.0825085392117683 & 593.690615813966 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 48.9780952380952 & 0.0797784665662981 & 613.926255368585 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 48.97725 & 0.078164838560439 & 626.589281088702 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 48.9771052631579 & 0.0763050588423942 & 641.859216232551 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 48.9794444444444 & 0.0744364482793981 & 658.003512749554 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 48.9823529411765 & 0.0718386720311777 & 681.838229413795 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 48.985625 & 0.0680872564873027 & 719.453647087912 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 48.9863333333333 & 0.0643669139920366 & 761.048344486328 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 48.9839285714286 & 0.062963286702738 & 777.976041858984 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 48.9838461538462 & 0.0625830572379972 & 782.70139420587 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 48.9833333333333 & 0.0620094273649225 & 789.933650653936 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 48.9827272727273 & 0.0606465232893996 & 807.675767974138 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 48.983 & 0.0583595930868538 & 839.330732260264 \tabularnewline
Median & 49.04 &  &  \tabularnewline
Midrange & 49.54 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 48.9632258064516 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 48.9863333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 48.9632258064516 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 48.9863333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 48.9863333333333 &  &  \tabularnewline
Midmean - Closest Observation & 48.9632258064516 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 48.9863333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 48.985625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10371&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]49.0715[/C][C]0.105293194365358[/C][C]466.046265342908[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]49.0648786941376[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]49.0583008557927[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]49.0781644420408[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]49.0713333333333[/C][C]0.105240501179500[/C][C]466.278027787388[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]49.0716666666667[/C][C]0.105025734448381[/C][C]467.234691805796[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]49.0396666666667[/C][C]0.0957536170539146[/C][C]512.144273767273[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]49.0356666666667[/C][C]0.0945705029999565[/C][C]518.509102850909[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]49.0306666666667[/C][C]0.0925031276510985[/C][C]530.043339200373[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]49.0276666666667[/C][C]0.0914884348427775[/C][C]535.889227429898[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]49.03[/C][C]0.091103405581101[/C][C]538.179661750988[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]49.0206666666667[/C][C]0.0891735015068835[/C][C]549.722348436465[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]48.9831666666667[/C][C]0.0820222829261773[/C][C]597.193407927369[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]48.9781666666667[/C][C]0.080568773186676[/C][C]607.905081950117[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]48.9616666666667[/C][C]0.0777959690859777[/C][C]629.359942962543[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]48.9596666666667[/C][C]0.0774709592633926[/C][C]631.97444735658[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]48.9596666666667[/C][C]0.0774709592633926[/C][C]631.97444735658[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]48.9806666666667[/C][C]0.0723245457965027[/C][C]677.234348688232[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]49.0031666666667[/C][C]0.0598880743562036[/C][C]818.245822619117[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]48.9845[/C][C]0.0537231998617901[/C][C]911.794162038356[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]48.9873333333333[/C][C]0.0524559899832461[/C][C]933.874917792598[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]48.9873333333333[/C][C]0.0524559899832461[/C][C]933.874917792598[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]48.981[/C][C]0.0515147392653977[/C][C]950.815255953365[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]49.0176666666667[/C][C]0.0462469218194873[/C][C]1059.91198415311[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]49.0553448275862[/C][C]0.101847190945668[/C][C]481.656336047162[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]49.0382142857143[/C][C]0.0976111112284379[/C][C]502.38352651217[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]49.0196296296296[/C][C]0.0924149798947239[/C][C]530.429478916418[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]49.0119230769231[/C][C]0.0905830112949405[/C][C]541.071911567822[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]49.0048[/C][C]0.0886967960675755[/C][C]552.497972561091[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]48.9983333333333[/C][C]0.0869628055597762[/C][C]563.44011693198[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]48.9919565217391[/C][C]0.0849999258682357[/C][C]576.376461759331[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]48.9845454545455[/C][C]0.0825085392117683[/C][C]593.690615813966[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]48.9780952380952[/C][C]0.0797784665662981[/C][C]613.926255368585[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]48.97725[/C][C]0.078164838560439[/C][C]626.589281088702[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]48.9771052631579[/C][C]0.0763050588423942[/C][C]641.859216232551[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]48.9794444444444[/C][C]0.0744364482793981[/C][C]658.003512749554[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]48.9823529411765[/C][C]0.0718386720311777[/C][C]681.838229413795[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]48.985625[/C][C]0.0680872564873027[/C][C]719.453647087912[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]48.9863333333333[/C][C]0.0643669139920366[/C][C]761.048344486328[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]48.9839285714286[/C][C]0.062963286702738[/C][C]777.976041858984[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]48.9838461538462[/C][C]0.0625830572379972[/C][C]782.70139420587[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]48.9833333333333[/C][C]0.0620094273649225[/C][C]789.933650653936[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]48.9827272727273[/C][C]0.0606465232893996[/C][C]807.675767974138[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]48.983[/C][C]0.0583595930868538[/C][C]839.330732260264[/C][/ROW]
[ROW][C]Median[/C][C]49.04[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]49.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]48.9632258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]48.9863333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]48.9632258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]48.9863333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]48.9863333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]48.9632258064516[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]48.9863333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]48.985625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10371&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10371&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 Mean49.07150.105293194365358466.046265342908
Geometric Mean49.0648786941376
Harmonic Mean49.0583008557927
Quadratic Mean49.0781644420408
Winsorized Mean ( 1 / 20 )49.07133333333330.105240501179500466.278027787388
Winsorized Mean ( 2 / 20 )49.07166666666670.105025734448381467.234691805796
Winsorized Mean ( 3 / 20 )49.03966666666670.0957536170539146512.144273767273
Winsorized Mean ( 4 / 20 )49.03566666666670.0945705029999565518.509102850909
Winsorized Mean ( 5 / 20 )49.03066666666670.0925031276510985530.043339200373
Winsorized Mean ( 6 / 20 )49.02766666666670.0914884348427775535.889227429898
Winsorized Mean ( 7 / 20 )49.030.091103405581101538.179661750988
Winsorized Mean ( 8 / 20 )49.02066666666670.0891735015068835549.722348436465
Winsorized Mean ( 9 / 20 )48.98316666666670.0820222829261773597.193407927369
Winsorized Mean ( 10 / 20 )48.97816666666670.080568773186676607.905081950117
Winsorized Mean ( 11 / 20 )48.96166666666670.0777959690859777629.359942962543
Winsorized Mean ( 12 / 20 )48.95966666666670.0774709592633926631.97444735658
Winsorized Mean ( 13 / 20 )48.95966666666670.0774709592633926631.97444735658
Winsorized Mean ( 14 / 20 )48.98066666666670.0723245457965027677.234348688232
Winsorized Mean ( 15 / 20 )49.00316666666670.0598880743562036818.245822619117
Winsorized Mean ( 16 / 20 )48.98450.0537231998617901911.794162038356
Winsorized Mean ( 17 / 20 )48.98733333333330.0524559899832461933.874917792598
Winsorized Mean ( 18 / 20 )48.98733333333330.0524559899832461933.874917792598
Winsorized Mean ( 19 / 20 )48.9810.0515147392653977950.815255953365
Winsorized Mean ( 20 / 20 )49.01766666666670.04624692181948731059.91198415311
Trimmed Mean ( 1 / 20 )49.05534482758620.101847190945668481.656336047162
Trimmed Mean ( 2 / 20 )49.03821428571430.0976111112284379502.38352651217
Trimmed Mean ( 3 / 20 )49.01962962962960.0924149798947239530.429478916418
Trimmed Mean ( 4 / 20 )49.01192307692310.0905830112949405541.071911567822
Trimmed Mean ( 5 / 20 )49.00480.0886967960675755552.497972561091
Trimmed Mean ( 6 / 20 )48.99833333333330.0869628055597762563.44011693198
Trimmed Mean ( 7 / 20 )48.99195652173910.0849999258682357576.376461759331
Trimmed Mean ( 8 / 20 )48.98454545454550.0825085392117683593.690615813966
Trimmed Mean ( 9 / 20 )48.97809523809520.0797784665662981613.926255368585
Trimmed Mean ( 10 / 20 )48.977250.078164838560439626.589281088702
Trimmed Mean ( 11 / 20 )48.97710526315790.0763050588423942641.859216232551
Trimmed Mean ( 12 / 20 )48.97944444444440.0744364482793981658.003512749554
Trimmed Mean ( 13 / 20 )48.98235294117650.0718386720311777681.838229413795
Trimmed Mean ( 14 / 20 )48.9856250.0680872564873027719.453647087912
Trimmed Mean ( 15 / 20 )48.98633333333330.0643669139920366761.048344486328
Trimmed Mean ( 16 / 20 )48.98392857142860.062963286702738777.976041858984
Trimmed Mean ( 17 / 20 )48.98384615384620.0625830572379972782.70139420587
Trimmed Mean ( 18 / 20 )48.98333333333330.0620094273649225789.933650653936
Trimmed Mean ( 19 / 20 )48.98272727272730.0606465232893996807.675767974138
Trimmed Mean ( 20 / 20 )48.9830.0583595930868538839.330732260264
Median49.04
Midrange49.54
Midmean - Weighted Average at Xnp48.9632258064516
Midmean - Weighted Average at X(n+1)p48.9863333333333
Midmean - Empirical Distribution Function48.9632258064516
Midmean - Empirical Distribution Function - Averaging48.9863333333333
Midmean - Empirical Distribution Function - Interpolation48.9863333333333
Midmean - Closest Observation48.9632258064516
Midmean - True Basic - Statistics Graphics Toolkit48.9863333333333
Midmean - MS Excel (old versions)48.985625
Number of observations60



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')