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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Oct 2011 11:01:12 -0400
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/Oct/18/t1318950124zd0gmlcf54iimsx.htm/, Retrieved Thu, 16 May 2024 17:51:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132134, Retrieved Thu, 16 May 2024 17:51:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [] [2011-10-18 14:52:10] [c804c9d9debe6cbacd66d26bebf6dd2f]
- RMPD    [Central Tendency] [] [2011-10-18 15:01:12] [c81f0c87bb000ca3e7f952ee43cfaf8d] [Current]
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Dataseries X:
99.96
100.21
100.37
101.11
101.04
101.02
101.02
101.11
100.96
101.27
101.01
101.07
101.07
101.07
101.24
101.29
101.67
101.66
101.66
101.66
101.8
102.32
102.38
102.4
102.39
102.78
102.81
102.82
102.96
102.98
102.98
103.03
103.26
103.47
103.58
103.52
103.52
103.52
103.54
103.74
103.94
103.9
103.9
103.9
103.87
104.51
104.82
104.87
104.87
105.13
105.22
105.02
104.7
104.76
104.76
104.57
104.64
104.72
104.49
104.42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132134&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]2 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=132134&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132134&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 time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean102.8713333333330.194772134961444528.162477418535
Geometric Mean102.860439062122
Harmonic Mean102.849530211868
Quadratic Mean102.882211565784
Winsorized Mean ( 1 / 20 )102.8740.193456399560918531.768399667781
Winsorized Mean ( 2 / 20 )102.8756666666670.191532234850475537.119335275233
Winsorized Mean ( 3 / 20 )102.8976666666670.184227102336776558.537073869645
Winsorized Mean ( 4 / 20 )102.9010.18363909274493560.34365266075
Winsorized Mean ( 5 / 20 )102.8976666666670.182743741214081563.070811525763
Winsorized Mean ( 6 / 20 )102.8916666666670.181685947248254566.316042737617
Winsorized Mean ( 7 / 20 )102.8940.181280006283004567.597067706228
Winsorized Mean ( 8 / 20 )102.8926666666670.179664449741572572.6935229238
Winsorized Mean ( 9 / 20 )102.8896666666670.17914895589773574.3246794327
Winsorized Mean ( 10 / 20 )102.8796666666670.177451826305434579.761103667584
Winsorized Mean ( 11 / 20 )102.8741666666670.174049361734396591.06316530856
Winsorized Mean ( 12 / 20 )102.8621666666670.17208460861896597.741817191974
Winsorized Mean ( 13 / 20 )102.8860.166589281469622617.602759867606
Winsorized Mean ( 14 / 20 )102.8766666666670.16277218259732632.028550733216
Winsorized Mean ( 15 / 20 )102.7616666666670.143869088065997714.272037503477
Winsorized Mean ( 16 / 20 )102.8496666666670.125876131083887817.070446803969
Winsorized Mean ( 17 / 20 )102.8496666666670.125876131083887817.070446803969
Winsorized Mean ( 18 / 20 )102.8496666666670.125876131083887817.070446803969
Winsorized Mean ( 19 / 20 )102.8433333333330.124030401473357829.178428124534
Winsorized Mean ( 20 / 20 )102.8433333333330.111098436188546925.695598080219
Trimmed Mean ( 1 / 20 )102.8810344827590.190754652753733539.336959793999
Trimmed Mean ( 2 / 20 )102.8885714285710.187343948666726549.196129156027
Trimmed Mean ( 3 / 20 )102.8957407407410.184300024636981558.305626618426
Trimmed Mean ( 4 / 20 )102.8950.183775655907887559.894614396444
Trimmed Mean ( 5 / 20 )102.89320.183072738973071562.03452560534
Trimmed Mean ( 6 / 20 )102.8920833333330.182199660165168564.721598492881
Trimmed Mean ( 7 / 20 )102.8921739130430.181110346976584568.118694656063
Trimmed Mean ( 8 / 20 )102.8918181818180.179526412670768573.129138220518
Trimmed Mean ( 9 / 20 )102.8916666666670.177604042454683579.331783469514
Trimmed Mean ( 10 / 20 )102.8920.174915437444527588.238531162415
Trimmed Mean ( 11 / 20 )102.8939473684210.171499760283201599.965546298782
Trimmed Mean ( 12 / 20 )102.8969444444440.16752532120593614.217264015622
Trimmed Mean ( 13 / 20 )102.9020588235290.162329180428216633.909803228716
Trimmed Mean ( 14 / 20 )102.9043750.156451925974496657.737987941262
Trimmed Mean ( 15 / 20 )102.9083333333330.148991308342755690.700246061283
Trimmed Mean ( 16 / 20 )102.9292857142860.143726784250397716.145471779048
Trimmed Mean ( 17 / 20 )102.9407692307690.141748339376433726.222047352494
Trimmed Mean ( 18 / 20 )102.9541666666670.137888997399592746.645262553567
Trimmed Mean ( 19 / 20 )102.970.13093404043152786.426506511531
Trimmed Mean ( 20 / 20 )102.990.119344701996933862.962479915081
Median102.98
Midrange102.59
Midmean - Weighted Average at Xnp102.855483870968
Midmean - Weighted Average at X(n+1)p102.908333333333
Midmean - Empirical Distribution Function102.855483870968
Midmean - Empirical Distribution Function - Averaging102.908333333333
Midmean - Empirical Distribution Function - Interpolation102.908333333333
Midmean - Closest Observation102.855483870968
Midmean - True Basic - Statistics Graphics Toolkit102.908333333333
Midmean - MS Excel (old versions)102.904375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 102.871333333333 & 0.194772134961444 & 528.162477418535 \tabularnewline
Geometric Mean & 102.860439062122 &  &  \tabularnewline
Harmonic Mean & 102.849530211868 &  &  \tabularnewline
Quadratic Mean & 102.882211565784 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 102.874 & 0.193456399560918 & 531.768399667781 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 102.875666666667 & 0.191532234850475 & 537.119335275233 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 102.897666666667 & 0.184227102336776 & 558.537073869645 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 102.901 & 0.18363909274493 & 560.34365266075 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 102.897666666667 & 0.182743741214081 & 563.070811525763 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 102.891666666667 & 0.181685947248254 & 566.316042737617 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 102.894 & 0.181280006283004 & 567.597067706228 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 102.892666666667 & 0.179664449741572 & 572.6935229238 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 102.889666666667 & 0.17914895589773 & 574.3246794327 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 102.879666666667 & 0.177451826305434 & 579.761103667584 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 102.874166666667 & 0.174049361734396 & 591.06316530856 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 102.862166666667 & 0.17208460861896 & 597.741817191974 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 102.886 & 0.166589281469622 & 617.602759867606 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 102.876666666667 & 0.16277218259732 & 632.028550733216 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 102.761666666667 & 0.143869088065997 & 714.272037503477 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 102.849666666667 & 0.125876131083887 & 817.070446803969 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 102.849666666667 & 0.125876131083887 & 817.070446803969 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 102.849666666667 & 0.125876131083887 & 817.070446803969 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 102.843333333333 & 0.124030401473357 & 829.178428124534 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 102.843333333333 & 0.111098436188546 & 925.695598080219 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 102.881034482759 & 0.190754652753733 & 539.336959793999 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 102.888571428571 & 0.187343948666726 & 549.196129156027 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 102.895740740741 & 0.184300024636981 & 558.305626618426 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 102.895 & 0.183775655907887 & 559.894614396444 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 102.8932 & 0.183072738973071 & 562.03452560534 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 102.892083333333 & 0.182199660165168 & 564.721598492881 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 102.892173913043 & 0.181110346976584 & 568.118694656063 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 102.891818181818 & 0.179526412670768 & 573.129138220518 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 102.891666666667 & 0.177604042454683 & 579.331783469514 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 102.892 & 0.174915437444527 & 588.238531162415 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 102.893947368421 & 0.171499760283201 & 599.965546298782 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 102.896944444444 & 0.16752532120593 & 614.217264015622 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 102.902058823529 & 0.162329180428216 & 633.909803228716 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 102.904375 & 0.156451925974496 & 657.737987941262 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 102.908333333333 & 0.148991308342755 & 690.700246061283 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 102.929285714286 & 0.143726784250397 & 716.145471779048 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 102.940769230769 & 0.141748339376433 & 726.222047352494 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 102.954166666667 & 0.137888997399592 & 746.645262553567 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 102.97 & 0.13093404043152 & 786.426506511531 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 102.99 & 0.119344701996933 & 862.962479915081 \tabularnewline
Median & 102.98 &  &  \tabularnewline
Midrange & 102.59 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.855483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 102.908333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 102.855483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 102.908333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 102.908333333333 &  &  \tabularnewline
Midmean - Closest Observation & 102.855483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 102.908333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 102.904375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132134&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]102.871333333333[/C][C]0.194772134961444[/C][C]528.162477418535[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]102.860439062122[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]102.849530211868[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]102.882211565784[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]102.874[/C][C]0.193456399560918[/C][C]531.768399667781[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]102.875666666667[/C][C]0.191532234850475[/C][C]537.119335275233[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]102.897666666667[/C][C]0.184227102336776[/C][C]558.537073869645[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]102.901[/C][C]0.18363909274493[/C][C]560.34365266075[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]102.897666666667[/C][C]0.182743741214081[/C][C]563.070811525763[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]102.891666666667[/C][C]0.181685947248254[/C][C]566.316042737617[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]102.894[/C][C]0.181280006283004[/C][C]567.597067706228[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]102.892666666667[/C][C]0.179664449741572[/C][C]572.6935229238[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]102.889666666667[/C][C]0.17914895589773[/C][C]574.3246794327[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]102.879666666667[/C][C]0.177451826305434[/C][C]579.761103667584[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]102.874166666667[/C][C]0.174049361734396[/C][C]591.06316530856[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]102.862166666667[/C][C]0.17208460861896[/C][C]597.741817191974[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]102.886[/C][C]0.166589281469622[/C][C]617.602759867606[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]102.876666666667[/C][C]0.16277218259732[/C][C]632.028550733216[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]102.761666666667[/C][C]0.143869088065997[/C][C]714.272037503477[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]102.849666666667[/C][C]0.125876131083887[/C][C]817.070446803969[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]102.849666666667[/C][C]0.125876131083887[/C][C]817.070446803969[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]102.849666666667[/C][C]0.125876131083887[/C][C]817.070446803969[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]102.843333333333[/C][C]0.124030401473357[/C][C]829.178428124534[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]102.843333333333[/C][C]0.111098436188546[/C][C]925.695598080219[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]102.881034482759[/C][C]0.190754652753733[/C][C]539.336959793999[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]102.888571428571[/C][C]0.187343948666726[/C][C]549.196129156027[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]102.895740740741[/C][C]0.184300024636981[/C][C]558.305626618426[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]102.895[/C][C]0.183775655907887[/C][C]559.894614396444[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]102.8932[/C][C]0.183072738973071[/C][C]562.03452560534[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]102.892083333333[/C][C]0.182199660165168[/C][C]564.721598492881[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]102.892173913043[/C][C]0.181110346976584[/C][C]568.118694656063[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]102.891818181818[/C][C]0.179526412670768[/C][C]573.129138220518[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]102.891666666667[/C][C]0.177604042454683[/C][C]579.331783469514[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]102.892[/C][C]0.174915437444527[/C][C]588.238531162415[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]102.893947368421[/C][C]0.171499760283201[/C][C]599.965546298782[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]102.896944444444[/C][C]0.16752532120593[/C][C]614.217264015622[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]102.902058823529[/C][C]0.162329180428216[/C][C]633.909803228716[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]102.904375[/C][C]0.156451925974496[/C][C]657.737987941262[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]102.908333333333[/C][C]0.148991308342755[/C][C]690.700246061283[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]102.929285714286[/C][C]0.143726784250397[/C][C]716.145471779048[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]102.940769230769[/C][C]0.141748339376433[/C][C]726.222047352494[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]102.954166666667[/C][C]0.137888997399592[/C][C]746.645262553567[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]102.97[/C][C]0.13093404043152[/C][C]786.426506511531[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]102.99[/C][C]0.119344701996933[/C][C]862.962479915081[/C][/ROW]
[ROW][C]Median[/C][C]102.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102.59[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.855483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]102.908333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]102.855483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]102.908333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]102.908333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]102.855483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]102.908333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]102.904375[/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=132134&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132134&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 Mean102.8713333333330.194772134961444528.162477418535
Geometric Mean102.860439062122
Harmonic Mean102.849530211868
Quadratic Mean102.882211565784
Winsorized Mean ( 1 / 20 )102.8740.193456399560918531.768399667781
Winsorized Mean ( 2 / 20 )102.8756666666670.191532234850475537.119335275233
Winsorized Mean ( 3 / 20 )102.8976666666670.184227102336776558.537073869645
Winsorized Mean ( 4 / 20 )102.9010.18363909274493560.34365266075
Winsorized Mean ( 5 / 20 )102.8976666666670.182743741214081563.070811525763
Winsorized Mean ( 6 / 20 )102.8916666666670.181685947248254566.316042737617
Winsorized Mean ( 7 / 20 )102.8940.181280006283004567.597067706228
Winsorized Mean ( 8 / 20 )102.8926666666670.179664449741572572.6935229238
Winsorized Mean ( 9 / 20 )102.8896666666670.17914895589773574.3246794327
Winsorized Mean ( 10 / 20 )102.8796666666670.177451826305434579.761103667584
Winsorized Mean ( 11 / 20 )102.8741666666670.174049361734396591.06316530856
Winsorized Mean ( 12 / 20 )102.8621666666670.17208460861896597.741817191974
Winsorized Mean ( 13 / 20 )102.8860.166589281469622617.602759867606
Winsorized Mean ( 14 / 20 )102.8766666666670.16277218259732632.028550733216
Winsorized Mean ( 15 / 20 )102.7616666666670.143869088065997714.272037503477
Winsorized Mean ( 16 / 20 )102.8496666666670.125876131083887817.070446803969
Winsorized Mean ( 17 / 20 )102.8496666666670.125876131083887817.070446803969
Winsorized Mean ( 18 / 20 )102.8496666666670.125876131083887817.070446803969
Winsorized Mean ( 19 / 20 )102.8433333333330.124030401473357829.178428124534
Winsorized Mean ( 20 / 20 )102.8433333333330.111098436188546925.695598080219
Trimmed Mean ( 1 / 20 )102.8810344827590.190754652753733539.336959793999
Trimmed Mean ( 2 / 20 )102.8885714285710.187343948666726549.196129156027
Trimmed Mean ( 3 / 20 )102.8957407407410.184300024636981558.305626618426
Trimmed Mean ( 4 / 20 )102.8950.183775655907887559.894614396444
Trimmed Mean ( 5 / 20 )102.89320.183072738973071562.03452560534
Trimmed Mean ( 6 / 20 )102.8920833333330.182199660165168564.721598492881
Trimmed Mean ( 7 / 20 )102.8921739130430.181110346976584568.118694656063
Trimmed Mean ( 8 / 20 )102.8918181818180.179526412670768573.129138220518
Trimmed Mean ( 9 / 20 )102.8916666666670.177604042454683579.331783469514
Trimmed Mean ( 10 / 20 )102.8920.174915437444527588.238531162415
Trimmed Mean ( 11 / 20 )102.8939473684210.171499760283201599.965546298782
Trimmed Mean ( 12 / 20 )102.8969444444440.16752532120593614.217264015622
Trimmed Mean ( 13 / 20 )102.9020588235290.162329180428216633.909803228716
Trimmed Mean ( 14 / 20 )102.9043750.156451925974496657.737987941262
Trimmed Mean ( 15 / 20 )102.9083333333330.148991308342755690.700246061283
Trimmed Mean ( 16 / 20 )102.9292857142860.143726784250397716.145471779048
Trimmed Mean ( 17 / 20 )102.9407692307690.141748339376433726.222047352494
Trimmed Mean ( 18 / 20 )102.9541666666670.137888997399592746.645262553567
Trimmed Mean ( 19 / 20 )102.970.13093404043152786.426506511531
Trimmed Mean ( 20 / 20 )102.990.119344701996933862.962479915081
Median102.98
Midrange102.59
Midmean - Weighted Average at Xnp102.855483870968
Midmean - Weighted Average at X(n+1)p102.908333333333
Midmean - Empirical Distribution Function102.855483870968
Midmean - Empirical Distribution Function - Averaging102.908333333333
Midmean - Empirical Distribution Function - Interpolation102.908333333333
Midmean - Closest Observation102.855483870968
Midmean - True Basic - Statistics Graphics Toolkit102.908333333333
Midmean - MS Excel (old versions)102.904375
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')