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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 10:25:46 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t1331134132srb8umuia9wgnde.htm/, Retrieved Mon, 29 Apr 2024 06:09:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163618, Retrieved Mon, 29 Apr 2024 06:09:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-07 15:25:46] [48b933cf7efbf78e0756284cf4760cf4] [Current]
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Dataseries X:
1,05
1,07
1,07
1,06
1,08
1,11
1,09
1,1
1,11
1,12
1,13
1,13
1,13
1,18
1,21
1,22
1,22
1,24
1,24
1,25
1,25
1,26
1,26
1,26
1,26
1,3
1,32
1,34
1,35
1,35
1,34
1,33
1,32
1,32
1,33
1,31
1,33
1,34
1,34
1,33
1,3
1,28
1,27
1,28
1,27
1,29
1,28
1,29
1,28
1,28
1,28
1,25
1,24
1,24
1,25
1,25
1,26
1,26
1,26
1,28




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=163618&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=163618&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163618&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 Mean1.240666666666670.0110593332178801112.182772887323
Geometric Mean1.23763012747276
Harmonic Mean1.23446417308347
Quadratic Mean1.24357146959875
Winsorized Mean ( 1 / 20 )1.240833333333330.0110117853319004112.682303181004
Winsorized Mean ( 2 / 20 )1.240833333333330.0108671787685649114.181735642617
Winsorized Mean ( 3 / 20 )1.240833333333330.0108671787685649114.181735642617
Winsorized Mean ( 4 / 20 )1.24150.0106930068493491116.103918896823
Winsorized Mean ( 5 / 20 )1.242333333333330.0104836883433552118.501551424003
Winsorized Mean ( 6 / 20 )1.242333333333330.0100882172885135123.146964206238
Winsorized Mean ( 7 / 20 )1.24350.00981416306213472126.704640235468
Winsorized Mean ( 8 / 20 )1.24350.00981416306213472126.704640235468
Winsorized Mean ( 9 / 20 )1.2450.00947342402259417131.420276030152
Winsorized Mean ( 10 / 20 )1.2450.00885699315138134140.566892027666
Winsorized Mean ( 11 / 20 )1.2450.00885699315138134140.566892027666
Winsorized Mean ( 12 / 20 )1.2450.00885699315138134140.566892027666
Winsorized Mean ( 13 / 20 )1.253666666666670.00624349001827394200.795815000478
Winsorized Mean ( 14 / 20 )1.258333333333330.00454212341558556277.036359033215
Winsorized Mean ( 15 / 20 )1.260833333333330.0041051962845691307.131071435644
Winsorized Mean ( 16 / 20 )1.258166666666670.00369372399981609340.6228150044
Winsorized Mean ( 17 / 20 )1.263833333333330.00277286759996404455.78567593697
Winsorized Mean ( 18 / 20 )1.260833333333330.00232028230635145543.39652113968
Winsorized Mean ( 19 / 20 )1.260833333333330.00232028230635145543.39652113968
Winsorized Mean ( 20 / 20 )1.260833333333330.00232028230635145543.39652113968
Trimmed Mean ( 1 / 20 )1.242068965517240.0107851442176216115.164798954459
Trimmed Mean ( 2 / 20 )1.243392857142860.0105013196007964118.403486838793
Trimmed Mean ( 3 / 20 )1.244814814814810.0102407795986591121.554692474566
Trimmed Mean ( 4 / 20 )1.246346153846150.00990919879078286125.776682874246
Trimmed Mean ( 5 / 20 )1.24780.0095587976359424130.5394305355
Trimmed Mean ( 6 / 20 )1.249166666666670.00918598866246066135.986088440485
Trimmed Mean ( 7 / 20 )1.250652173913040.00883231973354998141.599513111191
Trimmed Mean ( 8 / 20 )1.252045454545450.00845695196376294148.049256979385
Trimmed Mean ( 9 / 20 )1.253571428571430.00795473130435215157.588154848874
Trimmed Mean ( 10 / 20 )1.2550.00739022223044644169.818979844695
Trimmed Mean ( 11 / 20 )1.256578947368420.00681263485820008184.448304293886
Trimmed Mean ( 12 / 20 )1.258333333333330.00598277952072871210.325874281937
Trimmed Mean ( 13 / 20 )1.260294117647060.00469165630456356268.624561526635
Trimmed Mean ( 14 / 20 )1.261250.00398459736096789316.531354549116
Trimmed Mean ( 15 / 20 )1.261666666666670.00365410596746399345.273694277203
Trimmed Mean ( 16 / 20 )1.261785714285710.0033354585062195378.29453190106
Trimmed Mean ( 17 / 20 )1.262307692307690.00300295712245279420.354883814208
Trimmed Mean ( 18 / 20 )1.262083333333330.00288544364425206437.396632523897
Trimmed Mean ( 19 / 20 )1.262272727272730.00286279448904412440.923276925196
Trimmed Mean ( 20 / 20 )1.26250.00279802561968633451.211022199837
Median1.26
Midrange1.2
Midmean - Weighted Average at Xnp1.26125
Midmean - Weighted Average at X(n+1)p1.26290322580645
Midmean - Empirical Distribution Function1.26125
Midmean - Empirical Distribution Function - Averaging1.26290322580645
Midmean - Empirical Distribution Function - Interpolation1.26290322580645
Midmean - Closest Observation1.26125
Midmean - True Basic - Statistics Graphics Toolkit1.26290322580645
Midmean - MS Excel (old versions)1.26125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.24066666666667 & 0.0110593332178801 & 112.182772887323 \tabularnewline
Geometric Mean & 1.23763012747276 &  &  \tabularnewline
Harmonic Mean & 1.23446417308347 &  &  \tabularnewline
Quadratic Mean & 1.24357146959875 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.24083333333333 & 0.0110117853319004 & 112.682303181004 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.24083333333333 & 0.0108671787685649 & 114.181735642617 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.24083333333333 & 0.0108671787685649 & 114.181735642617 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.2415 & 0.0106930068493491 & 116.103918896823 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.24233333333333 & 0.0104836883433552 & 118.501551424003 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.24233333333333 & 0.0100882172885135 & 123.146964206238 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.2435 & 0.00981416306213472 & 126.704640235468 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.2435 & 0.00981416306213472 & 126.704640235468 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.245 & 0.00947342402259417 & 131.420276030152 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.245 & 0.00885699315138134 & 140.566892027666 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.245 & 0.00885699315138134 & 140.566892027666 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.245 & 0.00885699315138134 & 140.566892027666 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.25366666666667 & 0.00624349001827394 & 200.795815000478 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.25833333333333 & 0.00454212341558556 & 277.036359033215 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.26083333333333 & 0.0041051962845691 & 307.131071435644 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.25816666666667 & 0.00369372399981609 & 340.6228150044 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.26383333333333 & 0.00277286759996404 & 455.78567593697 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.26083333333333 & 0.00232028230635145 & 543.39652113968 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.26083333333333 & 0.00232028230635145 & 543.39652113968 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.26083333333333 & 0.00232028230635145 & 543.39652113968 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.24206896551724 & 0.0107851442176216 & 115.164798954459 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.24339285714286 & 0.0105013196007964 & 118.403486838793 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.24481481481481 & 0.0102407795986591 & 121.554692474566 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.24634615384615 & 0.00990919879078286 & 125.776682874246 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.2478 & 0.0095587976359424 & 130.5394305355 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.24916666666667 & 0.00918598866246066 & 135.986088440485 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.25065217391304 & 0.00883231973354998 & 141.599513111191 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.25204545454545 & 0.00845695196376294 & 148.049256979385 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.25357142857143 & 0.00795473130435215 & 157.588154848874 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.255 & 0.00739022223044644 & 169.818979844695 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.25657894736842 & 0.00681263485820008 & 184.448304293886 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.25833333333333 & 0.00598277952072871 & 210.325874281937 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.26029411764706 & 0.00469165630456356 & 268.624561526635 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.26125 & 0.00398459736096789 & 316.531354549116 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.26166666666667 & 0.00365410596746399 & 345.273694277203 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.26178571428571 & 0.0033354585062195 & 378.29453190106 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.26230769230769 & 0.00300295712245279 & 420.354883814208 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.26208333333333 & 0.00288544364425206 & 437.396632523897 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.26227272727273 & 0.00286279448904412 & 440.923276925196 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.2625 & 0.00279802561968633 & 451.211022199837 \tabularnewline
Median & 1.26 &  &  \tabularnewline
Midrange & 1.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.26125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.26290322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.26125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.26290322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.26290322580645 &  &  \tabularnewline
Midmean - Closest Observation & 1.26125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.26290322580645 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.26125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163618&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]1.24066666666667[/C][C]0.0110593332178801[/C][C]112.182772887323[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.23763012747276[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.23446417308347[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.24357146959875[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.24083333333333[/C][C]0.0110117853319004[/C][C]112.682303181004[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.24083333333333[/C][C]0.0108671787685649[/C][C]114.181735642617[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.24083333333333[/C][C]0.0108671787685649[/C][C]114.181735642617[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.2415[/C][C]0.0106930068493491[/C][C]116.103918896823[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.24233333333333[/C][C]0.0104836883433552[/C][C]118.501551424003[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.24233333333333[/C][C]0.0100882172885135[/C][C]123.146964206238[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.2435[/C][C]0.00981416306213472[/C][C]126.704640235468[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.2435[/C][C]0.00981416306213472[/C][C]126.704640235468[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.245[/C][C]0.00947342402259417[/C][C]131.420276030152[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.245[/C][C]0.00885699315138134[/C][C]140.566892027666[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.245[/C][C]0.00885699315138134[/C][C]140.566892027666[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.245[/C][C]0.00885699315138134[/C][C]140.566892027666[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.25366666666667[/C][C]0.00624349001827394[/C][C]200.795815000478[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.25833333333333[/C][C]0.00454212341558556[/C][C]277.036359033215[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.26083333333333[/C][C]0.0041051962845691[/C][C]307.131071435644[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.25816666666667[/C][C]0.00369372399981609[/C][C]340.6228150044[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.26383333333333[/C][C]0.00277286759996404[/C][C]455.78567593697[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.26083333333333[/C][C]0.00232028230635145[/C][C]543.39652113968[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.26083333333333[/C][C]0.00232028230635145[/C][C]543.39652113968[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.26083333333333[/C][C]0.00232028230635145[/C][C]543.39652113968[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.24206896551724[/C][C]0.0107851442176216[/C][C]115.164798954459[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.24339285714286[/C][C]0.0105013196007964[/C][C]118.403486838793[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.24481481481481[/C][C]0.0102407795986591[/C][C]121.554692474566[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.24634615384615[/C][C]0.00990919879078286[/C][C]125.776682874246[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.2478[/C][C]0.0095587976359424[/C][C]130.5394305355[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.24916666666667[/C][C]0.00918598866246066[/C][C]135.986088440485[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.25065217391304[/C][C]0.00883231973354998[/C][C]141.599513111191[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.25204545454545[/C][C]0.00845695196376294[/C][C]148.049256979385[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.25357142857143[/C][C]0.00795473130435215[/C][C]157.588154848874[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.255[/C][C]0.00739022223044644[/C][C]169.818979844695[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.25657894736842[/C][C]0.00681263485820008[/C][C]184.448304293886[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.25833333333333[/C][C]0.00598277952072871[/C][C]210.325874281937[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.26029411764706[/C][C]0.00469165630456356[/C][C]268.624561526635[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.26125[/C][C]0.00398459736096789[/C][C]316.531354549116[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.26166666666667[/C][C]0.00365410596746399[/C][C]345.273694277203[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.26178571428571[/C][C]0.0033354585062195[/C][C]378.29453190106[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.26230769230769[/C][C]0.00300295712245279[/C][C]420.354883814208[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.26208333333333[/C][C]0.00288544364425206[/C][C]437.396632523897[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.26227272727273[/C][C]0.00286279448904412[/C][C]440.923276925196[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.2625[/C][C]0.00279802561968633[/C][C]451.211022199837[/C][/ROW]
[ROW][C]Median[/C][C]1.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.26125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.26290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.26125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.26290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.26290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.26125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.26290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.26125[/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=163618&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163618&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 Mean1.240666666666670.0110593332178801112.182772887323
Geometric Mean1.23763012747276
Harmonic Mean1.23446417308347
Quadratic Mean1.24357146959875
Winsorized Mean ( 1 / 20 )1.240833333333330.0110117853319004112.682303181004
Winsorized Mean ( 2 / 20 )1.240833333333330.0108671787685649114.181735642617
Winsorized Mean ( 3 / 20 )1.240833333333330.0108671787685649114.181735642617
Winsorized Mean ( 4 / 20 )1.24150.0106930068493491116.103918896823
Winsorized Mean ( 5 / 20 )1.242333333333330.0104836883433552118.501551424003
Winsorized Mean ( 6 / 20 )1.242333333333330.0100882172885135123.146964206238
Winsorized Mean ( 7 / 20 )1.24350.00981416306213472126.704640235468
Winsorized Mean ( 8 / 20 )1.24350.00981416306213472126.704640235468
Winsorized Mean ( 9 / 20 )1.2450.00947342402259417131.420276030152
Winsorized Mean ( 10 / 20 )1.2450.00885699315138134140.566892027666
Winsorized Mean ( 11 / 20 )1.2450.00885699315138134140.566892027666
Winsorized Mean ( 12 / 20 )1.2450.00885699315138134140.566892027666
Winsorized Mean ( 13 / 20 )1.253666666666670.00624349001827394200.795815000478
Winsorized Mean ( 14 / 20 )1.258333333333330.00454212341558556277.036359033215
Winsorized Mean ( 15 / 20 )1.260833333333330.0041051962845691307.131071435644
Winsorized Mean ( 16 / 20 )1.258166666666670.00369372399981609340.6228150044
Winsorized Mean ( 17 / 20 )1.263833333333330.00277286759996404455.78567593697
Winsorized Mean ( 18 / 20 )1.260833333333330.00232028230635145543.39652113968
Winsorized Mean ( 19 / 20 )1.260833333333330.00232028230635145543.39652113968
Winsorized Mean ( 20 / 20 )1.260833333333330.00232028230635145543.39652113968
Trimmed Mean ( 1 / 20 )1.242068965517240.0107851442176216115.164798954459
Trimmed Mean ( 2 / 20 )1.243392857142860.0105013196007964118.403486838793
Trimmed Mean ( 3 / 20 )1.244814814814810.0102407795986591121.554692474566
Trimmed Mean ( 4 / 20 )1.246346153846150.00990919879078286125.776682874246
Trimmed Mean ( 5 / 20 )1.24780.0095587976359424130.5394305355
Trimmed Mean ( 6 / 20 )1.249166666666670.00918598866246066135.986088440485
Trimmed Mean ( 7 / 20 )1.250652173913040.00883231973354998141.599513111191
Trimmed Mean ( 8 / 20 )1.252045454545450.00845695196376294148.049256979385
Trimmed Mean ( 9 / 20 )1.253571428571430.00795473130435215157.588154848874
Trimmed Mean ( 10 / 20 )1.2550.00739022223044644169.818979844695
Trimmed Mean ( 11 / 20 )1.256578947368420.00681263485820008184.448304293886
Trimmed Mean ( 12 / 20 )1.258333333333330.00598277952072871210.325874281937
Trimmed Mean ( 13 / 20 )1.260294117647060.00469165630456356268.624561526635
Trimmed Mean ( 14 / 20 )1.261250.00398459736096789316.531354549116
Trimmed Mean ( 15 / 20 )1.261666666666670.00365410596746399345.273694277203
Trimmed Mean ( 16 / 20 )1.261785714285710.0033354585062195378.29453190106
Trimmed Mean ( 17 / 20 )1.262307692307690.00300295712245279420.354883814208
Trimmed Mean ( 18 / 20 )1.262083333333330.00288544364425206437.396632523897
Trimmed Mean ( 19 / 20 )1.262272727272730.00286279448904412440.923276925196
Trimmed Mean ( 20 / 20 )1.26250.00279802561968633451.211022199837
Median1.26
Midrange1.2
Midmean - Weighted Average at Xnp1.26125
Midmean - Weighted Average at X(n+1)p1.26290322580645
Midmean - Empirical Distribution Function1.26125
Midmean - Empirical Distribution Function - Averaging1.26290322580645
Midmean - Empirical Distribution Function - Interpolation1.26290322580645
Midmean - Closest Observation1.26125
Midmean - True Basic - Statistics Graphics Toolkit1.26290322580645
Midmean - MS Excel (old versions)1.26125
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')