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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 15 Dec 2008 01:22:41 -0700
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/Dec/15/t1229329419jge3djqmurginta.htm/, Retrieved Wed, 15 May 2024 01:40:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33614, Retrieved Wed, 15 May 2024 01:40:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency ...] [2008-12-15 08:22:41] [5c47fb92bd9179cc1ad56f5160f63d38] [Current]
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Dataseries X:
129.5
103.7
114.2
123.5
111.3
126.5
119.6
116.5
116.7
119.4
124
130.6
120.1
113.2
111.1
126
115.8
111
128.7
112.6
114.7
118.5
124.8
128.6
127
111.8
100.6
122.9
117.8
108.1
129.6
111.4
110
115.2
118.8
116.2
126.3
106.7
96.5
119.1
109.6
110.3
118.8
104.5
107.7
127.7
118.5
120.1
127.4
107.8
106.5
124.6
101.9
106.5
119.4
103.3
99.6
120.9
111.7
123.9




Summary of computational 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 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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33614&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33614&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33614&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean116.1551.11217561766107104.439441177713
Geometric Mean115.836104130157
Harmonic Mean115.512640880758
Quadratic Mean116.468721838383
Winsorized Mean ( 1 / 20 )116.191.09422392073129106.184847359531
Winsorized Mean ( 2 / 20 )116.221.08518216857035107.097226038197
Winsorized Mean ( 3 / 20 )116.2451.0616781966398109.491746527257
Winsorized Mean ( 4 / 20 )116.3316666666671.03974000353594111.885342750156
Winsorized Mean ( 5 / 20 )116.291.01807867121896114.224964423196
Winsorized Mean ( 6 / 20 )116.340.995958499804753116.812096109233
Winsorized Mean ( 7 / 20 )116.5266666666670.942561921317582123.627598390329
Winsorized Mean ( 8 / 20 )116.460.930184964292914125.200905702155
Winsorized Mean ( 9 / 20 )116.460.919297816040194126.683646983567
Winsorized Mean ( 10 / 20 )116.5766666666670.880986756304218132.325106855989
Winsorized Mean ( 11 / 20 )116.3750.839143446118625138.683082777183
Winsorized Mean ( 12 / 20 )116.3950.822028718895676141.594809675709
Winsorized Mean ( 13 / 20 )116.590.746410241480897156.200964993034
Winsorized Mean ( 14 / 20 )116.660.727833252151792160.283965668101
Winsorized Mean ( 15 / 20 )116.6350.699510825849197166.737948420465
Winsorized Mean ( 16 / 20 )116.6616666666670.64484523464769180.914210725934
Winsorized Mean ( 17 / 20 )116.1233333333330.552177848747878210.300600787691
Winsorized Mean ( 18 / 20 )115.9433333333330.508655959487757227.940577851667
Winsorized Mean ( 19 / 20 )115.9750.50376898682868230.214648047480
Winsorized Mean ( 20 / 20 )115.9083333333330.465634198868928248.925731002762
Trimmed Mean ( 1 / 20 )116.2448275862071.06975460210947108.664947415961
Trimmed Mean ( 2 / 20 )116.3035714285711.03943342548291111.891313649586
Trimmed Mean ( 3 / 20 )116.351.00780237072982115.449222366627
Trimmed Mean ( 4 / 20 )116.3903846153850.979700679253874118.801984197894
Trimmed Mean ( 5 / 20 )116.4080.952971036243163122.152715636467
Trimmed Mean ( 6 / 20 )116.43750.926350963812328125.694800943273
Trimmed Mean ( 7 / 20 )116.4586956521740.899068632884754129.532597837947
Trimmed Mean ( 8 / 20 )116.4454545454550.879328343439258132.425453375026
Trimmed Mean ( 9 / 20 )116.4428571428570.856390494426899135.969347979255
Trimmed Mean ( 10 / 20 )116.440.828512723700326140.540991911328
Trimmed Mean ( 11 / 20 )116.4184210526320.80141992820565145.265193633615
Trimmed Mean ( 12 / 20 )116.4250.775880196528484150.055382932725
Trimmed Mean ( 13 / 20 )116.4294117647060.744780164861317156.327218765803
Trimmed Mean ( 14 / 20 )116.406250.722896524462973161.027541371120
Trimmed Mean ( 15 / 20 )116.370.69576964744005167.253631181183
Trimmed Mean ( 16 / 20 )116.3321428571430.664123195116509175.166510841011
Trimmed Mean ( 17 / 20 )116.2846153846150.634657807439867183.224115454742
Trimmed Mean ( 18 / 20 )116.3083333333330.62208498961116186.965342799917
Trimmed Mean ( 19 / 20 )116.3636363636360.613856782602768189.561538882493
Trimmed Mean ( 20 / 20 )116.4250.596960502969219195.029653420811
Median116.6
Midrange113.55
Midmean - Weighted Average at Xnp116.164516129032
Midmean - Weighted Average at X(n+1)p116.37
Midmean - Empirical Distribution Function116.164516129032
Midmean - Empirical Distribution Function - Averaging116.37
Midmean - Empirical Distribution Function - Interpolation116.37
Midmean - Closest Observation116.164516129032
Midmean - True Basic - Statistics Graphics Toolkit116.37
Midmean - MS Excel (old versions)116.40625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 116.155 & 1.11217561766107 & 104.439441177713 \tabularnewline
Geometric Mean & 115.836104130157 &  &  \tabularnewline
Harmonic Mean & 115.512640880758 &  &  \tabularnewline
Quadratic Mean & 116.468721838383 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 116.19 & 1.09422392073129 & 106.184847359531 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 116.22 & 1.08518216857035 & 107.097226038197 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 116.245 & 1.0616781966398 & 109.491746527257 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 116.331666666667 & 1.03974000353594 & 111.885342750156 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 116.29 & 1.01807867121896 & 114.224964423196 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 116.34 & 0.995958499804753 & 116.812096109233 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 116.526666666667 & 0.942561921317582 & 123.627598390329 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 116.46 & 0.930184964292914 & 125.200905702155 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 116.46 & 0.919297816040194 & 126.683646983567 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 116.576666666667 & 0.880986756304218 & 132.325106855989 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 116.375 & 0.839143446118625 & 138.683082777183 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 116.395 & 0.822028718895676 & 141.594809675709 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 116.59 & 0.746410241480897 & 156.200964993034 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 116.66 & 0.727833252151792 & 160.283965668101 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 116.635 & 0.699510825849197 & 166.737948420465 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 116.661666666667 & 0.64484523464769 & 180.914210725934 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 116.123333333333 & 0.552177848747878 & 210.300600787691 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 115.943333333333 & 0.508655959487757 & 227.940577851667 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 115.975 & 0.50376898682868 & 230.214648047480 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 115.908333333333 & 0.465634198868928 & 248.925731002762 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 116.244827586207 & 1.06975460210947 & 108.664947415961 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 116.303571428571 & 1.03943342548291 & 111.891313649586 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 116.35 & 1.00780237072982 & 115.449222366627 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 116.390384615385 & 0.979700679253874 & 118.801984197894 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 116.408 & 0.952971036243163 & 122.152715636467 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 116.4375 & 0.926350963812328 & 125.694800943273 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 116.458695652174 & 0.899068632884754 & 129.532597837947 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 116.445454545455 & 0.879328343439258 & 132.425453375026 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 116.442857142857 & 0.856390494426899 & 135.969347979255 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 116.44 & 0.828512723700326 & 140.540991911328 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 116.418421052632 & 0.80141992820565 & 145.265193633615 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 116.425 & 0.775880196528484 & 150.055382932725 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 116.429411764706 & 0.744780164861317 & 156.327218765803 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 116.40625 & 0.722896524462973 & 161.027541371120 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 116.37 & 0.69576964744005 & 167.253631181183 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 116.332142857143 & 0.664123195116509 & 175.166510841011 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 116.284615384615 & 0.634657807439867 & 183.224115454742 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 116.308333333333 & 0.62208498961116 & 186.965342799917 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 116.363636363636 & 0.613856782602768 & 189.561538882493 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 116.425 & 0.596960502969219 & 195.029653420811 \tabularnewline
Median & 116.6 &  &  \tabularnewline
Midrange & 113.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.164516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.37 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 116.164516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.37 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.37 &  &  \tabularnewline
Midmean - Closest Observation & 116.164516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.37 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.40625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33614&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]116.155[/C][C]1.11217561766107[/C][C]104.439441177713[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]115.836104130157[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]115.512640880758[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]116.468721838383[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]116.19[/C][C]1.09422392073129[/C][C]106.184847359531[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]116.22[/C][C]1.08518216857035[/C][C]107.097226038197[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]116.245[/C][C]1.0616781966398[/C][C]109.491746527257[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]116.331666666667[/C][C]1.03974000353594[/C][C]111.885342750156[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]116.29[/C][C]1.01807867121896[/C][C]114.224964423196[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]116.34[/C][C]0.995958499804753[/C][C]116.812096109233[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]116.526666666667[/C][C]0.942561921317582[/C][C]123.627598390329[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]116.46[/C][C]0.930184964292914[/C][C]125.200905702155[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]116.46[/C][C]0.919297816040194[/C][C]126.683646983567[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]116.576666666667[/C][C]0.880986756304218[/C][C]132.325106855989[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]116.375[/C][C]0.839143446118625[/C][C]138.683082777183[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]116.395[/C][C]0.822028718895676[/C][C]141.594809675709[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]116.59[/C][C]0.746410241480897[/C][C]156.200964993034[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]116.66[/C][C]0.727833252151792[/C][C]160.283965668101[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]116.635[/C][C]0.699510825849197[/C][C]166.737948420465[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]116.661666666667[/C][C]0.64484523464769[/C][C]180.914210725934[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]116.123333333333[/C][C]0.552177848747878[/C][C]210.300600787691[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]115.943333333333[/C][C]0.508655959487757[/C][C]227.940577851667[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]115.975[/C][C]0.50376898682868[/C][C]230.214648047480[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]115.908333333333[/C][C]0.465634198868928[/C][C]248.925731002762[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]116.244827586207[/C][C]1.06975460210947[/C][C]108.664947415961[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]116.303571428571[/C][C]1.03943342548291[/C][C]111.891313649586[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]116.35[/C][C]1.00780237072982[/C][C]115.449222366627[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]116.390384615385[/C][C]0.979700679253874[/C][C]118.801984197894[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]116.408[/C][C]0.952971036243163[/C][C]122.152715636467[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]116.4375[/C][C]0.926350963812328[/C][C]125.694800943273[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]116.458695652174[/C][C]0.899068632884754[/C][C]129.532597837947[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]116.445454545455[/C][C]0.879328343439258[/C][C]132.425453375026[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]116.442857142857[/C][C]0.856390494426899[/C][C]135.969347979255[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]116.44[/C][C]0.828512723700326[/C][C]140.540991911328[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]116.418421052632[/C][C]0.80141992820565[/C][C]145.265193633615[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]116.425[/C][C]0.775880196528484[/C][C]150.055382932725[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]116.429411764706[/C][C]0.744780164861317[/C][C]156.327218765803[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]116.40625[/C][C]0.722896524462973[/C][C]161.027541371120[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]116.37[/C][C]0.69576964744005[/C][C]167.253631181183[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]116.332142857143[/C][C]0.664123195116509[/C][C]175.166510841011[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]116.284615384615[/C][C]0.634657807439867[/C][C]183.224115454742[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]116.308333333333[/C][C]0.62208498961116[/C][C]186.965342799917[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]116.363636363636[/C][C]0.613856782602768[/C][C]189.561538882493[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]116.425[/C][C]0.596960502969219[/C][C]195.029653420811[/C][/ROW]
[ROW][C]Median[/C][C]116.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]113.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.164516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]116.164516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]116.164516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.37[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.40625[/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=33614&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33614&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 Mean116.1551.11217561766107104.439441177713
Geometric Mean115.836104130157
Harmonic Mean115.512640880758
Quadratic Mean116.468721838383
Winsorized Mean ( 1 / 20 )116.191.09422392073129106.184847359531
Winsorized Mean ( 2 / 20 )116.221.08518216857035107.097226038197
Winsorized Mean ( 3 / 20 )116.2451.0616781966398109.491746527257
Winsorized Mean ( 4 / 20 )116.3316666666671.03974000353594111.885342750156
Winsorized Mean ( 5 / 20 )116.291.01807867121896114.224964423196
Winsorized Mean ( 6 / 20 )116.340.995958499804753116.812096109233
Winsorized Mean ( 7 / 20 )116.5266666666670.942561921317582123.627598390329
Winsorized Mean ( 8 / 20 )116.460.930184964292914125.200905702155
Winsorized Mean ( 9 / 20 )116.460.919297816040194126.683646983567
Winsorized Mean ( 10 / 20 )116.5766666666670.880986756304218132.325106855989
Winsorized Mean ( 11 / 20 )116.3750.839143446118625138.683082777183
Winsorized Mean ( 12 / 20 )116.3950.822028718895676141.594809675709
Winsorized Mean ( 13 / 20 )116.590.746410241480897156.200964993034
Winsorized Mean ( 14 / 20 )116.660.727833252151792160.283965668101
Winsorized Mean ( 15 / 20 )116.6350.699510825849197166.737948420465
Winsorized Mean ( 16 / 20 )116.6616666666670.64484523464769180.914210725934
Winsorized Mean ( 17 / 20 )116.1233333333330.552177848747878210.300600787691
Winsorized Mean ( 18 / 20 )115.9433333333330.508655959487757227.940577851667
Winsorized Mean ( 19 / 20 )115.9750.50376898682868230.214648047480
Winsorized Mean ( 20 / 20 )115.9083333333330.465634198868928248.925731002762
Trimmed Mean ( 1 / 20 )116.2448275862071.06975460210947108.664947415961
Trimmed Mean ( 2 / 20 )116.3035714285711.03943342548291111.891313649586
Trimmed Mean ( 3 / 20 )116.351.00780237072982115.449222366627
Trimmed Mean ( 4 / 20 )116.3903846153850.979700679253874118.801984197894
Trimmed Mean ( 5 / 20 )116.4080.952971036243163122.152715636467
Trimmed Mean ( 6 / 20 )116.43750.926350963812328125.694800943273
Trimmed Mean ( 7 / 20 )116.4586956521740.899068632884754129.532597837947
Trimmed Mean ( 8 / 20 )116.4454545454550.879328343439258132.425453375026
Trimmed Mean ( 9 / 20 )116.4428571428570.856390494426899135.969347979255
Trimmed Mean ( 10 / 20 )116.440.828512723700326140.540991911328
Trimmed Mean ( 11 / 20 )116.4184210526320.80141992820565145.265193633615
Trimmed Mean ( 12 / 20 )116.4250.775880196528484150.055382932725
Trimmed Mean ( 13 / 20 )116.4294117647060.744780164861317156.327218765803
Trimmed Mean ( 14 / 20 )116.406250.722896524462973161.027541371120
Trimmed Mean ( 15 / 20 )116.370.69576964744005167.253631181183
Trimmed Mean ( 16 / 20 )116.3321428571430.664123195116509175.166510841011
Trimmed Mean ( 17 / 20 )116.2846153846150.634657807439867183.224115454742
Trimmed Mean ( 18 / 20 )116.3083333333330.62208498961116186.965342799917
Trimmed Mean ( 19 / 20 )116.3636363636360.613856782602768189.561538882493
Trimmed Mean ( 20 / 20 )116.4250.596960502969219195.029653420811
Median116.6
Midrange113.55
Midmean - Weighted Average at Xnp116.164516129032
Midmean - Weighted Average at X(n+1)p116.37
Midmean - Empirical Distribution Function116.164516129032
Midmean - Empirical Distribution Function - Averaging116.37
Midmean - Empirical Distribution Function - Interpolation116.37
Midmean - Closest Observation116.164516129032
Midmean - True Basic - Statistics Graphics Toolkit116.37
Midmean - MS Excel (old versions)116.40625
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')