Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 08 Oct 2015 17:49:59 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/08/t1444323083k171qe7tp9i0zjc.htm/, Retrieved Wed, 15 May 2024 17:11:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281556, Retrieved Wed, 15 May 2024 17:11:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-08 16:49:59] [f684f3a3d8618606ffff76ddc8e0eec7] [Current]
Feedback Forum

Post a new message
Dataseries X:
94,9
95,8
98,8
100,6
100,6
100,1
99,4
99,9
101
100,4
101,6
106,8
109,3
112,6
118,8
121,9
118,3
117,9
119,2
116,3
119,2
118,7
120,3
120,5
124,3
128,3
131,4
130,3
126,6
121,8
125,1
128,5
129,5
128,5
127,2
126,2
125,9
127,3
125,7
122,5
121,3
121,5
123,4
121,6
121,8
118,9
118,7
119,8
118,5
118,9
117,4
116
115,5
116,5
114,9
113,9
114,3
112
108
97,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281556&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=281556&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281556&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'Sir Maurice George Kendall' @ kendall.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean116.211.2985187127868589.4942821044084
Geometric Mean115.762662323379
Harmonic Mean115.2962150286
Quadratic Mean116.637245337842
Winsorized Mean ( 1 / 20 )116.2066666666671.290908817224590.0192679112034
Winsorized Mean ( 2 / 20 )116.2433333333331.2697532272074691.5479723481266
Winsorized Mean ( 3 / 20 )116.2483333333331.2478399227036493.1596523065738
Winsorized Mean ( 4 / 20 )116.2883333333331.2384770392089893.8962367906372
Winsorized Mean ( 5 / 20 )116.3133333333331.2261613120175194.8597319075028
Winsorized Mean ( 6 / 20 )116.2333333333331.2055560328741596.4147083700651
Winsorized Mean ( 7 / 20 )116.2566666666671.1958411139729997.2174859253853
Winsorized Mean ( 8 / 20 )116.2033333333331.1776591899222398.6731427290157
Winsorized Mean ( 9 / 20 )116.1433333333331.1687947499917599.3701702836642
Winsorized Mean ( 10 / 20 )116.161.14656500009159101.31130811661
Winsorized Mean ( 11 / 20 )116.2333333333331.11674887967871104.081889356158
Winsorized Mean ( 12 / 20 )117.1533333333330.878218750231401133.398806735184
Winsorized Mean ( 13 / 20 )117.240.80052313404148146.454231007801
Winsorized Mean ( 14 / 20 )117.3333333333330.710850793925213165.060423841459
Winsorized Mean ( 15 / 20 )117.7833333333330.553275641945196212.883641360449
Winsorized Mean ( 16 / 20 )117.7833333333330.50241319719493234.435189980957
Winsorized Mean ( 17 / 20 )118.1233333333330.435833940974611271.028302819156
Winsorized Mean ( 18 / 20 )118.2433333333330.41634247274802284.004974445393
Winsorized Mean ( 19 / 20 )118.370.37707092950227313.919718383614
Winsorized Mean ( 20 / 20 )118.5366666666670.341506852522977347.098940448614
Trimmed Mean ( 1 / 20 )116.3155172413791.2641786348596892.0087668261299
Trimmed Mean ( 2 / 20 )116.4321428571431.2308615585240894.5940199779709
Trimmed Mean ( 3 / 20 )116.5370370370371.2033040243830496.8475419973672
Trimmed Mean ( 4 / 20 )116.6480769230771.1788818307721598.9480657672652
Trimmed Mean ( 5 / 20 )116.7561.1512377013015101.417804392616
Trimmed Mean ( 6 / 20 )116.8666666666671.11984173358302104.359985131776
Trimmed Mean ( 7 / 20 )117.0043478260871.08531683088324107.806627978733
Trimmed Mean ( 8 / 20 )117.151.04286815838421112.334429868402
Trimmed Mean ( 9 / 20 )117.3190476190480.99162719016032118.3096316672
Trimmed Mean ( 10 / 20 )117.5150.924506451836427127.111065332827
Trimmed Mean ( 11 / 20 )117.7289473684210.838510396809804140.402489720262
Trimmed Mean ( 12 / 20 )117.9555555555560.725405682277214162.606329723343
Trimmed Mean ( 13 / 20 )118.0735294117650.658866698674798179.20700750129
Trimmed Mean ( 14 / 20 )118.193750.590890823863264200.026375815494
Trimmed Mean ( 15 / 20 )118.3166666666670.524899187547592225.40836311723
Trimmed Mean ( 16 / 20 )118.3928571428570.490840133119918241.204516815524
Trimmed Mean ( 17 / 20 )118.4807692307690.457552661307769258.944552725646
Trimmed Mean ( 18 / 20 )118.5333333333330.434085189439609273.064679968364
Trimmed Mean ( 19 / 20 )118.5772727272730.403927247863167293.560965135587
Trimmed Mean ( 20 / 20 )118.610.372396223622664318.504841016281
Median118.75
Midrange113.15
Midmean - Weighted Average at Xnp118.025806451613
Midmean - Weighted Average at X(n+1)p118.316666666667
Midmean - Empirical Distribution Function118.025806451613
Midmean - Empirical Distribution Function - Averaging118.316666666667
Midmean - Empirical Distribution Function - Interpolation118.316666666667
Midmean - Closest Observation118.025806451613
Midmean - True Basic - Statistics Graphics Toolkit118.316666666667
Midmean - MS Excel (old versions)118.19375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 116.21 & 1.29851871278685 & 89.4942821044084 \tabularnewline
Geometric Mean & 115.762662323379 &  &  \tabularnewline
Harmonic Mean & 115.2962150286 &  &  \tabularnewline
Quadratic Mean & 116.637245337842 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 116.206666666667 & 1.2909088172245 & 90.0192679112034 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 116.243333333333 & 1.26975322720746 & 91.5479723481266 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 116.248333333333 & 1.24783992270364 & 93.1596523065738 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 116.288333333333 & 1.23847703920898 & 93.8962367906372 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 116.313333333333 & 1.22616131201751 & 94.8597319075028 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 116.233333333333 & 1.20555603287415 & 96.4147083700651 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 116.256666666667 & 1.19584111397299 & 97.2174859253853 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 116.203333333333 & 1.17765918992223 & 98.6731427290157 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 116.143333333333 & 1.16879474999175 & 99.3701702836642 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 116.16 & 1.14656500009159 & 101.31130811661 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 116.233333333333 & 1.11674887967871 & 104.081889356158 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 117.153333333333 & 0.878218750231401 & 133.398806735184 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 117.24 & 0.80052313404148 & 146.454231007801 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 117.333333333333 & 0.710850793925213 & 165.060423841459 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 117.783333333333 & 0.553275641945196 & 212.883641360449 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 117.783333333333 & 0.50241319719493 & 234.435189980957 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 118.123333333333 & 0.435833940974611 & 271.028302819156 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 118.243333333333 & 0.41634247274802 & 284.004974445393 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 118.37 & 0.37707092950227 & 313.919718383614 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 118.536666666667 & 0.341506852522977 & 347.098940448614 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 116.315517241379 & 1.26417863485968 & 92.0087668261299 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 116.432142857143 & 1.23086155852408 & 94.5940199779709 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 116.537037037037 & 1.20330402438304 & 96.8475419973672 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 116.648076923077 & 1.17888183077215 & 98.9480657672652 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 116.756 & 1.1512377013015 & 101.417804392616 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 116.866666666667 & 1.11984173358302 & 104.359985131776 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 117.004347826087 & 1.08531683088324 & 107.806627978733 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 117.15 & 1.04286815838421 & 112.334429868402 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 117.319047619048 & 0.99162719016032 & 118.3096316672 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 117.515 & 0.924506451836427 & 127.111065332827 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 117.728947368421 & 0.838510396809804 & 140.402489720262 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 117.955555555556 & 0.725405682277214 & 162.606329723343 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 118.073529411765 & 0.658866698674798 & 179.20700750129 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 118.19375 & 0.590890823863264 & 200.026375815494 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 118.316666666667 & 0.524899187547592 & 225.40836311723 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 118.392857142857 & 0.490840133119918 & 241.204516815524 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 118.480769230769 & 0.457552661307769 & 258.944552725646 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 118.533333333333 & 0.434085189439609 & 273.064679968364 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 118.577272727273 & 0.403927247863167 & 293.560965135587 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 118.61 & 0.372396223622664 & 318.504841016281 \tabularnewline
Median & 118.75 &  &  \tabularnewline
Midrange & 113.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 118.025806451613 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 118.316666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 118.025806451613 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 118.316666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 118.316666666667 &  &  \tabularnewline
Midmean - Closest Observation & 118.025806451613 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 118.316666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 118.19375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281556&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]116.21[/C][C]1.29851871278685[/C][C]89.4942821044084[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]115.762662323379[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]115.2962150286[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]116.637245337842[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]116.206666666667[/C][C]1.2909088172245[/C][C]90.0192679112034[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]116.243333333333[/C][C]1.26975322720746[/C][C]91.5479723481266[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]116.248333333333[/C][C]1.24783992270364[/C][C]93.1596523065738[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]116.288333333333[/C][C]1.23847703920898[/C][C]93.8962367906372[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]116.313333333333[/C][C]1.22616131201751[/C][C]94.8597319075028[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]116.233333333333[/C][C]1.20555603287415[/C][C]96.4147083700651[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]116.256666666667[/C][C]1.19584111397299[/C][C]97.2174859253853[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]116.203333333333[/C][C]1.17765918992223[/C][C]98.6731427290157[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]116.143333333333[/C][C]1.16879474999175[/C][C]99.3701702836642[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]116.16[/C][C]1.14656500009159[/C][C]101.31130811661[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]116.233333333333[/C][C]1.11674887967871[/C][C]104.081889356158[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]117.153333333333[/C][C]0.878218750231401[/C][C]133.398806735184[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]117.24[/C][C]0.80052313404148[/C][C]146.454231007801[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]117.333333333333[/C][C]0.710850793925213[/C][C]165.060423841459[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]117.783333333333[/C][C]0.553275641945196[/C][C]212.883641360449[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]117.783333333333[/C][C]0.50241319719493[/C][C]234.435189980957[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]118.123333333333[/C][C]0.435833940974611[/C][C]271.028302819156[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]118.243333333333[/C][C]0.41634247274802[/C][C]284.004974445393[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]118.37[/C][C]0.37707092950227[/C][C]313.919718383614[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]118.536666666667[/C][C]0.341506852522977[/C][C]347.098940448614[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]116.315517241379[/C][C]1.26417863485968[/C][C]92.0087668261299[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]116.432142857143[/C][C]1.23086155852408[/C][C]94.5940199779709[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]116.537037037037[/C][C]1.20330402438304[/C][C]96.8475419973672[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]116.648076923077[/C][C]1.17888183077215[/C][C]98.9480657672652[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]116.756[/C][C]1.1512377013015[/C][C]101.417804392616[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]116.866666666667[/C][C]1.11984173358302[/C][C]104.359985131776[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]117.004347826087[/C][C]1.08531683088324[/C][C]107.806627978733[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]117.15[/C][C]1.04286815838421[/C][C]112.334429868402[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]117.319047619048[/C][C]0.99162719016032[/C][C]118.3096316672[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]117.515[/C][C]0.924506451836427[/C][C]127.111065332827[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]117.728947368421[/C][C]0.838510396809804[/C][C]140.402489720262[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]117.955555555556[/C][C]0.725405682277214[/C][C]162.606329723343[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]118.073529411765[/C][C]0.658866698674798[/C][C]179.20700750129[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]118.19375[/C][C]0.590890823863264[/C][C]200.026375815494[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]118.316666666667[/C][C]0.524899187547592[/C][C]225.40836311723[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]118.392857142857[/C][C]0.490840133119918[/C][C]241.204516815524[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]118.480769230769[/C][C]0.457552661307769[/C][C]258.944552725646[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]118.533333333333[/C][C]0.434085189439609[/C][C]273.064679968364[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]118.577272727273[/C][C]0.403927247863167[/C][C]293.560965135587[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]118.61[/C][C]0.372396223622664[/C][C]318.504841016281[/C][/ROW]
[ROW][C]Median[/C][C]118.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]113.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]118.025806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]118.316666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]118.025806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]118.316666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]118.316666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]118.025806451613[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]118.316666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]118.19375[/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=281556&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281556&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 Mean116.211.2985187127868589.4942821044084
Geometric Mean115.762662323379
Harmonic Mean115.2962150286
Quadratic Mean116.637245337842
Winsorized Mean ( 1 / 20 )116.2066666666671.290908817224590.0192679112034
Winsorized Mean ( 2 / 20 )116.2433333333331.2697532272074691.5479723481266
Winsorized Mean ( 3 / 20 )116.2483333333331.2478399227036493.1596523065738
Winsorized Mean ( 4 / 20 )116.2883333333331.2384770392089893.8962367906372
Winsorized Mean ( 5 / 20 )116.3133333333331.2261613120175194.8597319075028
Winsorized Mean ( 6 / 20 )116.2333333333331.2055560328741596.4147083700651
Winsorized Mean ( 7 / 20 )116.2566666666671.1958411139729997.2174859253853
Winsorized Mean ( 8 / 20 )116.2033333333331.1776591899222398.6731427290157
Winsorized Mean ( 9 / 20 )116.1433333333331.1687947499917599.3701702836642
Winsorized Mean ( 10 / 20 )116.161.14656500009159101.31130811661
Winsorized Mean ( 11 / 20 )116.2333333333331.11674887967871104.081889356158
Winsorized Mean ( 12 / 20 )117.1533333333330.878218750231401133.398806735184
Winsorized Mean ( 13 / 20 )117.240.80052313404148146.454231007801
Winsorized Mean ( 14 / 20 )117.3333333333330.710850793925213165.060423841459
Winsorized Mean ( 15 / 20 )117.7833333333330.553275641945196212.883641360449
Winsorized Mean ( 16 / 20 )117.7833333333330.50241319719493234.435189980957
Winsorized Mean ( 17 / 20 )118.1233333333330.435833940974611271.028302819156
Winsorized Mean ( 18 / 20 )118.2433333333330.41634247274802284.004974445393
Winsorized Mean ( 19 / 20 )118.370.37707092950227313.919718383614
Winsorized Mean ( 20 / 20 )118.5366666666670.341506852522977347.098940448614
Trimmed Mean ( 1 / 20 )116.3155172413791.2641786348596892.0087668261299
Trimmed Mean ( 2 / 20 )116.4321428571431.2308615585240894.5940199779709
Trimmed Mean ( 3 / 20 )116.5370370370371.2033040243830496.8475419973672
Trimmed Mean ( 4 / 20 )116.6480769230771.1788818307721598.9480657672652
Trimmed Mean ( 5 / 20 )116.7561.1512377013015101.417804392616
Trimmed Mean ( 6 / 20 )116.8666666666671.11984173358302104.359985131776
Trimmed Mean ( 7 / 20 )117.0043478260871.08531683088324107.806627978733
Trimmed Mean ( 8 / 20 )117.151.04286815838421112.334429868402
Trimmed Mean ( 9 / 20 )117.3190476190480.99162719016032118.3096316672
Trimmed Mean ( 10 / 20 )117.5150.924506451836427127.111065332827
Trimmed Mean ( 11 / 20 )117.7289473684210.838510396809804140.402489720262
Trimmed Mean ( 12 / 20 )117.9555555555560.725405682277214162.606329723343
Trimmed Mean ( 13 / 20 )118.0735294117650.658866698674798179.20700750129
Trimmed Mean ( 14 / 20 )118.193750.590890823863264200.026375815494
Trimmed Mean ( 15 / 20 )118.3166666666670.524899187547592225.40836311723
Trimmed Mean ( 16 / 20 )118.3928571428570.490840133119918241.204516815524
Trimmed Mean ( 17 / 20 )118.4807692307690.457552661307769258.944552725646
Trimmed Mean ( 18 / 20 )118.5333333333330.434085189439609273.064679968364
Trimmed Mean ( 19 / 20 )118.5772727272730.403927247863167293.560965135587
Trimmed Mean ( 20 / 20 )118.610.372396223622664318.504841016281
Median118.75
Midrange113.15
Midmean - Weighted Average at Xnp118.025806451613
Midmean - Weighted Average at X(n+1)p118.316666666667
Midmean - Empirical Distribution Function118.025806451613
Midmean - Empirical Distribution Function - Averaging118.316666666667
Midmean - Empirical Distribution Function - Interpolation118.316666666667
Midmean - Closest Observation118.025806451613
Midmean - True Basic - Statistics Graphics Toolkit118.316666666667
Midmean - MS Excel (old versions)118.19375
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')