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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 27 Oct 2009 18:46:58 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/28/t12566909550s91h349xrtdldh.htm/, Retrieved Mon, 06 May 2024 00:08:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51323, Retrieved Mon, 06 May 2024 00:08:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmediaan
Estimated Impact119

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS3 Yt-Xt] [2009-10-28 00:46:58] [a54ad7d84632b3d861404e40e79a6400] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
91.83
93.17
94.50
96.79
96.82
98.10
99.17
99.59
100.98
100.91
98.86
98.28
97.64
97.65
98.01
99.53
100.20
100.49
100.89
101.11
99.10
98.15
98.35
98.62
97.16
97.68
99.11
99.90
100.42
101.23
101.52
101.09
101.65
102.55
104.69
103.56
103.48
103.66
105.58
106.46
108.64
109.71
109.16
106.61
106.61
105.22
102.30
99.72
98.25
99.03
99.10
100.30
100.94
102.32
101.43
102.34

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51323&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51323&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51323&T=0

As an alternative you can also use a QR Code:  
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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean100.7171428571430.485320533676624207.527058651617
Geometric Mean100.65331054725
Harmonic Mean100.589917341222
Quadratic Mean100.781433540254
Winsorized Mean ( 1 / 18 )100.731250.474625010047235212.233337619472
Winsorized Mean ( 2 / 18 )100.7601785714290.455878735518717221.024081013078
Winsorized Mean ( 3 / 18 )100.7741071428570.397310501819692253.640683247257
Winsorized Mean ( 4 / 18 )100.776250.396920987467541253.894989637556
Winsorized Mean ( 5 / 18 )100.7932142857140.388016526889186259.765260757823
Winsorized Mean ( 6 / 18 )100.7503571428570.355326990824175283.542651542368
Winsorized Mean ( 7 / 18 )100.7066071428570.344198794566295292.582683997345
Winsorized Mean ( 8 / 18 )100.6351785714290.325897461273294308.793993602291
Winsorized Mean ( 9 / 18 )100.5226785714290.281584972650921356.988789654077
Winsorized Mean ( 10 / 18 )100.5208928571430.275396323243821365.004483985601
Winsorized Mean ( 11 / 18 )100.5150.270689955388175371.328887530605
Winsorized Mean ( 12 / 18 )100.3371428571430.229732723625232436.755988758594
Winsorized Mean ( 13 / 18 )100.2953571428570.220190732593022455.493089839675
Winsorized Mean ( 14 / 18 )100.3078571428570.216450815367137463.421017715818
Winsorized Mean ( 15 / 18 )100.3748214285710.203925277738543492.213729174193
Winsorized Mean ( 16 / 18 )100.2576785714290.162644339706012616.422795608194
Winsorized Mean ( 17 / 18 )100.2698214285710.148601159534600674.758001502838
Winsorized Mean ( 18 / 18 )100.2633928571430.140811949017424712.037533439272
Trimmed Mean ( 1 / 18 )100.7151851851850.444548447533117226.556150952889
Trimmed Mean ( 2 / 18 )100.6978846153850.40608942693087247.969727693814
Trimmed Mean ( 3 / 18 )100.6630.370210006590302271.907831252654
Trimmed Mean ( 4 / 18 )100.6197916666670.355634296184488282.930506832978
Trimmed Mean ( 5 / 18 )100.5721739130430.336868200985368298.550512096010
Trimmed Mean ( 6 / 18 )100.5159090909090.3156047783687318.486651597788
Trimmed Mean ( 7 / 18 )100.4638095238100.299462730745917335.480175691877
Trimmed Mean ( 8 / 18 )100.415250.281698371944905356.463721485899
Trimmed Mean ( 9 / 18 )100.3747368421050.263975983013032380.241928437672
Trimmed Mean ( 10 / 18 )100.3491666666670.25443101007717394.406195362076
Trimmed Mean ( 11 / 18 )100.3208823529410.242849383589896413.099184646705
Trimmed Mean ( 12 / 18 )100.290.227733396760335440.383366808271
Trimmed Mean ( 13 / 18 )100.2826666666670.220179620160676455.458441582765
Trimmed Mean ( 14 / 18 )100.2807142857140.211861820154086473.330750263453
Trimmed Mean ( 15 / 18 )100.2765384615380.200179106192962500.934090318484
Trimmed Mean ( 16 / 18 )100.261250.186512921124454537.556590693783
Trimmed Mean ( 17 / 18 )100.2618181818180.182041853761861550.762454402251
Trimmed Mean ( 18 / 18 )100.26050.179252064511344559.32689128752
Median100.36
Midrange100.77
Midmean - Weighted Average at Xnp100.211724137931
Midmean - Weighted Average at X(n+1)p100.280714285714
Midmean - Empirical Distribution Function100.211724137931
Midmean - Empirical Distribution Function - Averaging100.280714285714
Midmean - Empirical Distribution Function - Interpolation100.280714285714
Midmean - Closest Observation100.211724137931
Midmean - True Basic - Statistics Graphics Toolkit100.280714285714
Midmean - MS Excel (old versions)100.282666666667
Number of observations56

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 100.717142857143 & 0.485320533676624 & 207.527058651617 \tabularnewline
Geometric Mean & 100.65331054725 &  &  \tabularnewline
Harmonic Mean & 100.589917341222 &  &  \tabularnewline
Quadratic Mean & 100.781433540254 &  &  \tabularnewline
Winsorized Mean ( 1 / 18 ) & 100.73125 & 0.474625010047235 & 212.233337619472 \tabularnewline
Winsorized Mean ( 2 / 18 ) & 100.760178571429 & 0.455878735518717 & 221.024081013078 \tabularnewline
Winsorized Mean ( 3 / 18 ) & 100.774107142857 & 0.397310501819692 & 253.640683247257 \tabularnewline
Winsorized Mean ( 4 / 18 ) & 100.77625 & 0.396920987467541 & 253.894989637556 \tabularnewline
Winsorized Mean ( 5 / 18 ) & 100.793214285714 & 0.388016526889186 & 259.765260757823 \tabularnewline
Winsorized Mean ( 6 / 18 ) & 100.750357142857 & 0.355326990824175 & 283.542651542368 \tabularnewline
Winsorized Mean ( 7 / 18 ) & 100.706607142857 & 0.344198794566295 & 292.582683997345 \tabularnewline
Winsorized Mean ( 8 / 18 ) & 100.635178571429 & 0.325897461273294 & 308.793993602291 \tabularnewline
Winsorized Mean ( 9 / 18 ) & 100.522678571429 & 0.281584972650921 & 356.988789654077 \tabularnewline
Winsorized Mean ( 10 / 18 ) & 100.520892857143 & 0.275396323243821 & 365.004483985601 \tabularnewline
Winsorized Mean ( 11 / 18 ) & 100.515 & 0.270689955388175 & 371.328887530605 \tabularnewline
Winsorized Mean ( 12 / 18 ) & 100.337142857143 & 0.229732723625232 & 436.755988758594 \tabularnewline
Winsorized Mean ( 13 / 18 ) & 100.295357142857 & 0.220190732593022 & 455.493089839675 \tabularnewline
Winsorized Mean ( 14 / 18 ) & 100.307857142857 & 0.216450815367137 & 463.421017715818 \tabularnewline
Winsorized Mean ( 15 / 18 ) & 100.374821428571 & 0.203925277738543 & 492.213729174193 \tabularnewline
Winsorized Mean ( 16 / 18 ) & 100.257678571429 & 0.162644339706012 & 616.422795608194 \tabularnewline
Winsorized Mean ( 17 / 18 ) & 100.269821428571 & 0.148601159534600 & 674.758001502838 \tabularnewline
Winsorized Mean ( 18 / 18 ) & 100.263392857143 & 0.140811949017424 & 712.037533439272 \tabularnewline
Trimmed Mean ( 1 / 18 ) & 100.715185185185 & 0.444548447533117 & 226.556150952889 \tabularnewline
Trimmed Mean ( 2 / 18 ) & 100.697884615385 & 0.40608942693087 & 247.969727693814 \tabularnewline
Trimmed Mean ( 3 / 18 ) & 100.663 & 0.370210006590302 & 271.907831252654 \tabularnewline
Trimmed Mean ( 4 / 18 ) & 100.619791666667 & 0.355634296184488 & 282.930506832978 \tabularnewline
Trimmed Mean ( 5 / 18 ) & 100.572173913043 & 0.336868200985368 & 298.550512096010 \tabularnewline
Trimmed Mean ( 6 / 18 ) & 100.515909090909 & 0.3156047783687 & 318.486651597788 \tabularnewline
Trimmed Mean ( 7 / 18 ) & 100.463809523810 & 0.299462730745917 & 335.480175691877 \tabularnewline
Trimmed Mean ( 8 / 18 ) & 100.41525 & 0.281698371944905 & 356.463721485899 \tabularnewline
Trimmed Mean ( 9 / 18 ) & 100.374736842105 & 0.263975983013032 & 380.241928437672 \tabularnewline
Trimmed Mean ( 10 / 18 ) & 100.349166666667 & 0.25443101007717 & 394.406195362076 \tabularnewline
Trimmed Mean ( 11 / 18 ) & 100.320882352941 & 0.242849383589896 & 413.099184646705 \tabularnewline
Trimmed Mean ( 12 / 18 ) & 100.29 & 0.227733396760335 & 440.383366808271 \tabularnewline
Trimmed Mean ( 13 / 18 ) & 100.282666666667 & 0.220179620160676 & 455.458441582765 \tabularnewline
Trimmed Mean ( 14 / 18 ) & 100.280714285714 & 0.211861820154086 & 473.330750263453 \tabularnewline
Trimmed Mean ( 15 / 18 ) & 100.276538461538 & 0.200179106192962 & 500.934090318484 \tabularnewline
Trimmed Mean ( 16 / 18 ) & 100.26125 & 0.186512921124454 & 537.556590693783 \tabularnewline
Trimmed Mean ( 17 / 18 ) & 100.261818181818 & 0.182041853761861 & 550.762454402251 \tabularnewline
Trimmed Mean ( 18 / 18 ) & 100.2605 & 0.179252064511344 & 559.32689128752 \tabularnewline
Median & 100.36 &  &  \tabularnewline
Midrange & 100.77 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 100.211724137931 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 100.280714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 100.211724137931 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 100.280714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 100.280714285714 &  &  \tabularnewline
Midmean - Closest Observation & 100.211724137931 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 100.280714285714 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 100.282666666667 &  &  \tabularnewline
Number of observations & 56 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51323&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]100.717142857143[/C][C]0.485320533676624[/C][C]207.527058651617[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]100.65331054725[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]100.589917341222[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.781433540254[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 18 )[/C][C]100.73125[/C][C]0.474625010047235[/C][C]212.233337619472[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 18 )[/C][C]100.760178571429[/C][C]0.455878735518717[/C][C]221.024081013078[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 18 )[/C][C]100.774107142857[/C][C]0.397310501819692[/C][C]253.640683247257[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 18 )[/C][C]100.77625[/C][C]0.396920987467541[/C][C]253.894989637556[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 18 )[/C][C]100.793214285714[/C][C]0.388016526889186[/C][C]259.765260757823[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 18 )[/C][C]100.750357142857[/C][C]0.355326990824175[/C][C]283.542651542368[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 18 )[/C][C]100.706607142857[/C][C]0.344198794566295[/C][C]292.582683997345[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 18 )[/C][C]100.635178571429[/C][C]0.325897461273294[/C][C]308.793993602291[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 18 )[/C][C]100.522678571429[/C][C]0.281584972650921[/C][C]356.988789654077[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 18 )[/C][C]100.520892857143[/C][C]0.275396323243821[/C][C]365.004483985601[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 18 )[/C][C]100.515[/C][C]0.270689955388175[/C][C]371.328887530605[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 18 )[/C][C]100.337142857143[/C][C]0.229732723625232[/C][C]436.755988758594[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 18 )[/C][C]100.295357142857[/C][C]0.220190732593022[/C][C]455.493089839675[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 18 )[/C][C]100.307857142857[/C][C]0.216450815367137[/C][C]463.421017715818[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 18 )[/C][C]100.374821428571[/C][C]0.203925277738543[/C][C]492.213729174193[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 18 )[/C][C]100.257678571429[/C][C]0.162644339706012[/C][C]616.422795608194[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 18 )[/C][C]100.269821428571[/C][C]0.148601159534600[/C][C]674.758001502838[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 18 )[/C][C]100.263392857143[/C][C]0.140811949017424[/C][C]712.037533439272[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 18 )[/C][C]100.715185185185[/C][C]0.444548447533117[/C][C]226.556150952889[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 18 )[/C][C]100.697884615385[/C][C]0.40608942693087[/C][C]247.969727693814[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 18 )[/C][C]100.663[/C][C]0.370210006590302[/C][C]271.907831252654[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 18 )[/C][C]100.619791666667[/C][C]0.355634296184488[/C][C]282.930506832978[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 18 )[/C][C]100.572173913043[/C][C]0.336868200985368[/C][C]298.550512096010[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 18 )[/C][C]100.515909090909[/C][C]0.3156047783687[/C][C]318.486651597788[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 18 )[/C][C]100.463809523810[/C][C]0.299462730745917[/C][C]335.480175691877[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 18 )[/C][C]100.41525[/C][C]0.281698371944905[/C][C]356.463721485899[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 18 )[/C][C]100.374736842105[/C][C]0.263975983013032[/C][C]380.241928437672[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 18 )[/C][C]100.349166666667[/C][C]0.25443101007717[/C][C]394.406195362076[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 18 )[/C][C]100.320882352941[/C][C]0.242849383589896[/C][C]413.099184646705[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 18 )[/C][C]100.29[/C][C]0.227733396760335[/C][C]440.383366808271[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 18 )[/C][C]100.282666666667[/C][C]0.220179620160676[/C][C]455.458441582765[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 18 )[/C][C]100.280714285714[/C][C]0.211861820154086[/C][C]473.330750263453[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 18 )[/C][C]100.276538461538[/C][C]0.200179106192962[/C][C]500.934090318484[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 18 )[/C][C]100.26125[/C][C]0.186512921124454[/C][C]537.556590693783[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 18 )[/C][C]100.261818181818[/C][C]0.182041853761861[/C][C]550.762454402251[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 18 )[/C][C]100.2605[/C][C]0.179252064511344[/C][C]559.32689128752[/C][/ROW]
[ROW][C]Median[/C][C]100.36[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]100.77[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]100.211724137931[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]100.280714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]100.211724137931[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]100.280714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]100.280714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]100.211724137931[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]100.280714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]100.282666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]56[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51323&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51323&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean100.7171428571430.485320533676624207.527058651617
Geometric Mean100.65331054725
Harmonic Mean100.589917341222
Quadratic Mean100.781433540254
Winsorized Mean ( 1 / 18 )100.731250.474625010047235212.233337619472
Winsorized Mean ( 2 / 18 )100.7601785714290.455878735518717221.024081013078
Winsorized Mean ( 3 / 18 )100.7741071428570.397310501819692253.640683247257
Winsorized Mean ( 4 / 18 )100.776250.396920987467541253.894989637556
Winsorized Mean ( 5 / 18 )100.7932142857140.388016526889186259.765260757823
Winsorized Mean ( 6 / 18 )100.7503571428570.355326990824175283.542651542368
Winsorized Mean ( 7 / 18 )100.7066071428570.344198794566295292.582683997345
Winsorized Mean ( 8 / 18 )100.6351785714290.325897461273294308.793993602291
Winsorized Mean ( 9 / 18 )100.5226785714290.281584972650921356.988789654077
Winsorized Mean ( 10 / 18 )100.5208928571430.275396323243821365.004483985601
Winsorized Mean ( 11 / 18 )100.5150.270689955388175371.328887530605
Winsorized Mean ( 12 / 18 )100.3371428571430.229732723625232436.755988758594
Winsorized Mean ( 13 / 18 )100.2953571428570.220190732593022455.493089839675
Winsorized Mean ( 14 / 18 )100.3078571428570.216450815367137463.421017715818
Winsorized Mean ( 15 / 18 )100.3748214285710.203925277738543492.213729174193
Winsorized Mean ( 16 / 18 )100.2576785714290.162644339706012616.422795608194
Winsorized Mean ( 17 / 18 )100.2698214285710.148601159534600674.758001502838
Winsorized Mean ( 18 / 18 )100.2633928571430.140811949017424712.037533439272
Trimmed Mean ( 1 / 18 )100.7151851851850.444548447533117226.556150952889
Trimmed Mean ( 2 / 18 )100.6978846153850.40608942693087247.969727693814
Trimmed Mean ( 3 / 18 )100.6630.370210006590302271.907831252654
Trimmed Mean ( 4 / 18 )100.6197916666670.355634296184488282.930506832978
Trimmed Mean ( 5 / 18 )100.5721739130430.336868200985368298.550512096010
Trimmed Mean ( 6 / 18 )100.5159090909090.3156047783687318.486651597788
Trimmed Mean ( 7 / 18 )100.4638095238100.299462730745917335.480175691877
Trimmed Mean ( 8 / 18 )100.415250.281698371944905356.463721485899
Trimmed Mean ( 9 / 18 )100.3747368421050.263975983013032380.241928437672
Trimmed Mean ( 10 / 18 )100.3491666666670.25443101007717394.406195362076
Trimmed Mean ( 11 / 18 )100.3208823529410.242849383589896413.099184646705
Trimmed Mean ( 12 / 18 )100.290.227733396760335440.383366808271
Trimmed Mean ( 13 / 18 )100.2826666666670.220179620160676455.458441582765
Trimmed Mean ( 14 / 18 )100.2807142857140.211861820154086473.330750263453
Trimmed Mean ( 15 / 18 )100.2765384615380.200179106192962500.934090318484
Trimmed Mean ( 16 / 18 )100.261250.186512921124454537.556590693783
Trimmed Mean ( 17 / 18 )100.2618181818180.182041853761861550.762454402251
Trimmed Mean ( 18 / 18 )100.26050.179252064511344559.32689128752
Median100.36
Midrange100.77
Midmean - Weighted Average at Xnp100.211724137931
Midmean - Weighted Average at X(n+1)p100.280714285714
Midmean - Empirical Distribution Function100.211724137931
Midmean - Empirical Distribution Function - Averaging100.280714285714
Midmean - Empirical Distribution Function - Interpolation100.280714285714
Midmean - Closest Observation100.211724137931
Midmean - True Basic - Statistics Graphics Toolkit100.280714285714
Midmean - MS Excel (old versions)100.282666666667
Number of observations56


Figures (Output of Computation)

Input Parameters & R Code

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')