Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 05 Mar 2016 10:36:06 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/05/t1457174288z6iwzvrv9361luj.htm/, Retrieved Sat, 27 Apr 2024 11:46:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293437, Retrieved Sat, 27 Apr 2024 11:46:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Centrummaten Cons...] [2016-03-05 10:36:06] [fcb50c3fd850be3d4e9c7b78a2663ee0] [Current]
Feedback Forum

Post a new message
Dataseries X:
86,37
86,84
86,73
90,99
92,61
93,83
94,2
94,01
93,47
93,27
94,3
94,53
94,59
94,69
94,67
96,55
97,14
97,32
97,97
98,49
99,11
99,09
98,76
99,2
99,61
99,54
99,68
100,75
100,38
100,79
100,39
100,39
100,12
100
99,17
99,17
99,59
99,96
99,68
101,03
100,99
101,38
101,84
101,52
101,37
101,22
101,45
101,99
104,05
104,61
105,06
105,4
104,71
104,8
104,83
104,81
104,49
104,59
104,5
104,61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293437&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293437&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293437&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.95333333333330.60039053517434164.814945499765
Geometric Mean98.8426313735227
Harmonic Mean98.7285421311501
Quadratic Mean99.0607381189271
Winsorized Mean ( 1 / 20 )98.95366666666670.59727748458902165.674530213969
Winsorized Mean ( 2 / 20 )98.94966666666670.594702079270379166.385271072307
Winsorized Mean ( 3 / 20 )99.15616666666670.531192991180675186.666933323562
Winsorized Mean ( 4 / 20 )99.26350.504888130194501196.604938923322
Winsorized Mean ( 5 / 20 )99.3110.491617800884887202.008551808428
Winsorized Mean ( 6 / 20 )99.3210.485639115272324204.516063217654
Winsorized Mean ( 7 / 20 )99.3630.477222679548768208.21097625526
Winsorized Mean ( 8 / 20 )99.38433333333330.472051022251076210.537269593015
Winsorized Mean ( 9 / 20 )99.39933333333330.464075769837921214.187724922697
Winsorized Mean ( 10 / 20 )99.41433333333330.460614142148577215.829963165278
Winsorized Mean ( 11 / 20 )99.37583333333330.437854637002978226.960787748052
Winsorized Mean ( 12 / 20 )98.97583333333330.36898649491207268.237007852874
Winsorized Mean ( 13 / 20 )98.96066666666670.361047899436325274.092902413132
Winsorized Mean ( 14 / 20 )98.89066666666670.350303489619965282.299975869354
Winsorized Mean ( 15 / 20 )99.33816666666670.257341744651912386.016527559625
Winsorized Mean ( 16 / 20 )99.47683333333330.226468153142881439.253077983873
Winsorized Mean ( 17 / 20 )99.5250.217213802872176458.189114522192
Winsorized Mean ( 18 / 20 )99.6750.177970114294285560.065943629057
Winsorized Mean ( 19 / 20 )99.77950.143056115772403697.485035583838
Winsorized Mean ( 20 / 20 )99.85616666666670.127620795036703782.44432373226
Trimmed Mean ( 1 / 20 )99.05913793103450.570368974753473173.675536916871
Trimmed Mean ( 2 / 20 )99.17214285714290.536576855358917184.823743079277
Trimmed Mean ( 3 / 20 )99.29574074074070.495210929362305200.512013877816
Trimmed Mean ( 4 / 20 )99.34942307692310.476569045694159208.468057198749
Trimmed Mean ( 5 / 20 )99.37520.463859253811907214.235674255399
Trimmed Mean ( 6 / 20 )99.391250.452244856264536219.773091110321
Trimmed Mean ( 7 / 20 )99.40652173913040.43909329254125226.390435535501
Trimmed Mean ( 8 / 20 )99.4150.424491425592663234.197898959206
Trimmed Mean ( 9 / 20 )99.42047619047620.406772794035676244.412796647744
Trimmed Mean ( 10 / 20 )99.4240.385534726893733257.885977745929
Trimmed Mean ( 11 / 20 )99.42552631578950.357756900178968277.913651046428
Trimmed Mean ( 12 / 20 )99.43305555555560.326841503126186304.22407988121
Trimmed Mean ( 13 / 20 )99.50029411764710.305115473098441326.107008298281
Trimmed Mean ( 14 / 20 )99.5781250.27579300526669361.061096903849
Trimmed Mean ( 15 / 20 )99.67633333333330.233659779851618426.587465744559
Trimmed Mean ( 16 / 20 )99.72464285714290.213666952766355466.729372820663
Trimmed Mean ( 17 / 20 )99.76038461538460.196352493682021508.067826105329
Trimmed Mean ( 18 / 20 )99.7950.172813462304368577.472372055344
Trimmed Mean ( 19 / 20 )99.81318181818180.155119541060726643.45975455863
Trimmed Mean ( 20 / 20 )99.81850.14404545152577692.965303261533
Median99.68
Midrange95.885
Midmean - Weighted Average at Xnp99.5154838709677
Midmean - Weighted Average at X(n+1)p99.6763333333333
Midmean - Empirical Distribution Function99.5154838709677
Midmean - Empirical Distribution Function - Averaging99.6763333333333
Midmean - Empirical Distribution Function - Interpolation99.6763333333333
Midmean - Closest Observation99.5154838709677
Midmean - True Basic - Statistics Graphics Toolkit99.6763333333333
Midmean - MS Excel (old versions)99.578125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.9533333333333 & 0.60039053517434 & 164.814945499765 \tabularnewline
Geometric Mean & 98.8426313735227 &  &  \tabularnewline
Harmonic Mean & 98.7285421311501 &  &  \tabularnewline
Quadratic Mean & 99.0607381189271 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 98.9536666666667 & 0.59727748458902 & 165.674530213969 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 98.9496666666667 & 0.594702079270379 & 166.385271072307 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 99.1561666666667 & 0.531192991180675 & 186.666933323562 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 99.2635 & 0.504888130194501 & 196.604938923322 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 99.311 & 0.491617800884887 & 202.008551808428 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 99.321 & 0.485639115272324 & 204.516063217654 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 99.363 & 0.477222679548768 & 208.21097625526 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 99.3843333333333 & 0.472051022251076 & 210.537269593015 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 99.3993333333333 & 0.464075769837921 & 214.187724922697 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 99.4143333333333 & 0.460614142148577 & 215.829963165278 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 99.3758333333333 & 0.437854637002978 & 226.960787748052 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 98.9758333333333 & 0.36898649491207 & 268.237007852874 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 98.9606666666667 & 0.361047899436325 & 274.092902413132 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 98.8906666666667 & 0.350303489619965 & 282.299975869354 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 99.3381666666667 & 0.257341744651912 & 386.016527559625 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 99.4768333333333 & 0.226468153142881 & 439.253077983873 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 99.525 & 0.217213802872176 & 458.189114522192 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 99.675 & 0.177970114294285 & 560.065943629057 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 99.7795 & 0.143056115772403 & 697.485035583838 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 99.8561666666667 & 0.127620795036703 & 782.44432373226 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 99.0591379310345 & 0.570368974753473 & 173.675536916871 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 99.1721428571429 & 0.536576855358917 & 184.823743079277 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 99.2957407407407 & 0.495210929362305 & 200.512013877816 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 99.3494230769231 & 0.476569045694159 & 208.468057198749 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 99.3752 & 0.463859253811907 & 214.235674255399 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 99.39125 & 0.452244856264536 & 219.773091110321 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 99.4065217391304 & 0.43909329254125 & 226.390435535501 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 99.415 & 0.424491425592663 & 234.197898959206 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 99.4204761904762 & 0.406772794035676 & 244.412796647744 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 99.424 & 0.385534726893733 & 257.885977745929 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 99.4255263157895 & 0.357756900178968 & 277.913651046428 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 99.4330555555556 & 0.326841503126186 & 304.22407988121 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 99.5002941176471 & 0.305115473098441 & 326.107008298281 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 99.578125 & 0.27579300526669 & 361.061096903849 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 99.6763333333333 & 0.233659779851618 & 426.587465744559 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 99.7246428571429 & 0.213666952766355 & 466.729372820663 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 99.7603846153846 & 0.196352493682021 & 508.067826105329 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 99.795 & 0.172813462304368 & 577.472372055344 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 99.8131818181818 & 0.155119541060726 & 643.45975455863 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 99.8185 & 0.14404545152577 & 692.965303261533 \tabularnewline
Median & 99.68 &  &  \tabularnewline
Midrange & 95.885 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.5154838709677 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.6763333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.5154838709677 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.6763333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.6763333333333 &  &  \tabularnewline
Midmean - Closest Observation & 99.5154838709677 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.6763333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.578125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293437&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]98.9533333333333[/C][C]0.60039053517434[/C][C]164.814945499765[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.8426313735227[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.7285421311501[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.0607381189271[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]98.9536666666667[/C][C]0.59727748458902[/C][C]165.674530213969[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]98.9496666666667[/C][C]0.594702079270379[/C][C]166.385271072307[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]99.1561666666667[/C][C]0.531192991180675[/C][C]186.666933323562[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]99.2635[/C][C]0.504888130194501[/C][C]196.604938923322[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]99.311[/C][C]0.491617800884887[/C][C]202.008551808428[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]99.321[/C][C]0.485639115272324[/C][C]204.516063217654[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]99.363[/C][C]0.477222679548768[/C][C]208.21097625526[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]99.3843333333333[/C][C]0.472051022251076[/C][C]210.537269593015[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]99.3993333333333[/C][C]0.464075769837921[/C][C]214.187724922697[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]99.4143333333333[/C][C]0.460614142148577[/C][C]215.829963165278[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]99.3758333333333[/C][C]0.437854637002978[/C][C]226.960787748052[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]98.9758333333333[/C][C]0.36898649491207[/C][C]268.237007852874[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]98.9606666666667[/C][C]0.361047899436325[/C][C]274.092902413132[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]98.8906666666667[/C][C]0.350303489619965[/C][C]282.299975869354[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]99.3381666666667[/C][C]0.257341744651912[/C][C]386.016527559625[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]99.4768333333333[/C][C]0.226468153142881[/C][C]439.253077983873[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]99.525[/C][C]0.217213802872176[/C][C]458.189114522192[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]99.675[/C][C]0.177970114294285[/C][C]560.065943629057[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]99.7795[/C][C]0.143056115772403[/C][C]697.485035583838[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]99.8561666666667[/C][C]0.127620795036703[/C][C]782.44432373226[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]99.0591379310345[/C][C]0.570368974753473[/C][C]173.675536916871[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]99.1721428571429[/C][C]0.536576855358917[/C][C]184.823743079277[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]99.2957407407407[/C][C]0.495210929362305[/C][C]200.512013877816[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]99.3494230769231[/C][C]0.476569045694159[/C][C]208.468057198749[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]99.3752[/C][C]0.463859253811907[/C][C]214.235674255399[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]99.39125[/C][C]0.452244856264536[/C][C]219.773091110321[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]99.4065217391304[/C][C]0.43909329254125[/C][C]226.390435535501[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]99.415[/C][C]0.424491425592663[/C][C]234.197898959206[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]99.4204761904762[/C][C]0.406772794035676[/C][C]244.412796647744[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]99.424[/C][C]0.385534726893733[/C][C]257.885977745929[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]99.4255263157895[/C][C]0.357756900178968[/C][C]277.913651046428[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]99.4330555555556[/C][C]0.326841503126186[/C][C]304.22407988121[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]99.5002941176471[/C][C]0.305115473098441[/C][C]326.107008298281[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]99.578125[/C][C]0.27579300526669[/C][C]361.061096903849[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]99.6763333333333[/C][C]0.233659779851618[/C][C]426.587465744559[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]99.7246428571429[/C][C]0.213666952766355[/C][C]466.729372820663[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]99.7603846153846[/C][C]0.196352493682021[/C][C]508.067826105329[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]99.795[/C][C]0.172813462304368[/C][C]577.472372055344[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]99.8131818181818[/C][C]0.155119541060726[/C][C]643.45975455863[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]99.8185[/C][C]0.14404545152577[/C][C]692.965303261533[/C][/ROW]
[ROW][C]Median[/C][C]99.68[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95.885[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.5154838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.6763333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.5154838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.6763333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.6763333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.5154838709677[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.6763333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.578125[/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=293437&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293437&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 Mean98.95333333333330.60039053517434164.814945499765
Geometric Mean98.8426313735227
Harmonic Mean98.7285421311501
Quadratic Mean99.0607381189271
Winsorized Mean ( 1 / 20 )98.95366666666670.59727748458902165.674530213969
Winsorized Mean ( 2 / 20 )98.94966666666670.594702079270379166.385271072307
Winsorized Mean ( 3 / 20 )99.15616666666670.531192991180675186.666933323562
Winsorized Mean ( 4 / 20 )99.26350.504888130194501196.604938923322
Winsorized Mean ( 5 / 20 )99.3110.491617800884887202.008551808428
Winsorized Mean ( 6 / 20 )99.3210.485639115272324204.516063217654
Winsorized Mean ( 7 / 20 )99.3630.477222679548768208.21097625526
Winsorized Mean ( 8 / 20 )99.38433333333330.472051022251076210.537269593015
Winsorized Mean ( 9 / 20 )99.39933333333330.464075769837921214.187724922697
Winsorized Mean ( 10 / 20 )99.41433333333330.460614142148577215.829963165278
Winsorized Mean ( 11 / 20 )99.37583333333330.437854637002978226.960787748052
Winsorized Mean ( 12 / 20 )98.97583333333330.36898649491207268.237007852874
Winsorized Mean ( 13 / 20 )98.96066666666670.361047899436325274.092902413132
Winsorized Mean ( 14 / 20 )98.89066666666670.350303489619965282.299975869354
Winsorized Mean ( 15 / 20 )99.33816666666670.257341744651912386.016527559625
Winsorized Mean ( 16 / 20 )99.47683333333330.226468153142881439.253077983873
Winsorized Mean ( 17 / 20 )99.5250.217213802872176458.189114522192
Winsorized Mean ( 18 / 20 )99.6750.177970114294285560.065943629057
Winsorized Mean ( 19 / 20 )99.77950.143056115772403697.485035583838
Winsorized Mean ( 20 / 20 )99.85616666666670.127620795036703782.44432373226
Trimmed Mean ( 1 / 20 )99.05913793103450.570368974753473173.675536916871
Trimmed Mean ( 2 / 20 )99.17214285714290.536576855358917184.823743079277
Trimmed Mean ( 3 / 20 )99.29574074074070.495210929362305200.512013877816
Trimmed Mean ( 4 / 20 )99.34942307692310.476569045694159208.468057198749
Trimmed Mean ( 5 / 20 )99.37520.463859253811907214.235674255399
Trimmed Mean ( 6 / 20 )99.391250.452244856264536219.773091110321
Trimmed Mean ( 7 / 20 )99.40652173913040.43909329254125226.390435535501
Trimmed Mean ( 8 / 20 )99.4150.424491425592663234.197898959206
Trimmed Mean ( 9 / 20 )99.42047619047620.406772794035676244.412796647744
Trimmed Mean ( 10 / 20 )99.4240.385534726893733257.885977745929
Trimmed Mean ( 11 / 20 )99.42552631578950.357756900178968277.913651046428
Trimmed Mean ( 12 / 20 )99.43305555555560.326841503126186304.22407988121
Trimmed Mean ( 13 / 20 )99.50029411764710.305115473098441326.107008298281
Trimmed Mean ( 14 / 20 )99.5781250.27579300526669361.061096903849
Trimmed Mean ( 15 / 20 )99.67633333333330.233659779851618426.587465744559
Trimmed Mean ( 16 / 20 )99.72464285714290.213666952766355466.729372820663
Trimmed Mean ( 17 / 20 )99.76038461538460.196352493682021508.067826105329
Trimmed Mean ( 18 / 20 )99.7950.172813462304368577.472372055344
Trimmed Mean ( 19 / 20 )99.81318181818180.155119541060726643.45975455863
Trimmed Mean ( 20 / 20 )99.81850.14404545152577692.965303261533
Median99.68
Midrange95.885
Midmean - Weighted Average at Xnp99.5154838709677
Midmean - Weighted Average at X(n+1)p99.6763333333333
Midmean - Empirical Distribution Function99.5154838709677
Midmean - Empirical Distribution Function - Averaging99.6763333333333
Midmean - Empirical Distribution Function - Interpolation99.6763333333333
Midmean - Closest Observation99.5154838709677
Midmean - True Basic - Statistics Graphics Toolkit99.6763333333333
Midmean - MS Excel (old versions)99.578125
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')