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Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Wed, 19 Oct 2011 06:42:35 -0400

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/19/t13190210899iz1qz2mp7x7v9a.htm/, Retrieved Wed, 15 May 2024 04:05:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132750, Retrieved Wed, 15 May 2024 04:05:42 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDG2011W52a

Estimated Impact

137

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Central Tendency] [] [2011-10-19 10:42:35] [704adabfc46bcbd971bf5c1481d7b31c] [Current]

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2,02
2,02
2,02
2,02
2,03
2,03
2,03
2,04
2,04
2,05
2,06
2,06
2,07
2,08
2,08
2,08
2,09
2,09
2,09
2,1
2,1
2,1
2,11
2,11
2,11
2,13
2,18
2,2
2,21
2,21
2,22
2,22
2,23
2,23
2,23
2,23
2,24
2,25
2,26
2,27
2,28
2,29
2,3
2,3
2,3
2,32
2,32
2,32
2,33
2,34
2,34
2,34
2,35
2,35
2,36
2,37
2,37
2,37
2,38
2,38
2,38
2,39
2,4
2,41
2,42
2,43
2,43
2,43
2,43
2,44
2,44
2,45

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132750&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132750&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132750&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.23194444444444	0.0165767986616503	134.642670759339
Geometric Mean	2.22754717567212
Harmonic Mean	2.22313121581492
Quadratic Mean	2.23631082614003
Winsorized Mean ( 1 / 24 )	2.23180555555556	0.0165516292699594	134.839025159064
Winsorized Mean ( 2 / 24 )	2.23180555555556	0.0165516292699594	134.839025159064
Winsorized Mean ( 3 / 24 )	2.23138888888889	0.0164793529892253	135.405127273373
Winsorized Mean ( 4 / 24 )	2.23194444444444	0.0163809296075607	136.252611903922
Winsorized Mean ( 5 / 24 )	2.23194444444444	0.0163809296075607	136.252611903922
Winsorized Mean ( 6 / 24 )	2.23194444444444	0.0163809296075607	136.252611903922
Winsorized Mean ( 7 / 24 )	2.23194444444444	0.0160516075093478	139.0480326126
Winsorized Mean ( 8 / 24 )	2.23083333333333	0.015871587097556	140.555151770352
Winsorized Mean ( 9 / 24 )	2.23083333333333	0.0154671012364075	144.230861312413
Winsorized Mean ( 10 / 24 )	2.23083333333333	0.0150309409628433	148.41607979487
Winsorized Mean ( 11 / 24 )	2.22930555555556	0.0148074844524458	150.552618354249
Winsorized Mean ( 12 / 24 )	2.23097222222222	0.0145433351171962	153.401692544669
Winsorized Mean ( 13 / 24 )	2.23277777777778	0.0142663878014273	156.506174432914
Winsorized Mean ( 14 / 24 )	2.23083333333333	0.0139888033697779	159.472777932738
Winsorized Mean ( 15 / 24 )	2.23083333333333	0.0139888033697779	159.472777932738
Winsorized Mean ( 16 / 24 )	2.23305555555556	0.0136560689599935	163.521110071827
Winsorized Mean ( 17 / 24 )	2.23069444444444	0.0133279425559023	167.36975231459
Winsorized Mean ( 18 / 24 )	2.22819444444444	0.0129920018565789	171.505089749978
Winsorized Mean ( 19 / 24 )	2.23083333333333	0.0126013108839414	177.031846438787
Winsorized Mean ( 20 / 24 )	2.22805555555556	0.012237284430715	182.07107697548
Winsorized Mean ( 21 / 24 )	2.22805555555556	0.012237284430715	182.07107697548
Winsorized Mean ( 22 / 24 )	2.23111111111111	0.0117910133207999	189.221320543784
Winsorized Mean ( 23 / 24 )	2.22791666666667	0.0113813837441298	195.750948808466
Winsorized Mean ( 24 / 24 )	2.22458333333333	0.0109664759819032	202.853071214886
Trimmed Mean ( 1 / 24 )	2.23185714285714	0.0164829956386364	135.403611806196
Trimmed Mean ( 2 / 24 )	2.23191176470588	0.0163910955624553	136.166112643392
Trimmed Mean ( 3 / 24 )	2.2319696969697	0.0162716159934474	137.169516406269
Trimmed Mean ( 4 / 24 )	2.2321875	0.016150440970809	138.212170431417
Trimmed Mean ( 5 / 24 )	2.23225806451613	0.0160288267467309	139.265218832776
Trimmed Mean ( 6 / 24 )	2.23233333333333	0.0158708891499672	140.655845569808
Trimmed Mean ( 7 / 24 )	2.23241379310345	0.0156688167260303	142.47494447968
Trimmed Mean ( 8 / 24 )	2.2325	0.0154945528761294	144.082892733184
Trimmed Mean ( 9 / 24 )	2.23277777777778	0.0153104757773939	145.833337267971
Trimmed Mean ( 10 / 24 )	2.23307692307692	0.0151601268652847	147.299355930224
Trimmed Mean ( 11 / 24 )	2.2334	0.0150498762622888	148.399891206836
Trimmed Mean ( 12 / 24 )	2.23395833333333	0.0149370415842099	149.558285738112
Trimmed Mean ( 13 / 24 )	2.23434782608696	0.0148280064491926	150.684303634668
Trimmed Mean ( 14 / 24 )	2.23454545454545	0.0147224302324989	151.778301493515
Trimmed Mean ( 15 / 24 )	2.235	0.0146156726214999	152.91803927739
Trimmed Mean ( 16 / 24 )	2.2355	0.0144468521990619	154.739590963986
Trimmed Mean ( 17 / 24 )	2.23578947368421	0.0142704599890742	156.672558235403
Trimmed Mean ( 18 / 24 )	2.23638888888889	0.014075492479347	158.885303101852
Trimmed Mean ( 19 / 24 )	2.23735294117647	0.0138511878647179	161.527874939557
Trimmed Mean ( 20 / 24 )	2.238125	0.013607676172163	164.475180896684
Trimmed Mean ( 21 / 24 )	2.23933333333333	0.0133126276008851	168.21122023908
Trimmed Mean ( 22 / 24 )	2.24071428571429	0.0128372862540082	174.54734913422
Trimmed Mean ( 23 / 24 )	2.24192307692308	0.0122539692880964	182.954847055223
Trimmed Mean ( 24 / 24 )	2.24375	0.0114495190076809	195.968930965116
Median	2.235
Midrange	2.235
Midmean - Weighted Average at Xnp	2.22868421052631
Midmean - Weighted Average at X(n+1)p	2.22868421052631
Midmean - Empirical Distribution Function	2.22868421052631
Midmean - Empirical Distribution Function - Averaging	2.22868421052631
Midmean - Empirical Distribution Function - Interpolation	2.22868421052631
Midmean - Closest Observation	2.22868421052631
Midmean - True Basic - Statistics Graphics Toolkit	2.22868421052631
Midmean - MS Excel (old versions)	2.23205128205128
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.23194444444444 & 0.0165767986616503 & 134.642670759339 \tabularnewline
Geometric Mean & 2.22754717567212 &  &  \tabularnewline
Harmonic Mean & 2.22313121581492 &  &  \tabularnewline
Quadratic Mean & 2.23631082614003 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.23180555555556 & 0.0165516292699594 & 134.839025159064 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.23180555555556 & 0.0165516292699594 & 134.839025159064 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.23138888888889 & 0.0164793529892253 & 135.405127273373 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.23194444444444 & 0.0163809296075607 & 136.252611903922 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.23194444444444 & 0.0163809296075607 & 136.252611903922 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.23194444444444 & 0.0163809296075607 & 136.252611903922 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.23194444444444 & 0.0160516075093478 & 139.0480326126 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.23083333333333 & 0.015871587097556 & 140.555151770352 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.23083333333333 & 0.0154671012364075 & 144.230861312413 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.23083333333333 & 0.0150309409628433 & 148.41607979487 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.22930555555556 & 0.0148074844524458 & 150.552618354249 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.23097222222222 & 0.0145433351171962 & 153.401692544669 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.23277777777778 & 0.0142663878014273 & 156.506174432914 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.23083333333333 & 0.0139888033697779 & 159.472777932738 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.23083333333333 & 0.0139888033697779 & 159.472777932738 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.23305555555556 & 0.0136560689599935 & 163.521110071827 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.23069444444444 & 0.0133279425559023 & 167.36975231459 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.22819444444444 & 0.0129920018565789 & 171.505089749978 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.23083333333333 & 0.0126013108839414 & 177.031846438787 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.22805555555556 & 0.012237284430715 & 182.07107697548 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.22805555555556 & 0.012237284430715 & 182.07107697548 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.23111111111111 & 0.0117910133207999 & 189.221320543784 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.22791666666667 & 0.0113813837441298 & 195.750948808466 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.22458333333333 & 0.0109664759819032 & 202.853071214886 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.23185714285714 & 0.0164829956386364 & 135.403611806196 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.23191176470588 & 0.0163910955624553 & 136.166112643392 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.2319696969697 & 0.0162716159934474 & 137.169516406269 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.2321875 & 0.016150440970809 & 138.212170431417 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.23225806451613 & 0.0160288267467309 & 139.265218832776 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.23233333333333 & 0.0158708891499672 & 140.655845569808 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.23241379310345 & 0.0156688167260303 & 142.47494447968 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.2325 & 0.0154945528761294 & 144.082892733184 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.23277777777778 & 0.0153104757773939 & 145.833337267971 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.23307692307692 & 0.0151601268652847 & 147.299355930224 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.2334 & 0.0150498762622888 & 148.399891206836 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.23395833333333 & 0.0149370415842099 & 149.558285738112 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.23434782608696 & 0.0148280064491926 & 150.684303634668 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.23454545454545 & 0.0147224302324989 & 151.778301493515 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.235 & 0.0146156726214999 & 152.91803927739 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.2355 & 0.0144468521990619 & 154.739590963986 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.23578947368421 & 0.0142704599890742 & 156.672558235403 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.23638888888889 & 0.014075492479347 & 158.885303101852 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.23735294117647 & 0.0138511878647179 & 161.527874939557 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.238125 & 0.013607676172163 & 164.475180896684 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.23933333333333 & 0.0133126276008851 & 168.21122023908 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.24071428571429 & 0.0128372862540082 & 174.54734913422 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.24192307692308 & 0.0122539692880964 & 182.954847055223 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.24375 & 0.0114495190076809 & 195.968930965116 \tabularnewline
Median & 2.235 &  &  \tabularnewline
Midrange & 2.235 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.22868421052631 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.22868421052631 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.22868421052631 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.22868421052631 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.22868421052631 &  &  \tabularnewline
Midmean - Closest Observation & 2.22868421052631 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.22868421052631 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.23205128205128 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132750&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]2.23194444444444[/C][C]0.0165767986616503[/C][C]134.642670759339[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.22754717567212[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.22313121581492[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.23631082614003[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.23180555555556[/C][C]0.0165516292699594[/C][C]134.839025159064[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.23180555555556[/C][C]0.0165516292699594[/C][C]134.839025159064[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.23138888888889[/C][C]0.0164793529892253[/C][C]135.405127273373[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.23194444444444[/C][C]0.0163809296075607[/C][C]136.252611903922[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.23194444444444[/C][C]0.0163809296075607[/C][C]136.252611903922[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.23194444444444[/C][C]0.0163809296075607[/C][C]136.252611903922[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.23194444444444[/C][C]0.0160516075093478[/C][C]139.0480326126[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.23083333333333[/C][C]0.015871587097556[/C][C]140.555151770352[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.23083333333333[/C][C]0.0154671012364075[/C][C]144.230861312413[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.23083333333333[/C][C]0.0150309409628433[/C][C]148.41607979487[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.22930555555556[/C][C]0.0148074844524458[/C][C]150.552618354249[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.23097222222222[/C][C]0.0145433351171962[/C][C]153.401692544669[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.23277777777778[/C][C]0.0142663878014273[/C][C]156.506174432914[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.23083333333333[/C][C]0.0139888033697779[/C][C]159.472777932738[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.23083333333333[/C][C]0.0139888033697779[/C][C]159.472777932738[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.23305555555556[/C][C]0.0136560689599935[/C][C]163.521110071827[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.23069444444444[/C][C]0.0133279425559023[/C][C]167.36975231459[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.22819444444444[/C][C]0.0129920018565789[/C][C]171.505089749978[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.23083333333333[/C][C]0.0126013108839414[/C][C]177.031846438787[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.22805555555556[/C][C]0.012237284430715[/C][C]182.07107697548[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.22805555555556[/C][C]0.012237284430715[/C][C]182.07107697548[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.23111111111111[/C][C]0.0117910133207999[/C][C]189.221320543784[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.22791666666667[/C][C]0.0113813837441298[/C][C]195.750948808466[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.22458333333333[/C][C]0.0109664759819032[/C][C]202.853071214886[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.23185714285714[/C][C]0.0164829956386364[/C][C]135.403611806196[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.23191176470588[/C][C]0.0163910955624553[/C][C]136.166112643392[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.2319696969697[/C][C]0.0162716159934474[/C][C]137.169516406269[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.2321875[/C][C]0.016150440970809[/C][C]138.212170431417[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.23225806451613[/C][C]0.0160288267467309[/C][C]139.265218832776[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.23233333333333[/C][C]0.0158708891499672[/C][C]140.655845569808[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.23241379310345[/C][C]0.0156688167260303[/C][C]142.47494447968[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.2325[/C][C]0.0154945528761294[/C][C]144.082892733184[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.23277777777778[/C][C]0.0153104757773939[/C][C]145.833337267971[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.23307692307692[/C][C]0.0151601268652847[/C][C]147.299355930224[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.2334[/C][C]0.0150498762622888[/C][C]148.399891206836[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.23395833333333[/C][C]0.0149370415842099[/C][C]149.558285738112[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.23434782608696[/C][C]0.0148280064491926[/C][C]150.684303634668[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.23454545454545[/C][C]0.0147224302324989[/C][C]151.778301493515[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.235[/C][C]0.0146156726214999[/C][C]152.91803927739[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.2355[/C][C]0.0144468521990619[/C][C]154.739590963986[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.23578947368421[/C][C]0.0142704599890742[/C][C]156.672558235403[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.23638888888889[/C][C]0.014075492479347[/C][C]158.885303101852[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.23735294117647[/C][C]0.0138511878647179[/C][C]161.527874939557[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.238125[/C][C]0.013607676172163[/C][C]164.475180896684[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.23933333333333[/C][C]0.0133126276008851[/C][C]168.21122023908[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.24071428571429[/C][C]0.0128372862540082[/C][C]174.54734913422[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.24192307692308[/C][C]0.0122539692880964[/C][C]182.954847055223[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.24375[/C][C]0.0114495190076809[/C][C]195.968930965116[/C][/ROW]
[ROW][C]Median[/C][C]2.235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.22868421052631[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.22868421052631[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.22868421052631[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.22868421052631[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.22868421052631[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.22868421052631[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.22868421052631[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.23205128205128[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132750&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132750&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
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.23194444444444	0.0165767986616503	134.642670759339
Geometric Mean	2.22754717567212
Harmonic Mean	2.22313121581492
Quadratic Mean	2.23631082614003
Winsorized Mean ( 1 / 24 )	2.23180555555556	0.0165516292699594	134.839025159064
Winsorized Mean ( 2 / 24 )	2.23180555555556	0.0165516292699594	134.839025159064
Winsorized Mean ( 3 / 24 )	2.23138888888889	0.0164793529892253	135.405127273373
Winsorized Mean ( 4 / 24 )	2.23194444444444	0.0163809296075607	136.252611903922
Winsorized Mean ( 5 / 24 )	2.23194444444444	0.0163809296075607	136.252611903922
Winsorized Mean ( 6 / 24 )	2.23194444444444	0.0163809296075607	136.252611903922
Winsorized Mean ( 7 / 24 )	2.23194444444444	0.0160516075093478	139.0480326126
Winsorized Mean ( 8 / 24 )	2.23083333333333	0.015871587097556	140.555151770352
Winsorized Mean ( 9 / 24 )	2.23083333333333	0.0154671012364075	144.230861312413
Winsorized Mean ( 10 / 24 )	2.23083333333333	0.0150309409628433	148.41607979487
Winsorized Mean ( 11 / 24 )	2.22930555555556	0.0148074844524458	150.552618354249
Winsorized Mean ( 12 / 24 )	2.23097222222222	0.0145433351171962	153.401692544669
Winsorized Mean ( 13 / 24 )	2.23277777777778	0.0142663878014273	156.506174432914
Winsorized Mean ( 14 / 24 )	2.23083333333333	0.0139888033697779	159.472777932738
Winsorized Mean ( 15 / 24 )	2.23083333333333	0.0139888033697779	159.472777932738
Winsorized Mean ( 16 / 24 )	2.23305555555556	0.0136560689599935	163.521110071827
Winsorized Mean ( 17 / 24 )	2.23069444444444	0.0133279425559023	167.36975231459
Winsorized Mean ( 18 / 24 )	2.22819444444444	0.0129920018565789	171.505089749978
Winsorized Mean ( 19 / 24 )	2.23083333333333	0.0126013108839414	177.031846438787
Winsorized Mean ( 20 / 24 )	2.22805555555556	0.012237284430715	182.07107697548
Winsorized Mean ( 21 / 24 )	2.22805555555556	0.012237284430715	182.07107697548
Winsorized Mean ( 22 / 24 )	2.23111111111111	0.0117910133207999	189.221320543784
Winsorized Mean ( 23 / 24 )	2.22791666666667	0.0113813837441298	195.750948808466
Winsorized Mean ( 24 / 24 )	2.22458333333333	0.0109664759819032	202.853071214886
Trimmed Mean ( 1 / 24 )	2.23185714285714	0.0164829956386364	135.403611806196
Trimmed Mean ( 2 / 24 )	2.23191176470588	0.0163910955624553	136.166112643392
Trimmed Mean ( 3 / 24 )	2.2319696969697	0.0162716159934474	137.169516406269
Trimmed Mean ( 4 / 24 )	2.2321875	0.016150440970809	138.212170431417
Trimmed Mean ( 5 / 24 )	2.23225806451613	0.0160288267467309	139.265218832776
Trimmed Mean ( 6 / 24 )	2.23233333333333	0.0158708891499672	140.655845569808
Trimmed Mean ( 7 / 24 )	2.23241379310345	0.0156688167260303	142.47494447968
Trimmed Mean ( 8 / 24 )	2.2325	0.0154945528761294	144.082892733184
Trimmed Mean ( 9 / 24 )	2.23277777777778	0.0153104757773939	145.833337267971
Trimmed Mean ( 10 / 24 )	2.23307692307692	0.0151601268652847	147.299355930224
Trimmed Mean ( 11 / 24 )	2.2334	0.0150498762622888	148.399891206836
Trimmed Mean ( 12 / 24 )	2.23395833333333	0.0149370415842099	149.558285738112
Trimmed Mean ( 13 / 24 )	2.23434782608696	0.0148280064491926	150.684303634668
Trimmed Mean ( 14 / 24 )	2.23454545454545	0.0147224302324989	151.778301493515
Trimmed Mean ( 15 / 24 )	2.235	0.0146156726214999	152.91803927739
Trimmed Mean ( 16 / 24 )	2.2355	0.0144468521990619	154.739590963986
Trimmed Mean ( 17 / 24 )	2.23578947368421	0.0142704599890742	156.672558235403
Trimmed Mean ( 18 / 24 )	2.23638888888889	0.014075492479347	158.885303101852
Trimmed Mean ( 19 / 24 )	2.23735294117647	0.0138511878647179	161.527874939557
Trimmed Mean ( 20 / 24 )	2.238125	0.013607676172163	164.475180896684
Trimmed Mean ( 21 / 24 )	2.23933333333333	0.0133126276008851	168.21122023908
Trimmed Mean ( 22 / 24 )	2.24071428571429	0.0128372862540082	174.54734913422
Trimmed Mean ( 23 / 24 )	2.24192307692308	0.0122539692880964	182.954847055223
Trimmed Mean ( 24 / 24 )	2.24375	0.0114495190076809	195.968930965116
Median	2.235
Midrange	2.235
Midmean - Weighted Average at Xnp	2.22868421052631
Midmean - Weighted Average at X(n+1)p	2.22868421052631
Midmean - Empirical Distribution Function	2.22868421052631
Midmean - Empirical Distribution Function - Averaging	2.22868421052631
Midmean - Empirical Distribution Function - Interpolation	2.22868421052631
Midmean - Closest Observation	2.22868421052631
Midmean - True Basic - Statistics Graphics Toolkit	2.22868421052631
Midmean - MS Excel (old versions)	2.23205128205128
Number of observations	72

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code