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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 11 Oct 2013 04:45:11 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Oct/11/t1381481138gqq4svgdcevjlo2.htm/, Retrieved Sat, 27 Apr 2024 21:53:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=214698, Retrieved Sat, 27 Apr 2024 21:53:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-10-11 08:45:11] [180e98ae07f6df0eca7781798569558e] [Current]
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Dataseries X:
25
24
25
27
24
26
24
24
21
23
24
23
22
25
26
22
24
22
23
25
24
24
21
22
21
21
20
20
22
21
23
22
24
21
22
20
23
21
21
21
22
24
21
23
25
23
24
25
28
26
25
24
25
26
24
21
22
25
27
26
24
27
23
23
23
25
26
22
23
27
25
24
21
24
22
26
22
25
20
21
23
24
24
18




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214698&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214698&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214698&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean23.34523809523810.218542377984355106.822476768828
Geometric Mean23.2595809924262
Harmonic Mean23.1731166347812
Quadratic Mean23.4299868910396
Winsorized Mean ( 1 / 28 )23.35714285714290.209938696310393111.256968189464
Winsorized Mean ( 2 / 28 )23.35714285714290.209938696310393111.256968189464
Winsorized Mean ( 3 / 28 )23.35714285714290.209938696310393111.256968189464
Winsorized Mean ( 4 / 28 )23.35714285714290.209938696310393111.256968189464
Winsorized Mean ( 5 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 6 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 7 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 8 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 9 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 10 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 11 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 12 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 13 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 14 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 15 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 16 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 17 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 18 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 19 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 20 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 21 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 22 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 23 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 24 / 28 )23.14285714285710.100404884791981230.495330887581
Winsorized Mean ( 25 / 28 )23.14285714285710.100404884791981230.495330887581
Winsorized Mean ( 26 / 28 )23.14285714285710.100404884791981230.495330887581
Winsorized Mean ( 27 / 28 )23.14285714285710.100404884791981230.495330887581
Winsorized Mean ( 28 / 28 )23.14285714285710.100404884791981230.495330887581
Trimmed Mean ( 1 / 28 )23.35365853658540.206322783527567113.189916001037
Trimmed Mean ( 2 / 28 )23.350.202124789127279115.522693187803
Trimmed Mean ( 3 / 28 )23.34615384615380.197239459257066118.364519625489
Trimmed Mean ( 4 / 28 )23.34210526315790.191533636438486121.869483069386
Trimmed Mean ( 5 / 28 )23.33783783783780.184835124732019126.263002617462
Trimmed Mean ( 6 / 28 )23.33333333333330.183429338925693127.206113645678
Trimmed Mean ( 7 / 28 )23.32857142857140.181689139763052128.398271129442
Trimmed Mean ( 8 / 28 )23.32352941176470.179553118655864129.897656951686
Trimmed Mean ( 9 / 28 )23.31818181818180.176945187816503131.781949573918
Trimmed Mean ( 10 / 28 )23.31250.17376976877375134.157397828808
Trimmed Mean ( 11 / 28 )23.30645161290320.169904800664837137.173590867975
Trimmed Mean ( 12 / 28 )23.30.165191209188686141.048667870613
Trimmed Mean ( 13 / 28 )23.31034482758620.163534198535283142.541101716758
Trimmed Mean ( 14 / 28 )23.32142857142860.16138029389577144.512245011099
Trimmed Mean ( 15 / 28 )23.33333333333330.158610317143629147.111069150716
Trimmed Mean ( 16 / 28 )23.34615384615380.155066801604148150.555461289203
Trimmed Mean ( 17 / 28 )23.360.150536455683651155.17835791943
Trimmed Mean ( 18 / 28 )23.3750.144720934685242161.517751739504
Trimmed Mean ( 19 / 28 )23.36956521739130.143653823199993162.679730318465
Trimmed Mean ( 20 / 28 )23.36363636363640.142058667461584164.464701669501
Trimmed Mean ( 21 / 28 )23.35714285714290.139775116261562167.105157783839
Trimmed Mean ( 22 / 28 )23.350.136579083881267170.963220256324
Trimmed Mean ( 23 / 28 )23.34210526315790.132146712453765176.637805282706
Trimmed Mean ( 24 / 28 )23.33333333333330.125988157669742185.202591774521
Trimmed Mean ( 25 / 28 )23.35294117647060.125829532290289185.59189366289
Trimmed Mean ( 26 / 28 )23.3750.125187
Trimmed Mean ( 27 / 28 )23.40.123176352410288189.971528967321
Trimmed Mean ( 28 / 28 )23.42857142857140.119838641829694195.5009759028
Median23.5
Midrange23
Midmean - Weighted Average at Xnp23.5555555555556
Midmean - Weighted Average at X(n+1)p23.5555555555556
Midmean - Empirical Distribution Function23.5555555555556
Midmean - Empirical Distribution Function - Averaging23.5555555555556
Midmean - Empirical Distribution Function - Interpolation23.5555555555556
Midmean - Closest Observation23.5555555555556
Midmean - True Basic - Statistics Graphics Toolkit23.5555555555556
Midmean - MS Excel (old versions)23.5555555555556
Number of observations84

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 23.3452380952381 & 0.218542377984355 & 106.822476768828 \tabularnewline
Geometric Mean & 23.2595809924262 &  &  \tabularnewline
Harmonic Mean & 23.1731166347812 &  &  \tabularnewline
Quadratic Mean & 23.4299868910396 &  &  \tabularnewline
Winsorized Mean ( 1 / 28 ) & 23.3571428571429 & 0.209938696310393 & 111.256968189464 \tabularnewline
Winsorized Mean ( 2 / 28 ) & 23.3571428571429 & 0.209938696310393 & 111.256968189464 \tabularnewline
Winsorized Mean ( 3 / 28 ) & 23.3571428571429 & 0.209938696310393 & 111.256968189464 \tabularnewline
Winsorized Mean ( 4 / 28 ) & 23.3571428571429 & 0.209938696310393 & 111.256968189464 \tabularnewline
Winsorized Mean ( 5 / 28 ) & 23.3571428571429 & 0.188330571679591 & 124.022046175703 \tabularnewline
Winsorized Mean ( 6 / 28 ) & 23.3571428571429 & 0.188330571679591 & 124.022046175703 \tabularnewline
Winsorized Mean ( 7 / 28 ) & 23.3571428571429 & 0.188330571679591 & 124.022046175703 \tabularnewline
Winsorized Mean ( 8 / 28 ) & 23.3571428571429 & 0.188330571679591 & 124.022046175703 \tabularnewline
Winsorized Mean ( 9 / 28 ) & 23.3571428571429 & 0.188330571679591 & 124.022046175703 \tabularnewline
Winsorized Mean ( 10 / 28 ) & 23.3571428571429 & 0.188330571679591 & 124.022046175703 \tabularnewline
Winsorized Mean ( 11 / 28 ) & 23.3571428571429 & 0.188330571679591 & 124.022046175703 \tabularnewline
Winsorized Mean ( 12 / 28 ) & 23.2142857142857 & 0.166871442105329 & 139.11479053218 \tabularnewline
Winsorized Mean ( 13 / 28 ) & 23.2142857142857 & 0.166871442105329 & 139.11479053218 \tabularnewline
Winsorized Mean ( 14 / 28 ) & 23.2142857142857 & 0.166871442105329 & 139.11479053218 \tabularnewline
Winsorized Mean ( 15 / 28 ) & 23.2142857142857 & 0.166871442105329 & 139.11479053218 \tabularnewline
Winsorized Mean ( 16 / 28 ) & 23.2142857142857 & 0.166871442105329 & 139.11479053218 \tabularnewline
Winsorized Mean ( 17 / 28 ) & 23.2142857142857 & 0.166871442105329 & 139.11479053218 \tabularnewline
Winsorized Mean ( 18 / 28 ) & 23.4285714285714 & 0.135798053683817 & 172.525089962784 \tabularnewline
Winsorized Mean ( 19 / 28 ) & 23.4285714285714 & 0.135798053683817 & 172.525089962784 \tabularnewline
Winsorized Mean ( 20 / 28 ) & 23.4285714285714 & 0.135798053683817 & 172.525089962784 \tabularnewline
Winsorized Mean ( 21 / 28 ) & 23.4285714285714 & 0.135798053683817 & 172.525089962784 \tabularnewline
Winsorized Mean ( 22 / 28 ) & 23.4285714285714 & 0.135798053683817 & 172.525089962784 \tabularnewline
Winsorized Mean ( 23 / 28 ) & 23.4285714285714 & 0.135798053683817 & 172.525089962784 \tabularnewline
Winsorized Mean ( 24 / 28 ) & 23.1428571428571 & 0.100404884791981 & 230.495330887581 \tabularnewline
Winsorized Mean ( 25 / 28 ) & 23.1428571428571 & 0.100404884791981 & 230.495330887581 \tabularnewline
Winsorized Mean ( 26 / 28 ) & 23.1428571428571 & 0.100404884791981 & 230.495330887581 \tabularnewline
Winsorized Mean ( 27 / 28 ) & 23.1428571428571 & 0.100404884791981 & 230.495330887581 \tabularnewline
Winsorized Mean ( 28 / 28 ) & 23.1428571428571 & 0.100404884791981 & 230.495330887581 \tabularnewline
Trimmed Mean ( 1 / 28 ) & 23.3536585365854 & 0.206322783527567 & 113.189916001037 \tabularnewline
Trimmed Mean ( 2 / 28 ) & 23.35 & 0.202124789127279 & 115.522693187803 \tabularnewline
Trimmed Mean ( 3 / 28 ) & 23.3461538461538 & 0.197239459257066 & 118.364519625489 \tabularnewline
Trimmed Mean ( 4 / 28 ) & 23.3421052631579 & 0.191533636438486 & 121.869483069386 \tabularnewline
Trimmed Mean ( 5 / 28 ) & 23.3378378378378 & 0.184835124732019 & 126.263002617462 \tabularnewline
Trimmed Mean ( 6 / 28 ) & 23.3333333333333 & 0.183429338925693 & 127.206113645678 \tabularnewline
Trimmed Mean ( 7 / 28 ) & 23.3285714285714 & 0.181689139763052 & 128.398271129442 \tabularnewline
Trimmed Mean ( 8 / 28 ) & 23.3235294117647 & 0.179553118655864 & 129.897656951686 \tabularnewline
Trimmed Mean ( 9 / 28 ) & 23.3181818181818 & 0.176945187816503 & 131.781949573918 \tabularnewline
Trimmed Mean ( 10 / 28 ) & 23.3125 & 0.17376976877375 & 134.157397828808 \tabularnewline
Trimmed Mean ( 11 / 28 ) & 23.3064516129032 & 0.169904800664837 & 137.173590867975 \tabularnewline
Trimmed Mean ( 12 / 28 ) & 23.3 & 0.165191209188686 & 141.048667870613 \tabularnewline
Trimmed Mean ( 13 / 28 ) & 23.3103448275862 & 0.163534198535283 & 142.541101716758 \tabularnewline
Trimmed Mean ( 14 / 28 ) & 23.3214285714286 & 0.16138029389577 & 144.512245011099 \tabularnewline
Trimmed Mean ( 15 / 28 ) & 23.3333333333333 & 0.158610317143629 & 147.111069150716 \tabularnewline
Trimmed Mean ( 16 / 28 ) & 23.3461538461538 & 0.155066801604148 & 150.555461289203 \tabularnewline
Trimmed Mean ( 17 / 28 ) & 23.36 & 0.150536455683651 & 155.17835791943 \tabularnewline
Trimmed Mean ( 18 / 28 ) & 23.375 & 0.144720934685242 & 161.517751739504 \tabularnewline
Trimmed Mean ( 19 / 28 ) & 23.3695652173913 & 0.143653823199993 & 162.679730318465 \tabularnewline
Trimmed Mean ( 20 / 28 ) & 23.3636363636364 & 0.142058667461584 & 164.464701669501 \tabularnewline
Trimmed Mean ( 21 / 28 ) & 23.3571428571429 & 0.139775116261562 & 167.105157783839 \tabularnewline
Trimmed Mean ( 22 / 28 ) & 23.35 & 0.136579083881267 & 170.963220256324 \tabularnewline
Trimmed Mean ( 23 / 28 ) & 23.3421052631579 & 0.132146712453765 & 176.637805282706 \tabularnewline
Trimmed Mean ( 24 / 28 ) & 23.3333333333333 & 0.125988157669742 & 185.202591774521 \tabularnewline
Trimmed Mean ( 25 / 28 ) & 23.3529411764706 & 0.125829532290289 & 185.59189366289 \tabularnewline
Trimmed Mean ( 26 / 28 ) & 23.375 & 0.125 & 187 \tabularnewline
Trimmed Mean ( 27 / 28 ) & 23.4 & 0.123176352410288 & 189.971528967321 \tabularnewline
Trimmed Mean ( 28 / 28 ) & 23.4285714285714 & 0.119838641829694 & 195.5009759028 \tabularnewline
Median & 23.5 &  &  \tabularnewline
Midrange & 23 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 23.5555555555556 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 23.5555555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 23.5555555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 23.5555555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 23.5555555555556 &  &  \tabularnewline
Midmean - Closest Observation & 23.5555555555556 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 23.5555555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 23.5555555555556 &  &  \tabularnewline
Number of observations & 84 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=214698&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]23.3452380952381[/C][C]0.218542377984355[/C][C]106.822476768828[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]23.2595809924262[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]23.1731166347812[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]23.4299868910396[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 28 )[/C][C]23.3571428571429[/C][C]0.209938696310393[/C][C]111.256968189464[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 28 )[/C][C]23.3571428571429[/C][C]0.209938696310393[/C][C]111.256968189464[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 28 )[/C][C]23.3571428571429[/C][C]0.209938696310393[/C][C]111.256968189464[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 28 )[/C][C]23.3571428571429[/C][C]0.209938696310393[/C][C]111.256968189464[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 28 )[/C][C]23.3571428571429[/C][C]0.188330571679591[/C][C]124.022046175703[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 28 )[/C][C]23.3571428571429[/C][C]0.188330571679591[/C][C]124.022046175703[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 28 )[/C][C]23.3571428571429[/C][C]0.188330571679591[/C][C]124.022046175703[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 28 )[/C][C]23.3571428571429[/C][C]0.188330571679591[/C][C]124.022046175703[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 28 )[/C][C]23.3571428571429[/C][C]0.188330571679591[/C][C]124.022046175703[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 28 )[/C][C]23.3571428571429[/C][C]0.188330571679591[/C][C]124.022046175703[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 28 )[/C][C]23.3571428571429[/C][C]0.188330571679591[/C][C]124.022046175703[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 28 )[/C][C]23.2142857142857[/C][C]0.166871442105329[/C][C]139.11479053218[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 28 )[/C][C]23.2142857142857[/C][C]0.166871442105329[/C][C]139.11479053218[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 28 )[/C][C]23.2142857142857[/C][C]0.166871442105329[/C][C]139.11479053218[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 28 )[/C][C]23.2142857142857[/C][C]0.166871442105329[/C][C]139.11479053218[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 28 )[/C][C]23.2142857142857[/C][C]0.166871442105329[/C][C]139.11479053218[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 28 )[/C][C]23.2142857142857[/C][C]0.166871442105329[/C][C]139.11479053218[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 28 )[/C][C]23.4285714285714[/C][C]0.135798053683817[/C][C]172.525089962784[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 28 )[/C][C]23.4285714285714[/C][C]0.135798053683817[/C][C]172.525089962784[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 28 )[/C][C]23.4285714285714[/C][C]0.135798053683817[/C][C]172.525089962784[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 28 )[/C][C]23.4285714285714[/C][C]0.135798053683817[/C][C]172.525089962784[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 28 )[/C][C]23.4285714285714[/C][C]0.135798053683817[/C][C]172.525089962784[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 28 )[/C][C]23.4285714285714[/C][C]0.135798053683817[/C][C]172.525089962784[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 28 )[/C][C]23.1428571428571[/C][C]0.100404884791981[/C][C]230.495330887581[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 28 )[/C][C]23.1428571428571[/C][C]0.100404884791981[/C][C]230.495330887581[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 28 )[/C][C]23.1428571428571[/C][C]0.100404884791981[/C][C]230.495330887581[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 28 )[/C][C]23.1428571428571[/C][C]0.100404884791981[/C][C]230.495330887581[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 28 )[/C][C]23.1428571428571[/C][C]0.100404884791981[/C][C]230.495330887581[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 28 )[/C][C]23.3536585365854[/C][C]0.206322783527567[/C][C]113.189916001037[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 28 )[/C][C]23.35[/C][C]0.202124789127279[/C][C]115.522693187803[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 28 )[/C][C]23.3461538461538[/C][C]0.197239459257066[/C][C]118.364519625489[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 28 )[/C][C]23.3421052631579[/C][C]0.191533636438486[/C][C]121.869483069386[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 28 )[/C][C]23.3378378378378[/C][C]0.184835124732019[/C][C]126.263002617462[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 28 )[/C][C]23.3333333333333[/C][C]0.183429338925693[/C][C]127.206113645678[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 28 )[/C][C]23.3285714285714[/C][C]0.181689139763052[/C][C]128.398271129442[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 28 )[/C][C]23.3235294117647[/C][C]0.179553118655864[/C][C]129.897656951686[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 28 )[/C][C]23.3181818181818[/C][C]0.176945187816503[/C][C]131.781949573918[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 28 )[/C][C]23.3125[/C][C]0.17376976877375[/C][C]134.157397828808[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 28 )[/C][C]23.3064516129032[/C][C]0.169904800664837[/C][C]137.173590867975[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 28 )[/C][C]23.3[/C][C]0.165191209188686[/C][C]141.048667870613[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 28 )[/C][C]23.3103448275862[/C][C]0.163534198535283[/C][C]142.541101716758[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 28 )[/C][C]23.3214285714286[/C][C]0.16138029389577[/C][C]144.512245011099[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 28 )[/C][C]23.3333333333333[/C][C]0.158610317143629[/C][C]147.111069150716[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 28 )[/C][C]23.3461538461538[/C][C]0.155066801604148[/C][C]150.555461289203[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 28 )[/C][C]23.36[/C][C]0.150536455683651[/C][C]155.17835791943[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 28 )[/C][C]23.375[/C][C]0.144720934685242[/C][C]161.517751739504[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 28 )[/C][C]23.3695652173913[/C][C]0.143653823199993[/C][C]162.679730318465[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 28 )[/C][C]23.3636363636364[/C][C]0.142058667461584[/C][C]164.464701669501[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 28 )[/C][C]23.3571428571429[/C][C]0.139775116261562[/C][C]167.105157783839[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 28 )[/C][C]23.35[/C][C]0.136579083881267[/C][C]170.963220256324[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 28 )[/C][C]23.3421052631579[/C][C]0.132146712453765[/C][C]176.637805282706[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 28 )[/C][C]23.3333333333333[/C][C]0.125988157669742[/C][C]185.202591774521[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 28 )[/C][C]23.3529411764706[/C][C]0.125829532290289[/C][C]185.59189366289[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 28 )[/C][C]23.375[/C][C]0.125[/C][C]187[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 28 )[/C][C]23.4[/C][C]0.123176352410288[/C][C]189.971528967321[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 28 )[/C][C]23.4285714285714[/C][C]0.119838641829694[/C][C]195.5009759028[/C][/ROW]
[ROW][C]Median[/C][C]23.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]23[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]23.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]23.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]23.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]23.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]23.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]23.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]23.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]23.5555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]84[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=214698&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=214698&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 Mean23.34523809523810.218542377984355106.822476768828
Geometric Mean23.2595809924262
Harmonic Mean23.1731166347812
Quadratic Mean23.4299868910396
Winsorized Mean ( 1 / 28 )23.35714285714290.209938696310393111.256968189464
Winsorized Mean ( 2 / 28 )23.35714285714290.209938696310393111.256968189464
Winsorized Mean ( 3 / 28 )23.35714285714290.209938696310393111.256968189464
Winsorized Mean ( 4 / 28 )23.35714285714290.209938696310393111.256968189464
Winsorized Mean ( 5 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 6 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 7 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 8 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 9 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 10 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 11 / 28 )23.35714285714290.188330571679591124.022046175703
Winsorized Mean ( 12 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 13 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 14 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 15 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 16 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 17 / 28 )23.21428571428570.166871442105329139.11479053218
Winsorized Mean ( 18 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 19 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 20 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 21 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 22 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 23 / 28 )23.42857142857140.135798053683817172.525089962784
Winsorized Mean ( 24 / 28 )23.14285714285710.100404884791981230.495330887581
Winsorized Mean ( 25 / 28 )23.14285714285710.100404884791981230.495330887581
Winsorized Mean ( 26 / 28 )23.14285714285710.100404884791981230.495330887581
Winsorized Mean ( 27 / 28 )23.14285714285710.100404884791981230.495330887581
Winsorized Mean ( 28 / 28 )23.14285714285710.100404884791981230.495330887581
Trimmed Mean ( 1 / 28 )23.35365853658540.206322783527567113.189916001037
Trimmed Mean ( 2 / 28 )23.350.202124789127279115.522693187803
Trimmed Mean ( 3 / 28 )23.34615384615380.197239459257066118.364519625489
Trimmed Mean ( 4 / 28 )23.34210526315790.191533636438486121.869483069386
Trimmed Mean ( 5 / 28 )23.33783783783780.184835124732019126.263002617462
Trimmed Mean ( 6 / 28 )23.33333333333330.183429338925693127.206113645678
Trimmed Mean ( 7 / 28 )23.32857142857140.181689139763052128.398271129442
Trimmed Mean ( 8 / 28 )23.32352941176470.179553118655864129.897656951686
Trimmed Mean ( 9 / 28 )23.31818181818180.176945187816503131.781949573918
Trimmed Mean ( 10 / 28 )23.31250.17376976877375134.157397828808
Trimmed Mean ( 11 / 28 )23.30645161290320.169904800664837137.173590867975
Trimmed Mean ( 12 / 28 )23.30.165191209188686141.048667870613
Trimmed Mean ( 13 / 28 )23.31034482758620.163534198535283142.541101716758
Trimmed Mean ( 14 / 28 )23.32142857142860.16138029389577144.512245011099
Trimmed Mean ( 15 / 28 )23.33333333333330.158610317143629147.111069150716
Trimmed Mean ( 16 / 28 )23.34615384615380.155066801604148150.555461289203
Trimmed Mean ( 17 / 28 )23.360.150536455683651155.17835791943
Trimmed Mean ( 18 / 28 )23.3750.144720934685242161.517751739504
Trimmed Mean ( 19 / 28 )23.36956521739130.143653823199993162.679730318465
Trimmed Mean ( 20 / 28 )23.36363636363640.142058667461584164.464701669501
Trimmed Mean ( 21 / 28 )23.35714285714290.139775116261562167.105157783839
Trimmed Mean ( 22 / 28 )23.350.136579083881267170.963220256324
Trimmed Mean ( 23 / 28 )23.34210526315790.132146712453765176.637805282706
Trimmed Mean ( 24 / 28 )23.33333333333330.125988157669742185.202591774521
Trimmed Mean ( 25 / 28 )23.35294117647060.125829532290289185.59189366289
Trimmed Mean ( 26 / 28 )23.3750.125187
Trimmed Mean ( 27 / 28 )23.40.123176352410288189.971528967321
Trimmed Mean ( 28 / 28 )23.42857142857140.119838641829694195.5009759028
Median23.5
Midrange23
Midmean - Weighted Average at Xnp23.5555555555556
Midmean - Weighted Average at X(n+1)p23.5555555555556
Midmean - Empirical Distribution Function23.5555555555556
Midmean - Empirical Distribution Function - Averaging23.5555555555556
Midmean - Empirical Distribution Function - Interpolation23.5555555555556
Midmean - Closest Observation23.5555555555556
Midmean - True Basic - Statistics Graphics Toolkit23.5555555555556
Midmean - MS Excel (old versions)23.5555555555556
Number of observations84



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')