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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 11 Dec 2009 06:53:31 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/11/t1260539965vs5lvvptvqq2c26.htm/, Retrieved Mon, 29 Apr 2024 03:50:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66202, Retrieved Mon, 29 Apr 2024 03:50:31 +0000
QR Codes:

Original text written by user:Paper
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper] [2009-12-11 13:53:31] [9b6f46453e60f88d91cef176fe926003] [Current]
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Dataseries X:
14,5
14,3
15,3
14,4
13,7
14,2
13,5
11,9
14,6
15,6
14,1
14,9
14,2
14,6
17,2
15,4
14,3
17,5
14,5
14,4
16,6
16,7
16,6
16,9
15,7
16,4
18,4
16,9
16,5
18,3
15,1
15,7
18,1
16,8
18,9
19
18,1
17,8
21,5
17,1
18,7
19
16,4
16,9
18,6
19,3
19,4
17,6
18,6
18,1
20,4
18,1
19,6
19,9
19,2
17,8
19,2
22
21,1
19,5
22,2
20,9
22,2
23,5
21,5
24,3
22,8
20,3
23,7
23,3
19,6
18
17,3
16,8
18,2
16,5
16
18,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66202&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66202&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17.75769230769230.30898154396024457.4716925810209
Geometric Mean17.5538780090592
Harmonic Mean17.3531217814873
Quadratic Mean17.9634850424909
Winsorized Mean ( 1 / 26 )17.77051282051280.30253182379729958.7393173963059
Winsorized Mean ( 2 / 26 )17.77051282051280.30032233196703659.1714665510235
Winsorized Mean ( 3 / 26 )17.77820512820510.29583999642178560.0939877745887
Winsorized Mean ( 4 / 26 )17.75769230769230.28900093868360461.4451025265814
Winsorized Mean ( 5 / 26 )17.71923076923080.28065060285013763.1362647693743
Winsorized Mean ( 6 / 26 )17.72692307692310.27941159499382563.4437632314967
Winsorized Mean ( 7 / 26 )17.70897435897440.27573161782136464.2254033066579
Winsorized Mean ( 8 / 26 )17.66794871794870.26406170374067866.908409919598
Winsorized Mean ( 9 / 26 )17.66794871794870.26406170374067866.908409919598
Winsorized Mean ( 10 / 26 )17.62948717948720.25258641429125269.7958646309416
Winsorized Mean ( 11 / 26 )17.60128205128210.24762941055975471.07912590631
Winsorized Mean ( 12 / 26 )17.53974358974360.23229400617893575.5066558894886
Winsorized Mean ( 13 / 26 )17.52307692307690.2296526433257276.3025265867445
Winsorized Mean ( 14 / 26 )17.50512820512820.20988633236542883.4028972151004
Winsorized Mean ( 15 / 26 )17.48589743589740.19539933545507589.488008724153
Winsorized Mean ( 16 / 26 )17.52692307692310.18900578580916892.7322039475521
Winsorized Mean ( 17 / 26 )17.52692307692310.18260767971725295.9813032182523
Winsorized Mean ( 18 / 26 )17.550.172499499292251101.739425749095
Winsorized Mean ( 19 / 26 )17.550.165575012955110105.994254125519
Winsorized Mean ( 20 / 26 )17.52435897435900.162093631314765108.112569458876
Winsorized Mean ( 21 / 26 )17.60512820512820.150588781582559116.908630378129
Winsorized Mean ( 22 / 26 )17.66153846153850.127780181520114138.218135640685
Winsorized Mean ( 23 / 26 )17.66153846153850.127780181520114138.218135640685
Winsorized Mean ( 24 / 26 )17.66153846153850.119707028997095147.539694281170
Winsorized Mean ( 25 / 26 )17.59743589743590.111269344368751158.151699349619
Winsorized Mean ( 26 / 26 )17.59743589743590.102774924850713171.223048063496
Trimmed Mean ( 1 / 26 )17.74868421052630.29506760106232660.1512471942907
Trimmed Mean ( 2 / 26 )17.72567567567570.28629086843741861.9149181125574
Trimmed Mean ( 3 / 26 )17.70138888888890.27732861768880763.828208702038
Trimmed Mean ( 4 / 26 )17.67285714285710.26872847925637365.7647346934035
Trimmed Mean ( 5 / 26 )17.64852941176470.26102126574733167.6133776350946
Trimmed Mean ( 6 / 26 )17.63181818181820.25446281542328169.2903525117763
Trimmed Mean ( 7 / 26 )17.61250.24690042816603571.3344246942982
Trimmed Mean ( 8 / 26 )17.59516129032260.23873263356681173.702371675963
Trimmed Mean ( 9 / 26 )17.58333333333330.23172366489813575.8806112490191
Trimmed Mean ( 10 / 26 )17.57068965517240.22313295568928878.7453812050942
Trimmed Mean ( 11 / 26 )17.56250.21525524715688481.5891841521518
Trimmed Mean ( 12 / 26 )17.55740740740740.20662679421704484.9715908042634
Trimmed Mean ( 13 / 26 )17.55961538461540.19932502269177288.0953888652948
Trimmed Mean ( 14 / 26 )17.5640.19069710998099192.1041750540994
Trimmed Mean ( 15 / 26 )17.57083333333330.18419265886347495.3937765041821
Trimmed Mean ( 16 / 26 )17.58043478260870.17898316022635398.2239600662731
Trimmed Mean ( 17 / 26 )17.58636363636360.173619316653205101.292667056693
Trimmed Mean ( 18 / 26 )17.59285714285710.167976024820661104.734334329200
Trimmed Mean ( 19 / 26 )17.59750.162807401551649108.087837729032
Trimmed Mean ( 20 / 26 )17.60263157894740.157437103524614111.807389648752
Trimmed Mean ( 21 / 26 )17.61111111111110.150858799627480116.739037792948
Trimmed Mean ( 22 / 26 )17.61176470588240.144893144343548121.550020780307
Trimmed Mean ( 23 / 26 )17.606250.142552869366127123.506808935433
Trimmed Mean ( 24 / 26 )17.60.138796137612298126.804681331713
Trimmed Mean ( 25 / 26 )17.59285714285710.13539366192177129.938557633682
Trimmed Mean ( 26 / 26 )17.59230769230770.132656070860307132.615926117948
Median17.7
Midrange18.1
Midmean - Weighted Average at Xnp17.5538461538462
Midmean - Weighted Average at X(n+1)p17.5975
Midmean - Empirical Distribution Function17.5975
Midmean - Empirical Distribution Function - Averaging17.5975
Midmean - Empirical Distribution Function - Interpolation17.5538461538462
Midmean - Closest Observation17.5975
Midmean - True Basic - Statistics Graphics Toolkit17.5975
Midmean - MS Excel (old versions)17.5975
Number of observations78

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17.7576923076923 & 0.308981543960244 & 57.4716925810209 \tabularnewline
Geometric Mean & 17.5538780090592 &  &  \tabularnewline
Harmonic Mean & 17.3531217814873 &  &  \tabularnewline
Quadratic Mean & 17.9634850424909 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 17.7705128205128 & 0.302531823797299 & 58.7393173963059 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 17.7705128205128 & 0.300322331967036 & 59.1714665510235 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 17.7782051282051 & 0.295839996421785 & 60.0939877745887 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 17.7576923076923 & 0.289000938683604 & 61.4451025265814 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 17.7192307692308 & 0.280650602850137 & 63.1362647693743 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 17.7269230769231 & 0.279411594993825 & 63.4437632314967 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 17.7089743589744 & 0.275731617821364 & 64.2254033066579 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 17.6679487179487 & 0.264061703740678 & 66.908409919598 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 17.6679487179487 & 0.264061703740678 & 66.908409919598 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 17.6294871794872 & 0.252586414291252 & 69.7958646309416 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 17.6012820512821 & 0.247629410559754 & 71.07912590631 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 17.5397435897436 & 0.232294006178935 & 75.5066558894886 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 17.5230769230769 & 0.22965264332572 & 76.3025265867445 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 17.5051282051282 & 0.209886332365428 & 83.4028972151004 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 17.4858974358974 & 0.195399335455075 & 89.488008724153 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 17.5269230769231 & 0.189005785809168 & 92.7322039475521 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 17.5269230769231 & 0.182607679717252 & 95.9813032182523 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 17.55 & 0.172499499292251 & 101.739425749095 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 17.55 & 0.165575012955110 & 105.994254125519 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 17.5243589743590 & 0.162093631314765 & 108.112569458876 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 17.6051282051282 & 0.150588781582559 & 116.908630378129 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 17.6615384615385 & 0.127780181520114 & 138.218135640685 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 17.6615384615385 & 0.127780181520114 & 138.218135640685 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 17.6615384615385 & 0.119707028997095 & 147.539694281170 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 17.5974358974359 & 0.111269344368751 & 158.151699349619 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 17.5974358974359 & 0.102774924850713 & 171.223048063496 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 17.7486842105263 & 0.295067601062326 & 60.1512471942907 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 17.7256756756757 & 0.286290868437418 & 61.9149181125574 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 17.7013888888889 & 0.277328617688807 & 63.828208702038 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 17.6728571428571 & 0.268728479256373 & 65.7647346934035 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 17.6485294117647 & 0.261021265747331 & 67.6133776350946 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 17.6318181818182 & 0.254462815423281 & 69.2903525117763 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 17.6125 & 0.246900428166035 & 71.3344246942982 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 17.5951612903226 & 0.238732633566811 & 73.702371675963 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 17.5833333333333 & 0.231723664898135 & 75.8806112490191 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 17.5706896551724 & 0.223132955689288 & 78.7453812050942 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 17.5625 & 0.215255247156884 & 81.5891841521518 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 17.5574074074074 & 0.206626794217044 & 84.9715908042634 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 17.5596153846154 & 0.199325022691772 & 88.0953888652948 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 17.564 & 0.190697109980991 & 92.1041750540994 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 17.5708333333333 & 0.184192658863474 & 95.3937765041821 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 17.5804347826087 & 0.178983160226353 & 98.2239600662731 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 17.5863636363636 & 0.173619316653205 & 101.292667056693 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 17.5928571428571 & 0.167976024820661 & 104.734334329200 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 17.5975 & 0.162807401551649 & 108.087837729032 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 17.6026315789474 & 0.157437103524614 & 111.807389648752 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 17.6111111111111 & 0.150858799627480 & 116.739037792948 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 17.6117647058824 & 0.144893144343548 & 121.550020780307 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 17.60625 & 0.142552869366127 & 123.506808935433 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 17.6 & 0.138796137612298 & 126.804681331713 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 17.5928571428571 & 0.13539366192177 & 129.938557633682 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 17.5923076923077 & 0.132656070860307 & 132.615926117948 \tabularnewline
Median & 17.7 &  &  \tabularnewline
Midrange & 18.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17.5538461538462 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17.5975 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17.5975 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17.5975 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17.5538461538462 &  &  \tabularnewline
Midmean - Closest Observation & 17.5975 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17.5975 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17.5975 &  &  \tabularnewline
Number of observations & 78 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66202&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]17.7576923076923[/C][C]0.308981543960244[/C][C]57.4716925810209[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]17.5538780090592[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]17.3531217814873[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17.9634850424909[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]17.7705128205128[/C][C]0.302531823797299[/C][C]58.7393173963059[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]17.7705128205128[/C][C]0.300322331967036[/C][C]59.1714665510235[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]17.7782051282051[/C][C]0.295839996421785[/C][C]60.0939877745887[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]17.7576923076923[/C][C]0.289000938683604[/C][C]61.4451025265814[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]17.7192307692308[/C][C]0.280650602850137[/C][C]63.1362647693743[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]17.7269230769231[/C][C]0.279411594993825[/C][C]63.4437632314967[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]17.7089743589744[/C][C]0.275731617821364[/C][C]64.2254033066579[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]17.6679487179487[/C][C]0.264061703740678[/C][C]66.908409919598[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]17.6679487179487[/C][C]0.264061703740678[/C][C]66.908409919598[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]17.6294871794872[/C][C]0.252586414291252[/C][C]69.7958646309416[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]17.6012820512821[/C][C]0.247629410559754[/C][C]71.07912590631[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]17.5397435897436[/C][C]0.232294006178935[/C][C]75.5066558894886[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]17.5230769230769[/C][C]0.22965264332572[/C][C]76.3025265867445[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]17.5051282051282[/C][C]0.209886332365428[/C][C]83.4028972151004[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]17.4858974358974[/C][C]0.195399335455075[/C][C]89.488008724153[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]17.5269230769231[/C][C]0.189005785809168[/C][C]92.7322039475521[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]17.5269230769231[/C][C]0.182607679717252[/C][C]95.9813032182523[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]17.55[/C][C]0.172499499292251[/C][C]101.739425749095[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]17.55[/C][C]0.165575012955110[/C][C]105.994254125519[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]17.5243589743590[/C][C]0.162093631314765[/C][C]108.112569458876[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]17.6051282051282[/C][C]0.150588781582559[/C][C]116.908630378129[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]17.6615384615385[/C][C]0.127780181520114[/C][C]138.218135640685[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]17.6615384615385[/C][C]0.127780181520114[/C][C]138.218135640685[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]17.6615384615385[/C][C]0.119707028997095[/C][C]147.539694281170[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]17.5974358974359[/C][C]0.111269344368751[/C][C]158.151699349619[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]17.5974358974359[/C][C]0.102774924850713[/C][C]171.223048063496[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]17.7486842105263[/C][C]0.295067601062326[/C][C]60.1512471942907[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]17.7256756756757[/C][C]0.286290868437418[/C][C]61.9149181125574[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]17.7013888888889[/C][C]0.277328617688807[/C][C]63.828208702038[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]17.6728571428571[/C][C]0.268728479256373[/C][C]65.7647346934035[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]17.6485294117647[/C][C]0.261021265747331[/C][C]67.6133776350946[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]17.6318181818182[/C][C]0.254462815423281[/C][C]69.2903525117763[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]17.6125[/C][C]0.246900428166035[/C][C]71.3344246942982[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]17.5951612903226[/C][C]0.238732633566811[/C][C]73.702371675963[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]17.5833333333333[/C][C]0.231723664898135[/C][C]75.8806112490191[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]17.5706896551724[/C][C]0.223132955689288[/C][C]78.7453812050942[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]17.5625[/C][C]0.215255247156884[/C][C]81.5891841521518[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]17.5574074074074[/C][C]0.206626794217044[/C][C]84.9715908042634[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]17.5596153846154[/C][C]0.199325022691772[/C][C]88.0953888652948[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]17.564[/C][C]0.190697109980991[/C][C]92.1041750540994[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]17.5708333333333[/C][C]0.184192658863474[/C][C]95.3937765041821[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]17.5804347826087[/C][C]0.178983160226353[/C][C]98.2239600662731[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]17.5863636363636[/C][C]0.173619316653205[/C][C]101.292667056693[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]17.5928571428571[/C][C]0.167976024820661[/C][C]104.734334329200[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]17.5975[/C][C]0.162807401551649[/C][C]108.087837729032[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]17.6026315789474[/C][C]0.157437103524614[/C][C]111.807389648752[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]17.6111111111111[/C][C]0.150858799627480[/C][C]116.739037792948[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]17.6117647058824[/C][C]0.144893144343548[/C][C]121.550020780307[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]17.60625[/C][C]0.142552869366127[/C][C]123.506808935433[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]17.6[/C][C]0.138796137612298[/C][C]126.804681331713[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]17.5928571428571[/C][C]0.13539366192177[/C][C]129.938557633682[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]17.5923076923077[/C][C]0.132656070860307[/C][C]132.615926117948[/C][/ROW]
[ROW][C]Median[/C][C]17.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]18.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17.5538461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17.5975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17.5975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17.5975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17.5538461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17.5975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17.5975[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17.5975[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]78[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66202&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 Mean17.75769230769230.30898154396024457.4716925810209
Geometric Mean17.5538780090592
Harmonic Mean17.3531217814873
Quadratic Mean17.9634850424909
Winsorized Mean ( 1 / 26 )17.77051282051280.30253182379729958.7393173963059
Winsorized Mean ( 2 / 26 )17.77051282051280.30032233196703659.1714665510235
Winsorized Mean ( 3 / 26 )17.77820512820510.29583999642178560.0939877745887
Winsorized Mean ( 4 / 26 )17.75769230769230.28900093868360461.4451025265814
Winsorized Mean ( 5 / 26 )17.71923076923080.28065060285013763.1362647693743
Winsorized Mean ( 6 / 26 )17.72692307692310.27941159499382563.4437632314967
Winsorized Mean ( 7 / 26 )17.70897435897440.27573161782136464.2254033066579
Winsorized Mean ( 8 / 26 )17.66794871794870.26406170374067866.908409919598
Winsorized Mean ( 9 / 26 )17.66794871794870.26406170374067866.908409919598
Winsorized Mean ( 10 / 26 )17.62948717948720.25258641429125269.7958646309416
Winsorized Mean ( 11 / 26 )17.60128205128210.24762941055975471.07912590631
Winsorized Mean ( 12 / 26 )17.53974358974360.23229400617893575.5066558894886
Winsorized Mean ( 13 / 26 )17.52307692307690.2296526433257276.3025265867445
Winsorized Mean ( 14 / 26 )17.50512820512820.20988633236542883.4028972151004
Winsorized Mean ( 15 / 26 )17.48589743589740.19539933545507589.488008724153
Winsorized Mean ( 16 / 26 )17.52692307692310.18900578580916892.7322039475521
Winsorized Mean ( 17 / 26 )17.52692307692310.18260767971725295.9813032182523
Winsorized Mean ( 18 / 26 )17.550.172499499292251101.739425749095
Winsorized Mean ( 19 / 26 )17.550.165575012955110105.994254125519
Winsorized Mean ( 20 / 26 )17.52435897435900.162093631314765108.112569458876
Winsorized Mean ( 21 / 26 )17.60512820512820.150588781582559116.908630378129
Winsorized Mean ( 22 / 26 )17.66153846153850.127780181520114138.218135640685
Winsorized Mean ( 23 / 26 )17.66153846153850.127780181520114138.218135640685
Winsorized Mean ( 24 / 26 )17.66153846153850.119707028997095147.539694281170
Winsorized Mean ( 25 / 26 )17.59743589743590.111269344368751158.151699349619
Winsorized Mean ( 26 / 26 )17.59743589743590.102774924850713171.223048063496
Trimmed Mean ( 1 / 26 )17.74868421052630.29506760106232660.1512471942907
Trimmed Mean ( 2 / 26 )17.72567567567570.28629086843741861.9149181125574
Trimmed Mean ( 3 / 26 )17.70138888888890.27732861768880763.828208702038
Trimmed Mean ( 4 / 26 )17.67285714285710.26872847925637365.7647346934035
Trimmed Mean ( 5 / 26 )17.64852941176470.26102126574733167.6133776350946
Trimmed Mean ( 6 / 26 )17.63181818181820.25446281542328169.2903525117763
Trimmed Mean ( 7 / 26 )17.61250.24690042816603571.3344246942982
Trimmed Mean ( 8 / 26 )17.59516129032260.23873263356681173.702371675963
Trimmed Mean ( 9 / 26 )17.58333333333330.23172366489813575.8806112490191
Trimmed Mean ( 10 / 26 )17.57068965517240.22313295568928878.7453812050942
Trimmed Mean ( 11 / 26 )17.56250.21525524715688481.5891841521518
Trimmed Mean ( 12 / 26 )17.55740740740740.20662679421704484.9715908042634
Trimmed Mean ( 13 / 26 )17.55961538461540.19932502269177288.0953888652948
Trimmed Mean ( 14 / 26 )17.5640.19069710998099192.1041750540994
Trimmed Mean ( 15 / 26 )17.57083333333330.18419265886347495.3937765041821
Trimmed Mean ( 16 / 26 )17.58043478260870.17898316022635398.2239600662731
Trimmed Mean ( 17 / 26 )17.58636363636360.173619316653205101.292667056693
Trimmed Mean ( 18 / 26 )17.59285714285710.167976024820661104.734334329200
Trimmed Mean ( 19 / 26 )17.59750.162807401551649108.087837729032
Trimmed Mean ( 20 / 26 )17.60263157894740.157437103524614111.807389648752
Trimmed Mean ( 21 / 26 )17.61111111111110.150858799627480116.739037792948
Trimmed Mean ( 22 / 26 )17.61176470588240.144893144343548121.550020780307
Trimmed Mean ( 23 / 26 )17.606250.142552869366127123.506808935433
Trimmed Mean ( 24 / 26 )17.60.138796137612298126.804681331713
Trimmed Mean ( 25 / 26 )17.59285714285710.13539366192177129.938557633682
Trimmed Mean ( 26 / 26 )17.59230769230770.132656070860307132.615926117948
Median17.7
Midrange18.1
Midmean - Weighted Average at Xnp17.5538461538462
Midmean - Weighted Average at X(n+1)p17.5975
Midmean - Empirical Distribution Function17.5975
Midmean - Empirical Distribution Function - Averaging17.5975
Midmean - Empirical Distribution Function - Interpolation17.5538461538462
Midmean - Closest Observation17.5975
Midmean - True Basic - Statistics Graphics Toolkit17.5975
Midmean - MS Excel (old versions)17.5975
Number of observations78



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')