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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 06 Mar 2013 13:55:57 -0500
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/Mar/06/t1362596184l6la3qd1fv8uivv.htm/, Retrieved Fri, 03 May 2024 19:01:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=207532, Retrieved Fri, 03 May 2024 19:01:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2013-03-06 18:55:57] [bda1405f45fc71f9cfac8f9f3e5dea22] [Current]
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Dataseries X:
120,6
119,9
119,48
117,45
118,37
117,07
114,98
112,59
111,7
112,04
110,79
109,82
109,11
109,84
109,31
108,29
107,42
106,71
105,11
104,43
105,55
106,12
105,78
105,33
104,63
104,62
105,57
107,5
107,52
107,76
106,74
106,21
105,77
105,27
104,35
103,52
102,28
100,93
101,04
99,95
99,55
99,56
99,01
98,64
98,98
100,8
100,32
100,72
280,8
280,4
280,4
280,3
281
280,9
279,7
283,1
290,6
291,6
291,7
291,8
291,7
291,5
291,7
293,4
293,1
293,1
292,6
292,1
292,2
292
292,1
293,4
292,2
292,1
291,6
290,9
290,9
290,8
290,5
290
290,2
290,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207532&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207532&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207532&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean182.5552439024399.9846792426803318.2835361522774
Geometric Mean161.486553108729
Harmonic Mean144.551127216689
Quadratic Mean203.47387169412
Winsorized Mean ( 1 / 27 )182.5593902439029.9842498781458318.2847377090892
Winsorized Mean ( 2 / 27 )182.5528048780499.983172694354218.2860509847023
Winsorized Mean ( 3 / 27 )182.572560975619.9811377781448618.2917584181013
Winsorized Mean ( 4 / 27 )182.5486585365859.9777598785490718.2955553910494
Winsorized Mean ( 5 / 27 )182.5480487804889.9720069417455718.3060491079575
Winsorized Mean ( 6 / 27 )182.575121951229.969243826412218.3138385548873
Winsorized Mean ( 7 / 27 )182.6007317073179.9646141880308118.3249173788034
Winsorized Mean ( 8 / 27 )182.6085365853669.963822729665318.3271563073563
Winsorized Mean ( 9 / 27 )182.6228048780499.9623773437310418.3312475102107
Winsorized Mean ( 10 / 27 )182.6240243902449.9593660300824918.3369125944989
Winsorized Mean ( 11 / 27 )182.7635365853669.9390042898860718.3885157159401
Winsorized Mean ( 12 / 27 )182.9303658536599.9189841726518418.4424496167688
Winsorized Mean ( 13 / 27 )183.0619512195129.9060272371408218.4798554291427
Winsorized Mean ( 14 / 27 )183.0756097560989.9046878484896318.4837334155881
Winsorized Mean ( 15 / 27 )183.0920731707329.8988073987439918.4963769669833
Winsorized Mean ( 16 / 27 )183.0940243902449.8986164418774818.4969309059839
Winsorized Mean ( 17 / 27 )183.1728048780499.8860917107160518.5283335657809
Winsorized Mean ( 18 / 27 )183.0762195121959.8648750031040318.5583922203362
Winsorized Mean ( 19 / 27 )183.090121951229.8635215917095518.5623481683367
Winsorized Mean ( 20 / 27 )183.1193902439029.8550125702424918.5813451721855
Winsorized Mean ( 21 / 27 )183.0732926829279.8476079723923118.5906357357209
Winsorized Mean ( 22 / 27 )183.100121951229.83878163411418.6100402224963
Winsorized Mean ( 23 / 27 )183.0187804878059.8271743337867918.6237441477525
Winsorized Mean ( 24 / 27 )183.0890243902449.8135879529241918.656685533214
Winsorized Mean ( 25 / 27 )183.0859756097569.8068278865604718.6692351214465
Winsorized Mean ( 26 / 27 )181.0567073170739.4991562741304419.0602935768258
Winsorized Mean ( 27 / 27 )180.375121951229.4066906622581219.1751943831774
Trimmed Mean ( 1 / 27 )182.21862510.08530824972118.0677298589302
Trimmed Mean ( 2 / 27 )181.86038461538510.18909607877517.848529762539
Trimmed Mean ( 3 / 27 )181.48684210526310.296311182763417.6263944323169
Trimmed Mean ( 4 / 27 )181.08581081081110.407264824427217.3999426233278
Trimmed Mean ( 5 / 27 )180.66930555555610.522374717332417.1700125122857
Trimmed Mean ( 6 / 27 )180.22914285714310.642255961788616.9352384968245
Trimmed Mean ( 7 / 27 )179.75764705882410.766255089134816.6963949461157
Trimmed Mean ( 8 / 27 )179.2530303030310.894831485563316.4530337656492
Trimmed Mean ( 9 / 27 )178.71562511.027381198857316.2065336980025
Trimmed Mean ( 10 / 27 )178.14145161290311.164090097839615.9566476131697
Trimmed Mean ( 11 / 27 )177.52883333333311.305289297796615.7031658949174
Trimmed Mean ( 12 / 27 )176.85603448275911.45362467807315.4410537671393
Trimmed Mean ( 13 / 27 )176.11482142857111.609183092592815.1703026839969
Trimmed Mean ( 14 / 27 )175.30333333333311.771104335389814.8926836716827
Trimmed Mean ( 15 / 27 )174.42788461538511.937881219854214.6112933612783
Trimmed Mean ( 16 / 27 )173.480612.109992239199414.3254096760238
Trimmed Mean ( 17 / 27 )172.45416666666712.286366189161114.0362222655226
Trimmed Mean ( 18 / 27 )171.33021739130412.46809955141813.7414861571119
Trimmed Mean ( 19 / 27 )170.11409090909112.656270510147313.4410915737539
Trimmed Mean ( 20 / 27 )168.78071428571412.846858030410613.1378983005948
Trimmed Mean ( 21 / 27 )167.31113.039109837675812.8314740870242
Trimmed Mean ( 22 / 27 )165.69131578947413.230553894465112.5233846678777
Trimmed Mean ( 23 / 27 )163.88888888888913.417358389608712.2146911582697
Trimmed Mean ( 24 / 27 )161.88294117647113.594725696424911.9077754705299
Trimmed Mean ( 25 / 27 )159.6187513.75370251286911.6055113050939
Trimmed Mean ( 26 / 27 )157.05313.879686679941111.3153130630083
Trimmed Mean ( 27 / 27 )154.34928571428614.037686199781610.9953509088049
Median113.785
Midrange196.02
Midmean - Weighted Average at Xnp165.804634146341
Midmean - Weighted Average at X(n+1)p168.780714285714
Midmean - Empirical Distribution Function168.780714285714
Midmean - Empirical Distribution Function - Averaging168.780714285714
Midmean - Empirical Distribution Function - Interpolation167.311
Midmean - Closest Observation168.780714285714
Midmean - True Basic - Statistics Graphics Toolkit168.780714285714
Midmean - MS Excel (old versions)168.780714285714
Number of observations82

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 182.555243902439 & 9.98467924268033 & 18.2835361522774 \tabularnewline
Geometric Mean & 161.486553108729 &  &  \tabularnewline
Harmonic Mean & 144.551127216689 &  &  \tabularnewline
Quadratic Mean & 203.47387169412 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 182.559390243902 & 9.98424987814583 & 18.2847377090892 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 182.552804878049 & 9.9831726943542 & 18.2860509847023 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 182.57256097561 & 9.98113777814486 & 18.2917584181013 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 182.548658536585 & 9.97775987854907 & 18.2955553910494 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 182.548048780488 & 9.97200694174557 & 18.3060491079575 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 182.57512195122 & 9.9692438264122 & 18.3138385548873 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 182.600731707317 & 9.96461418803081 & 18.3249173788034 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 182.608536585366 & 9.9638227296653 & 18.3271563073563 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 182.622804878049 & 9.96237734373104 & 18.3312475102107 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 182.624024390244 & 9.95936603008249 & 18.3369125944989 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 182.763536585366 & 9.93900428988607 & 18.3885157159401 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 182.930365853659 & 9.91898417265184 & 18.4424496167688 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 183.061951219512 & 9.90602723714082 & 18.4798554291427 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 183.075609756098 & 9.90468784848963 & 18.4837334155881 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 183.092073170732 & 9.89880739874399 & 18.4963769669833 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 183.094024390244 & 9.89861644187748 & 18.4969309059839 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 183.172804878049 & 9.88609171071605 & 18.5283335657809 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 183.076219512195 & 9.86487500310403 & 18.5583922203362 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 183.09012195122 & 9.86352159170955 & 18.5623481683367 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 183.119390243902 & 9.85501257024249 & 18.5813451721855 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 183.073292682927 & 9.84760797239231 & 18.5906357357209 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 183.10012195122 & 9.838781634114 & 18.6100402224963 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 183.018780487805 & 9.82717433378679 & 18.6237441477525 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 183.089024390244 & 9.81358795292419 & 18.656685533214 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 183.085975609756 & 9.80682788656047 & 18.6692351214465 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 181.056707317073 & 9.49915627413044 & 19.0602935768258 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 180.37512195122 & 9.40669066225812 & 19.1751943831774 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 182.218625 & 10.085308249721 & 18.0677298589302 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 181.860384615385 & 10.189096078775 & 17.848529762539 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 181.486842105263 & 10.2963111827634 & 17.6263944323169 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 181.085810810811 & 10.4072648244272 & 17.3999426233278 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 180.669305555556 & 10.5223747173324 & 17.1700125122857 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 180.229142857143 & 10.6422559617886 & 16.9352384968245 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 179.757647058824 & 10.7662550891348 & 16.6963949461157 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 179.25303030303 & 10.8948314855633 & 16.4530337656492 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 178.715625 & 11.0273811988573 & 16.2065336980025 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 178.141451612903 & 11.1640900978396 & 15.9566476131697 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 177.528833333333 & 11.3052892977966 & 15.7031658949174 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 176.856034482759 & 11.453624678073 & 15.4410537671393 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 176.114821428571 & 11.6091830925928 & 15.1703026839969 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 175.303333333333 & 11.7711043353898 & 14.8926836716827 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 174.427884615385 & 11.9378812198542 & 14.6112933612783 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 173.4806 & 12.1099922391994 & 14.3254096760238 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 172.454166666667 & 12.2863661891611 & 14.0362222655226 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 171.330217391304 & 12.468099551418 & 13.7414861571119 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 170.114090909091 & 12.6562705101473 & 13.4410915737539 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 168.780714285714 & 12.8468580304106 & 13.1378983005948 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 167.311 & 13.0391098376758 & 12.8314740870242 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 165.691315789474 & 13.2305538944651 & 12.5233846678777 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 163.888888888889 & 13.4173583896087 & 12.2146911582697 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 161.882941176471 & 13.5947256964249 & 11.9077754705299 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 159.61875 & 13.753702512869 & 11.6055113050939 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 157.053 & 13.8796866799411 & 11.3153130630083 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 154.349285714286 & 14.0376861997816 & 10.9953509088049 \tabularnewline
Median & 113.785 &  &  \tabularnewline
Midrange & 196.02 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 165.804634146341 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 168.780714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 168.780714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 168.780714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 167.311 &  &  \tabularnewline
Midmean - Closest Observation & 168.780714285714 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 168.780714285714 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 168.780714285714 &  &  \tabularnewline
Number of observations & 82 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=207532&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]182.555243902439[/C][C]9.98467924268033[/C][C]18.2835361522774[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]161.486553108729[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]144.551127216689[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]203.47387169412[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]182.559390243902[/C][C]9.98424987814583[/C][C]18.2847377090892[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]182.552804878049[/C][C]9.9831726943542[/C][C]18.2860509847023[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]182.57256097561[/C][C]9.98113777814486[/C][C]18.2917584181013[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]182.548658536585[/C][C]9.97775987854907[/C][C]18.2955553910494[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]182.548048780488[/C][C]9.97200694174557[/C][C]18.3060491079575[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]182.57512195122[/C][C]9.9692438264122[/C][C]18.3138385548873[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]182.600731707317[/C][C]9.96461418803081[/C][C]18.3249173788034[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]182.608536585366[/C][C]9.9638227296653[/C][C]18.3271563073563[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]182.622804878049[/C][C]9.96237734373104[/C][C]18.3312475102107[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]182.624024390244[/C][C]9.95936603008249[/C][C]18.3369125944989[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]182.763536585366[/C][C]9.93900428988607[/C][C]18.3885157159401[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]182.930365853659[/C][C]9.91898417265184[/C][C]18.4424496167688[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]183.061951219512[/C][C]9.90602723714082[/C][C]18.4798554291427[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]183.075609756098[/C][C]9.90468784848963[/C][C]18.4837334155881[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]183.092073170732[/C][C]9.89880739874399[/C][C]18.4963769669833[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]183.094024390244[/C][C]9.89861644187748[/C][C]18.4969309059839[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]183.172804878049[/C][C]9.88609171071605[/C][C]18.5283335657809[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]183.076219512195[/C][C]9.86487500310403[/C][C]18.5583922203362[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]183.09012195122[/C][C]9.86352159170955[/C][C]18.5623481683367[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]183.119390243902[/C][C]9.85501257024249[/C][C]18.5813451721855[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]183.073292682927[/C][C]9.84760797239231[/C][C]18.5906357357209[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]183.10012195122[/C][C]9.838781634114[/C][C]18.6100402224963[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]183.018780487805[/C][C]9.82717433378679[/C][C]18.6237441477525[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]183.089024390244[/C][C]9.81358795292419[/C][C]18.656685533214[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]183.085975609756[/C][C]9.80682788656047[/C][C]18.6692351214465[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]181.056707317073[/C][C]9.49915627413044[/C][C]19.0602935768258[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]180.37512195122[/C][C]9.40669066225812[/C][C]19.1751943831774[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]182.218625[/C][C]10.085308249721[/C][C]18.0677298589302[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]181.860384615385[/C][C]10.189096078775[/C][C]17.848529762539[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]181.486842105263[/C][C]10.2963111827634[/C][C]17.6263944323169[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]181.085810810811[/C][C]10.4072648244272[/C][C]17.3999426233278[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]180.669305555556[/C][C]10.5223747173324[/C][C]17.1700125122857[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]180.229142857143[/C][C]10.6422559617886[/C][C]16.9352384968245[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]179.757647058824[/C][C]10.7662550891348[/C][C]16.6963949461157[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]179.25303030303[/C][C]10.8948314855633[/C][C]16.4530337656492[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]178.715625[/C][C]11.0273811988573[/C][C]16.2065336980025[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]178.141451612903[/C][C]11.1640900978396[/C][C]15.9566476131697[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]177.528833333333[/C][C]11.3052892977966[/C][C]15.7031658949174[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]176.856034482759[/C][C]11.453624678073[/C][C]15.4410537671393[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]176.114821428571[/C][C]11.6091830925928[/C][C]15.1703026839969[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]175.303333333333[/C][C]11.7711043353898[/C][C]14.8926836716827[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]174.427884615385[/C][C]11.9378812198542[/C][C]14.6112933612783[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]173.4806[/C][C]12.1099922391994[/C][C]14.3254096760238[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]172.454166666667[/C][C]12.2863661891611[/C][C]14.0362222655226[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]171.330217391304[/C][C]12.468099551418[/C][C]13.7414861571119[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]170.114090909091[/C][C]12.6562705101473[/C][C]13.4410915737539[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]168.780714285714[/C][C]12.8468580304106[/C][C]13.1378983005948[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]167.311[/C][C]13.0391098376758[/C][C]12.8314740870242[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]165.691315789474[/C][C]13.2305538944651[/C][C]12.5233846678777[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]163.888888888889[/C][C]13.4173583896087[/C][C]12.2146911582697[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]161.882941176471[/C][C]13.5947256964249[/C][C]11.9077754705299[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]159.61875[/C][C]13.753702512869[/C][C]11.6055113050939[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]157.053[/C][C]13.8796866799411[/C][C]11.3153130630083[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]154.349285714286[/C][C]14.0376861997816[/C][C]10.9953509088049[/C][/ROW]
[ROW][C]Median[/C][C]113.785[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]196.02[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]165.804634146341[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]168.780714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]168.780714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]168.780714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]167.311[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]168.780714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]168.780714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]168.780714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]82[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=207532&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=207532&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 Mean182.5552439024399.9846792426803318.2835361522774
Geometric Mean161.486553108729
Harmonic Mean144.551127216689
Quadratic Mean203.47387169412
Winsorized Mean ( 1 / 27 )182.5593902439029.9842498781458318.2847377090892
Winsorized Mean ( 2 / 27 )182.5528048780499.983172694354218.2860509847023
Winsorized Mean ( 3 / 27 )182.572560975619.9811377781448618.2917584181013
Winsorized Mean ( 4 / 27 )182.5486585365859.9777598785490718.2955553910494
Winsorized Mean ( 5 / 27 )182.5480487804889.9720069417455718.3060491079575
Winsorized Mean ( 6 / 27 )182.575121951229.969243826412218.3138385548873
Winsorized Mean ( 7 / 27 )182.6007317073179.9646141880308118.3249173788034
Winsorized Mean ( 8 / 27 )182.6085365853669.963822729665318.3271563073563
Winsorized Mean ( 9 / 27 )182.6228048780499.9623773437310418.3312475102107
Winsorized Mean ( 10 / 27 )182.6240243902449.9593660300824918.3369125944989
Winsorized Mean ( 11 / 27 )182.7635365853669.9390042898860718.3885157159401
Winsorized Mean ( 12 / 27 )182.9303658536599.9189841726518418.4424496167688
Winsorized Mean ( 13 / 27 )183.0619512195129.9060272371408218.4798554291427
Winsorized Mean ( 14 / 27 )183.0756097560989.9046878484896318.4837334155881
Winsorized Mean ( 15 / 27 )183.0920731707329.8988073987439918.4963769669833
Winsorized Mean ( 16 / 27 )183.0940243902449.8986164418774818.4969309059839
Winsorized Mean ( 17 / 27 )183.1728048780499.8860917107160518.5283335657809
Winsorized Mean ( 18 / 27 )183.0762195121959.8648750031040318.5583922203362
Winsorized Mean ( 19 / 27 )183.090121951229.8635215917095518.5623481683367
Winsorized Mean ( 20 / 27 )183.1193902439029.8550125702424918.5813451721855
Winsorized Mean ( 21 / 27 )183.0732926829279.8476079723923118.5906357357209
Winsorized Mean ( 22 / 27 )183.100121951229.83878163411418.6100402224963
Winsorized Mean ( 23 / 27 )183.0187804878059.8271743337867918.6237441477525
Winsorized Mean ( 24 / 27 )183.0890243902449.8135879529241918.656685533214
Winsorized Mean ( 25 / 27 )183.0859756097569.8068278865604718.6692351214465
Winsorized Mean ( 26 / 27 )181.0567073170739.4991562741304419.0602935768258
Winsorized Mean ( 27 / 27 )180.375121951229.4066906622581219.1751943831774
Trimmed Mean ( 1 / 27 )182.21862510.08530824972118.0677298589302
Trimmed Mean ( 2 / 27 )181.86038461538510.18909607877517.848529762539
Trimmed Mean ( 3 / 27 )181.48684210526310.296311182763417.6263944323169
Trimmed Mean ( 4 / 27 )181.08581081081110.407264824427217.3999426233278
Trimmed Mean ( 5 / 27 )180.66930555555610.522374717332417.1700125122857
Trimmed Mean ( 6 / 27 )180.22914285714310.642255961788616.9352384968245
Trimmed Mean ( 7 / 27 )179.75764705882410.766255089134816.6963949461157
Trimmed Mean ( 8 / 27 )179.2530303030310.894831485563316.4530337656492
Trimmed Mean ( 9 / 27 )178.71562511.027381198857316.2065336980025
Trimmed Mean ( 10 / 27 )178.14145161290311.164090097839615.9566476131697
Trimmed Mean ( 11 / 27 )177.52883333333311.305289297796615.7031658949174
Trimmed Mean ( 12 / 27 )176.85603448275911.45362467807315.4410537671393
Trimmed Mean ( 13 / 27 )176.11482142857111.609183092592815.1703026839969
Trimmed Mean ( 14 / 27 )175.30333333333311.771104335389814.8926836716827
Trimmed Mean ( 15 / 27 )174.42788461538511.937881219854214.6112933612783
Trimmed Mean ( 16 / 27 )173.480612.109992239199414.3254096760238
Trimmed Mean ( 17 / 27 )172.45416666666712.286366189161114.0362222655226
Trimmed Mean ( 18 / 27 )171.33021739130412.46809955141813.7414861571119
Trimmed Mean ( 19 / 27 )170.11409090909112.656270510147313.4410915737539
Trimmed Mean ( 20 / 27 )168.78071428571412.846858030410613.1378983005948
Trimmed Mean ( 21 / 27 )167.31113.039109837675812.8314740870242
Trimmed Mean ( 22 / 27 )165.69131578947413.230553894465112.5233846678777
Trimmed Mean ( 23 / 27 )163.88888888888913.417358389608712.2146911582697
Trimmed Mean ( 24 / 27 )161.88294117647113.594725696424911.9077754705299
Trimmed Mean ( 25 / 27 )159.6187513.75370251286911.6055113050939
Trimmed Mean ( 26 / 27 )157.05313.879686679941111.3153130630083
Trimmed Mean ( 27 / 27 )154.34928571428614.037686199781610.9953509088049
Median113.785
Midrange196.02
Midmean - Weighted Average at Xnp165.804634146341
Midmean - Weighted Average at X(n+1)p168.780714285714
Midmean - Empirical Distribution Function168.780714285714
Midmean - Empirical Distribution Function - Averaging168.780714285714
Midmean - Empirical Distribution Function - Interpolation167.311
Midmean - Closest Observation168.780714285714
Midmean - True Basic - Statistics Graphics Toolkit168.780714285714
Midmean - MS Excel (old versions)168.780714285714
Number of observations82



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')