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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 12 Oct 2012 12:48:37 -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/2012/Oct/12/t1350060546vm5i212u9hd57fb.htm/, Retrieved Mon, 13 May 2024 13:19:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175569, Retrieved Mon, 13 May 2024 13:19:22 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-12 16:48:37] [44b559b455558ce8185c1073291404e7] [Current]
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Dataseries X:
98,68
99,21
99,36
100,72
102,27
102,62
102,97
102,88
102,9
103,01
103,02
103,73
104,18
103,73
103,78
103,61
103,84
103,86
104,14
104,05
104,01
104,49
104,83
104,78
104,95
105,28
105,28
105,91
106,81
106,39
107,02
106,92
107,01
106,79
107,41
107,13
107,54
108,48
108,5
108,27
109,42
110,09
109,98
109,99
109,54
108,85
106,76
107,56
106,24
108,85
111,11
111,85
110,68
106,96
106,74
105,73
105,66
104,01
106,86
108,84
110,66
106,93
103,74
101,64
102,17
101,13
100,64
100,43
99,77
99,79
99,47
99,63





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
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=175569&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]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=175569&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175569&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
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean105.1677777777780.387382685670596271.482907388394
Geometric Mean105.116997073381
Harmonic Mean105.066096935886
Quadratic Mean105.218421021332
Winsorized Mean ( 1 / 24 )105.1648611111110.383337211301856274.340340594537
Winsorized Mean ( 2 / 24 )105.1570833333330.379905856754128276.797742029521
Winsorized Mean ( 3 / 24 )105.1608333333330.378757840785087277.646617467658
Winsorized Mean ( 4 / 24 )105.1380555555560.370667177466595283.645442453644
Winsorized Mean ( 5 / 24 )105.1408333333330.367349755838004286.21451807824
Winsorized Mean ( 6 / 24 )105.1416666666670.366852065804002286.605082722475
Winsorized Mean ( 7 / 24 )105.1611111111110.346685431707927303.33293958457
Winsorized Mean ( 8 / 24 )105.1711111111110.339892079643242309.42501284967
Winsorized Mean ( 9 / 24 )105.1098611111110.325964710798661322.457792604533
Winsorized Mean ( 10 / 24 )105.1668055555560.31542751290813333.410375607234
Winsorized Mean ( 11 / 24 )105.2431944444440.301585133223979348.966785329844
Winsorized Mean ( 12 / 24 )105.2748611111110.277782550330675378.982988621102
Winsorized Mean ( 13 / 24 )105.2893055555560.274370978311819383.747968547518
Winsorized Mean ( 14 / 24 )105.3165277777780.257423823738705409.117253594516
Winsorized Mean ( 15 / 24 )105.2227777777780.226716131566092464.116854195279
Winsorized Mean ( 16 / 24 )105.2227777777780.225425803163034466.773440756815
Winsorized Mean ( 17 / 24 )105.2086111111110.218635538402173481.205442994282
Winsorized Mean ( 18 / 24 )105.1486111111110.207511741994408506.71162075226
Winsorized Mean ( 19 / 24 )105.1222222222220.203267154456104517.162856456101
Winsorized Mean ( 20 / 24 )105.2833333333330.180168370219479584.360802093501
Winsorized Mean ( 21 / 24 )105.303750.173681083708123606.305233429834
Winsorized Mean ( 22 / 24 )105.2945833333330.172453293386481610.568701041623
Winsorized Mean ( 23 / 24 )105.2945833333330.171619020861897613.536790995122
Winsorized Mean ( 24 / 24 )105.2879166666670.167264062862744629.471237662481
Trimmed Mean ( 1 / 24 )105.1650.37532322853764280.198484942569
Trimmed Mean ( 2 / 24 )105.1651470588240.365784512518235287.505740291781
Trimmed Mean ( 3 / 24 )105.1695454545450.356580001571402294.939550706929
Trimmed Mean ( 4 / 24 )105.17281250.346051958201796303.922026757235
Trimmed Mean ( 5 / 24 )105.1829032258060.336377283324849312.693241904295
Trimmed Mean ( 6 / 24 )105.1930.325697105482646322.978000814947
Trimmed Mean ( 7 / 24 )105.2036206896550.312767218916928336.363961203995
Trimmed Mean ( 8 / 24 )105.2114285714290.302483704463029347.825112622845
Trimmed Mean ( 9 / 24 )105.2181481481480.291503497224416360.949865610515
Trimmed Mean ( 10 / 24 )105.2348076923080.281237232374469374.185191639871
Trimmed Mean ( 11 / 24 )105.24460.270927689727766388.460109432713
Trimmed Mean ( 12 / 24 )105.2447916666670.261198137745358402.930865338978
Trimmed Mean ( 13 / 24 )105.2408695652170.254299231494781413.84658910138
Trimmed Mean ( 14 / 24 )105.2347727272730.246050513178811427.695806717525
Trimmed Mean ( 15 / 24 )105.2247619047620.239154345920164439.986827334882
Trimmed Mean ( 16 / 24 )105.2250.236884424919054444.203961640605
Trimmed Mean ( 17 / 24 )105.2252631578950.23367517571247450.3056982286
Trimmed Mean ( 18 / 24 )105.2272222222220.230448014697359456.620215888665
Trimmed Mean ( 19 / 24 )105.2364705882350.228094439877867461.372362450325
Trimmed Mean ( 20 / 24 )105.250.22512272638604467.522767201733
Trimmed Mean ( 21 / 24 )105.2460.226129654600309465.423255459464
Trimmed Mean ( 22 / 24 )105.2389285714290.227854229883024461.869541001966
Trimmed Mean ( 23 / 24 )105.2319230769230.229084478358644459.358590467997
Trimmed Mean ( 24 / 24 )105.223750.229345170927003458.800809167641
Median105.115
Midrange105.265
Midmean - Weighted Average at Xnp105.166216216216
Midmean - Weighted Average at X(n+1)p105.227222222222
Midmean - Empirical Distribution Function105.166216216216
Midmean - Empirical Distribution Function - Averaging105.227222222222
Midmean - Empirical Distribution Function - Interpolation105.227222222222
Midmean - Closest Observation105.166216216216
Midmean - True Basic - Statistics Graphics Toolkit105.227222222222
Midmean - MS Excel (old versions)105.225263157895
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 105.167777777778 & 0.387382685670596 & 271.482907388394 \tabularnewline
Geometric Mean & 105.116997073381 &  &  \tabularnewline
Harmonic Mean & 105.066096935886 &  &  \tabularnewline
Quadratic Mean & 105.218421021332 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 105.164861111111 & 0.383337211301856 & 274.340340594537 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 105.157083333333 & 0.379905856754128 & 276.797742029521 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 105.160833333333 & 0.378757840785087 & 277.646617467658 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 105.138055555556 & 0.370667177466595 & 283.645442453644 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 105.140833333333 & 0.367349755838004 & 286.21451807824 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 105.141666666667 & 0.366852065804002 & 286.605082722475 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 105.161111111111 & 0.346685431707927 & 303.33293958457 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 105.171111111111 & 0.339892079643242 & 309.42501284967 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 105.109861111111 & 0.325964710798661 & 322.457792604533 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 105.166805555556 & 0.31542751290813 & 333.410375607234 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 105.243194444444 & 0.301585133223979 & 348.966785329844 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 105.274861111111 & 0.277782550330675 & 378.982988621102 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 105.289305555556 & 0.274370978311819 & 383.747968547518 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 105.316527777778 & 0.257423823738705 & 409.117253594516 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 105.222777777778 & 0.226716131566092 & 464.116854195279 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 105.222777777778 & 0.225425803163034 & 466.773440756815 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 105.208611111111 & 0.218635538402173 & 481.205442994282 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 105.148611111111 & 0.207511741994408 & 506.71162075226 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 105.122222222222 & 0.203267154456104 & 517.162856456101 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 105.283333333333 & 0.180168370219479 & 584.360802093501 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 105.30375 & 0.173681083708123 & 606.305233429834 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 105.294583333333 & 0.172453293386481 & 610.568701041623 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 105.294583333333 & 0.171619020861897 & 613.536790995122 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 105.287916666667 & 0.167264062862744 & 629.471237662481 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 105.165 & 0.37532322853764 & 280.198484942569 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 105.165147058824 & 0.365784512518235 & 287.505740291781 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 105.169545454545 & 0.356580001571402 & 294.939550706929 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 105.1728125 & 0.346051958201796 & 303.922026757235 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 105.182903225806 & 0.336377283324849 & 312.693241904295 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 105.193 & 0.325697105482646 & 322.978000814947 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 105.203620689655 & 0.312767218916928 & 336.363961203995 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 105.211428571429 & 0.302483704463029 & 347.825112622845 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 105.218148148148 & 0.291503497224416 & 360.949865610515 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 105.234807692308 & 0.281237232374469 & 374.185191639871 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 105.2446 & 0.270927689727766 & 388.460109432713 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 105.244791666667 & 0.261198137745358 & 402.930865338978 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 105.240869565217 & 0.254299231494781 & 413.84658910138 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 105.234772727273 & 0.246050513178811 & 427.695806717525 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 105.224761904762 & 0.239154345920164 & 439.986827334882 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 105.225 & 0.236884424919054 & 444.203961640605 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 105.225263157895 & 0.23367517571247 & 450.3056982286 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 105.227222222222 & 0.230448014697359 & 456.620215888665 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 105.236470588235 & 0.228094439877867 & 461.372362450325 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 105.25 & 0.22512272638604 & 467.522767201733 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 105.246 & 0.226129654600309 & 465.423255459464 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 105.238928571429 & 0.227854229883024 & 461.869541001966 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 105.231923076923 & 0.229084478358644 & 459.358590467997 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 105.22375 & 0.229345170927003 & 458.800809167641 \tabularnewline
Median & 105.115 &  &  \tabularnewline
Midrange & 105.265 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 105.166216216216 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 105.227222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 105.166216216216 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 105.227222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 105.227222222222 &  &  \tabularnewline
Midmean - Closest Observation & 105.166216216216 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 105.227222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 105.225263157895 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175569&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]105.167777777778[/C][C]0.387382685670596[/C][C]271.482907388394[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]105.116997073381[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]105.066096935886[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]105.218421021332[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]105.164861111111[/C][C]0.383337211301856[/C][C]274.340340594537[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]105.157083333333[/C][C]0.379905856754128[/C][C]276.797742029521[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]105.160833333333[/C][C]0.378757840785087[/C][C]277.646617467658[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]105.138055555556[/C][C]0.370667177466595[/C][C]283.645442453644[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]105.140833333333[/C][C]0.367349755838004[/C][C]286.21451807824[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]105.141666666667[/C][C]0.366852065804002[/C][C]286.605082722475[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]105.161111111111[/C][C]0.346685431707927[/C][C]303.33293958457[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]105.171111111111[/C][C]0.339892079643242[/C][C]309.42501284967[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]105.109861111111[/C][C]0.325964710798661[/C][C]322.457792604533[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]105.166805555556[/C][C]0.31542751290813[/C][C]333.410375607234[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]105.243194444444[/C][C]0.301585133223979[/C][C]348.966785329844[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]105.274861111111[/C][C]0.277782550330675[/C][C]378.982988621102[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]105.289305555556[/C][C]0.274370978311819[/C][C]383.747968547518[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]105.316527777778[/C][C]0.257423823738705[/C][C]409.117253594516[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]105.222777777778[/C][C]0.226716131566092[/C][C]464.116854195279[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]105.222777777778[/C][C]0.225425803163034[/C][C]466.773440756815[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]105.208611111111[/C][C]0.218635538402173[/C][C]481.205442994282[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]105.148611111111[/C][C]0.207511741994408[/C][C]506.71162075226[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]105.122222222222[/C][C]0.203267154456104[/C][C]517.162856456101[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]105.283333333333[/C][C]0.180168370219479[/C][C]584.360802093501[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]105.30375[/C][C]0.173681083708123[/C][C]606.305233429834[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]105.294583333333[/C][C]0.172453293386481[/C][C]610.568701041623[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]105.294583333333[/C][C]0.171619020861897[/C][C]613.536790995122[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]105.287916666667[/C][C]0.167264062862744[/C][C]629.471237662481[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]105.165[/C][C]0.37532322853764[/C][C]280.198484942569[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]105.165147058824[/C][C]0.365784512518235[/C][C]287.505740291781[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]105.169545454545[/C][C]0.356580001571402[/C][C]294.939550706929[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]105.1728125[/C][C]0.346051958201796[/C][C]303.922026757235[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]105.182903225806[/C][C]0.336377283324849[/C][C]312.693241904295[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]105.193[/C][C]0.325697105482646[/C][C]322.978000814947[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]105.203620689655[/C][C]0.312767218916928[/C][C]336.363961203995[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]105.211428571429[/C][C]0.302483704463029[/C][C]347.825112622845[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]105.218148148148[/C][C]0.291503497224416[/C][C]360.949865610515[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]105.234807692308[/C][C]0.281237232374469[/C][C]374.185191639871[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]105.2446[/C][C]0.270927689727766[/C][C]388.460109432713[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]105.244791666667[/C][C]0.261198137745358[/C][C]402.930865338978[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]105.240869565217[/C][C]0.254299231494781[/C][C]413.84658910138[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]105.234772727273[/C][C]0.246050513178811[/C][C]427.695806717525[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]105.224761904762[/C][C]0.239154345920164[/C][C]439.986827334882[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]105.225[/C][C]0.236884424919054[/C][C]444.203961640605[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]105.225263157895[/C][C]0.23367517571247[/C][C]450.3056982286[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]105.227222222222[/C][C]0.230448014697359[/C][C]456.620215888665[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]105.236470588235[/C][C]0.228094439877867[/C][C]461.372362450325[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]105.25[/C][C]0.22512272638604[/C][C]467.522767201733[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]105.246[/C][C]0.226129654600309[/C][C]465.423255459464[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]105.238928571429[/C][C]0.227854229883024[/C][C]461.869541001966[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]105.231923076923[/C][C]0.229084478358644[/C][C]459.358590467997[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]105.22375[/C][C]0.229345170927003[/C][C]458.800809167641[/C][/ROW]
[ROW][C]Median[/C][C]105.115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]105.265[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]105.166216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]105.227222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]105.166216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]105.227222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]105.227222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]105.166216216216[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]105.227222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]105.225263157895[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175569&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175569&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 Mean105.1677777777780.387382685670596271.482907388394
Geometric Mean105.116997073381
Harmonic Mean105.066096935886
Quadratic Mean105.218421021332
Winsorized Mean ( 1 / 24 )105.1648611111110.383337211301856274.340340594537
Winsorized Mean ( 2 / 24 )105.1570833333330.379905856754128276.797742029521
Winsorized Mean ( 3 / 24 )105.1608333333330.378757840785087277.646617467658
Winsorized Mean ( 4 / 24 )105.1380555555560.370667177466595283.645442453644
Winsorized Mean ( 5 / 24 )105.1408333333330.367349755838004286.21451807824
Winsorized Mean ( 6 / 24 )105.1416666666670.366852065804002286.605082722475
Winsorized Mean ( 7 / 24 )105.1611111111110.346685431707927303.33293958457
Winsorized Mean ( 8 / 24 )105.1711111111110.339892079643242309.42501284967
Winsorized Mean ( 9 / 24 )105.1098611111110.325964710798661322.457792604533
Winsorized Mean ( 10 / 24 )105.1668055555560.31542751290813333.410375607234
Winsorized Mean ( 11 / 24 )105.2431944444440.301585133223979348.966785329844
Winsorized Mean ( 12 / 24 )105.2748611111110.277782550330675378.982988621102
Winsorized Mean ( 13 / 24 )105.2893055555560.274370978311819383.747968547518
Winsorized Mean ( 14 / 24 )105.3165277777780.257423823738705409.117253594516
Winsorized Mean ( 15 / 24 )105.2227777777780.226716131566092464.116854195279
Winsorized Mean ( 16 / 24 )105.2227777777780.225425803163034466.773440756815
Winsorized Mean ( 17 / 24 )105.2086111111110.218635538402173481.205442994282
Winsorized Mean ( 18 / 24 )105.1486111111110.207511741994408506.71162075226
Winsorized Mean ( 19 / 24 )105.1222222222220.203267154456104517.162856456101
Winsorized Mean ( 20 / 24 )105.2833333333330.180168370219479584.360802093501
Winsorized Mean ( 21 / 24 )105.303750.173681083708123606.305233429834
Winsorized Mean ( 22 / 24 )105.2945833333330.172453293386481610.568701041623
Winsorized Mean ( 23 / 24 )105.2945833333330.171619020861897613.536790995122
Winsorized Mean ( 24 / 24 )105.2879166666670.167264062862744629.471237662481
Trimmed Mean ( 1 / 24 )105.1650.37532322853764280.198484942569
Trimmed Mean ( 2 / 24 )105.1651470588240.365784512518235287.505740291781
Trimmed Mean ( 3 / 24 )105.1695454545450.356580001571402294.939550706929
Trimmed Mean ( 4 / 24 )105.17281250.346051958201796303.922026757235
Trimmed Mean ( 5 / 24 )105.1829032258060.336377283324849312.693241904295
Trimmed Mean ( 6 / 24 )105.1930.325697105482646322.978000814947
Trimmed Mean ( 7 / 24 )105.2036206896550.312767218916928336.363961203995
Trimmed Mean ( 8 / 24 )105.2114285714290.302483704463029347.825112622845
Trimmed Mean ( 9 / 24 )105.2181481481480.291503497224416360.949865610515
Trimmed Mean ( 10 / 24 )105.2348076923080.281237232374469374.185191639871
Trimmed Mean ( 11 / 24 )105.24460.270927689727766388.460109432713
Trimmed Mean ( 12 / 24 )105.2447916666670.261198137745358402.930865338978
Trimmed Mean ( 13 / 24 )105.2408695652170.254299231494781413.84658910138
Trimmed Mean ( 14 / 24 )105.2347727272730.246050513178811427.695806717525
Trimmed Mean ( 15 / 24 )105.2247619047620.239154345920164439.986827334882
Trimmed Mean ( 16 / 24 )105.2250.236884424919054444.203961640605
Trimmed Mean ( 17 / 24 )105.2252631578950.23367517571247450.3056982286
Trimmed Mean ( 18 / 24 )105.2272222222220.230448014697359456.620215888665
Trimmed Mean ( 19 / 24 )105.2364705882350.228094439877867461.372362450325
Trimmed Mean ( 20 / 24 )105.250.22512272638604467.522767201733
Trimmed Mean ( 21 / 24 )105.2460.226129654600309465.423255459464
Trimmed Mean ( 22 / 24 )105.2389285714290.227854229883024461.869541001966
Trimmed Mean ( 23 / 24 )105.2319230769230.229084478358644459.358590467997
Trimmed Mean ( 24 / 24 )105.223750.229345170927003458.800809167641
Median105.115
Midrange105.265
Midmean - Weighted Average at Xnp105.166216216216
Midmean - Weighted Average at X(n+1)p105.227222222222
Midmean - Empirical Distribution Function105.166216216216
Midmean - Empirical Distribution Function - Averaging105.227222222222
Midmean - Empirical Distribution Function - Interpolation105.227222222222
Midmean - Closest Observation105.166216216216
Midmean - True Basic - Statistics Graphics Toolkit105.227222222222
Midmean - MS Excel (old versions)105.225263157895
Number of observations72



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')