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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 12 Apr 2014 08:46:28 -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/2014/Apr/12/t1397306913qmiheqiwhp8d72y.htm/, Retrieved Thu, 16 May 2024 03:01:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234436, Retrieved Thu, 16 May 2024 03:01:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-04-12 12:46:28] [0f40cba20c222b7b9166042309a72bac] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
55,64
56,13
56,69
56,8
56,93
57
57,01
57,21
57,17
57,36
57,29
57,26
57,29
57,68
58,19
58,34
58,46
58,67
58,72
58,74
58,77
58,84
59,13
59,12
59,12
59,33
59,49
59,67
59,7
59,73
59,74
59,62
59,6
59,98
60,05
60,06
60,1
60,18
60,38
60,52
60,78
60,72
60,72
60,86
60,99
61,11
61,17
61,19
61,19
61,22
61,19
60,82
60,6
60,15
60,14
60,2
60,36
60,38
60,44
60,47

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234436&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234436&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234436&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean59.27350.195359125338714303.407889942338
Geometric Mean59.2542993964588
Harmonic Mean59.2348942438741
Quadratic Mean59.2924915004702
Winsorized Mean ( 1 / 20 )59.28116666666670.192855891819296307.385821130175
Winsorized Mean ( 2 / 20 )59.29983333333330.188071012502936315.305546262254
Winsorized Mean ( 3 / 20 )59.30533333333330.186799004743757317.482062683824
Winsorized Mean ( 4 / 20 )59.31266666666670.184638273123617321.237117653046
Winsorized Mean ( 5 / 20 )59.31350.182530366640082324.951409958848
Winsorized Mean ( 6 / 20 )59.30250.180362570340027328.796046143058
Winsorized Mean ( 7 / 20 )59.3060.174058273247426340.7249703994
Winsorized Mean ( 8 / 20 )59.3060.172152245062985344.497395188206
Winsorized Mean ( 9 / 20 )59.30750.169723208531197349.43659451912
Winsorized Mean ( 10 / 20 )59.30250.167248525282107354.577117496082
Winsorized Mean ( 11 / 20 )59.30250.167248525282107354.577117496082
Winsorized Mean ( 12 / 20 )59.29250.161020163140686368.230281497077
Winsorized Mean ( 13 / 20 )59.34450.144813814812165409.798609870022
Winsorized Mean ( 14 / 20 )59.45183333333330.120975202125023491.43818145385
Winsorized Mean ( 15 / 20 )59.48183333333330.113384374930335524.603441787107
Winsorized Mean ( 16 / 20 )59.49783333333330.105710694547049562.836462178878
Winsorized Mean ( 17 / 20 )59.55733333333330.0960899021916534619.808449950807
Winsorized Mean ( 18 / 20 )59.56633333333330.0928877479002542641.272231051371
Winsorized Mean ( 19 / 20 )59.5220.0847911358761271701.983755553845
Winsorized Mean ( 20 / 20 )59.52533333333330.0823309659075446723.00054635796
Trimmed Mean ( 1 / 20 )59.30258620689650.188976701231336313.808981850632
Trimmed Mean ( 2 / 20 )59.32553571428570.184115456373196322.219203552551
Trimmed Mean ( 3 / 20 )59.33981481481480.181204620959111327.474070477512
Trimmed Mean ( 4 / 20 )59.35307692307690.178068982358652333.315079004231
Trimmed Mean ( 5 / 20 )59.36520.174859999976658339.501315383305
Trimmed Mean ( 6 / 20 )59.3781250.171384551699301346.461360789278
Trimmed Mean ( 7 / 20 )59.39456521739130.167456305216286354.686944398287
Trimmed Mean ( 8 / 20 )59.41181818181820.164079942592087362.090681184109
Trimmed Mean ( 9 / 20 )59.43071428571430.160013934082984371.409618957892
Trimmed Mean ( 10 / 20 )59.451250.155129056074165383.237360585609
Trimmed Mean ( 11 / 20 )59.47473684210530.149059992906761398.998656059964
Trimmed Mean ( 12 / 20 )59.50083333333330.140552975382554423.333858080095
Trimmed Mean ( 13 / 20 )59.53147058823530.130364313567253456.654654630799
Trimmed Mean ( 14 / 20 )59.55843750.121482035522282490.265389807991
Trimmed Mean ( 15 / 20 )59.57366666666670.117097545871133508.752478316053
Trimmed Mean ( 16 / 20 )59.58678571428570.112992079100844527.353653357465
Trimmed Mean ( 17 / 20 )59.59961538461540.109185066278429545.858672949218
Trimmed Mean ( 18 / 20 )59.60583333333330.106617827360677559.060663763979
Trimmed Mean ( 19 / 20 )59.61181818181820.103201220595059577.627065242987
Trimmed Mean ( 20 / 20 )59.6260.100137799792927595.439485621806
Median59.685
Midrange58.43
Midmean - Weighted Average at Xnp59.5290322580645
Midmean - Weighted Average at X(n+1)p59.5736666666667
Midmean - Empirical Distribution Function59.5290322580645
Midmean - Empirical Distribution Function - Averaging59.5736666666667
Midmean - Empirical Distribution Function - Interpolation59.5736666666667
Midmean - Closest Observation59.5290322580645
Midmean - True Basic - Statistics Graphics Toolkit59.5736666666667
Midmean - MS Excel (old versions)59.5584375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 59.2735 & 0.195359125338714 & 303.407889942338 \tabularnewline
Geometric Mean & 59.2542993964588 &  &  \tabularnewline
Harmonic Mean & 59.2348942438741 &  &  \tabularnewline
Quadratic Mean & 59.2924915004702 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 59.2811666666667 & 0.192855891819296 & 307.385821130175 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 59.2998333333333 & 0.188071012502936 & 315.305546262254 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 59.3053333333333 & 0.186799004743757 & 317.482062683824 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 59.3126666666667 & 0.184638273123617 & 321.237117653046 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 59.3135 & 0.182530366640082 & 324.951409958848 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 59.3025 & 0.180362570340027 & 328.796046143058 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 59.306 & 0.174058273247426 & 340.7249703994 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 59.306 & 0.172152245062985 & 344.497395188206 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 59.3075 & 0.169723208531197 & 349.43659451912 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 59.3025 & 0.167248525282107 & 354.577117496082 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 59.3025 & 0.167248525282107 & 354.577117496082 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 59.2925 & 0.161020163140686 & 368.230281497077 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 59.3445 & 0.144813814812165 & 409.798609870022 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 59.4518333333333 & 0.120975202125023 & 491.43818145385 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 59.4818333333333 & 0.113384374930335 & 524.603441787107 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 59.4978333333333 & 0.105710694547049 & 562.836462178878 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 59.5573333333333 & 0.0960899021916534 & 619.808449950807 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 59.5663333333333 & 0.0928877479002542 & 641.272231051371 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 59.522 & 0.0847911358761271 & 701.983755553845 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 59.5253333333333 & 0.0823309659075446 & 723.00054635796 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 59.3025862068965 & 0.188976701231336 & 313.808981850632 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 59.3255357142857 & 0.184115456373196 & 322.219203552551 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 59.3398148148148 & 0.181204620959111 & 327.474070477512 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 59.3530769230769 & 0.178068982358652 & 333.315079004231 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 59.3652 & 0.174859999976658 & 339.501315383305 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 59.378125 & 0.171384551699301 & 346.461360789278 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 59.3945652173913 & 0.167456305216286 & 354.686944398287 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 59.4118181818182 & 0.164079942592087 & 362.090681184109 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 59.4307142857143 & 0.160013934082984 & 371.409618957892 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 59.45125 & 0.155129056074165 & 383.237360585609 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 59.4747368421053 & 0.149059992906761 & 398.998656059964 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 59.5008333333333 & 0.140552975382554 & 423.333858080095 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 59.5314705882353 & 0.130364313567253 & 456.654654630799 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 59.5584375 & 0.121482035522282 & 490.265389807991 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 59.5736666666667 & 0.117097545871133 & 508.752478316053 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 59.5867857142857 & 0.112992079100844 & 527.353653357465 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 59.5996153846154 & 0.109185066278429 & 545.858672949218 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 59.6058333333333 & 0.106617827360677 & 559.060663763979 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 59.6118181818182 & 0.103201220595059 & 577.627065242987 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 59.626 & 0.100137799792927 & 595.439485621806 \tabularnewline
Median & 59.685 &  &  \tabularnewline
Midrange & 58.43 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 59.5290322580645 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 59.5736666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 59.5290322580645 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 59.5736666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 59.5736666666667 &  &  \tabularnewline
Midmean - Closest Observation & 59.5290322580645 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 59.5736666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 59.5584375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234436&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]59.2735[/C][C]0.195359125338714[/C][C]303.407889942338[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]59.2542993964588[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]59.2348942438741[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]59.2924915004702[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]59.2811666666667[/C][C]0.192855891819296[/C][C]307.385821130175[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]59.2998333333333[/C][C]0.188071012502936[/C][C]315.305546262254[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]59.3053333333333[/C][C]0.186799004743757[/C][C]317.482062683824[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]59.3126666666667[/C][C]0.184638273123617[/C][C]321.237117653046[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]59.3135[/C][C]0.182530366640082[/C][C]324.951409958848[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]59.3025[/C][C]0.180362570340027[/C][C]328.796046143058[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]59.306[/C][C]0.174058273247426[/C][C]340.7249703994[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]59.306[/C][C]0.172152245062985[/C][C]344.497395188206[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]59.3075[/C][C]0.169723208531197[/C][C]349.43659451912[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]59.3025[/C][C]0.167248525282107[/C][C]354.577117496082[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]59.3025[/C][C]0.167248525282107[/C][C]354.577117496082[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]59.2925[/C][C]0.161020163140686[/C][C]368.230281497077[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]59.3445[/C][C]0.144813814812165[/C][C]409.798609870022[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]59.4518333333333[/C][C]0.120975202125023[/C][C]491.43818145385[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]59.4818333333333[/C][C]0.113384374930335[/C][C]524.603441787107[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]59.4978333333333[/C][C]0.105710694547049[/C][C]562.836462178878[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]59.5573333333333[/C][C]0.0960899021916534[/C][C]619.808449950807[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]59.5663333333333[/C][C]0.0928877479002542[/C][C]641.272231051371[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]59.522[/C][C]0.0847911358761271[/C][C]701.983755553845[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]59.5253333333333[/C][C]0.0823309659075446[/C][C]723.00054635796[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]59.3025862068965[/C][C]0.188976701231336[/C][C]313.808981850632[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]59.3255357142857[/C][C]0.184115456373196[/C][C]322.219203552551[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]59.3398148148148[/C][C]0.181204620959111[/C][C]327.474070477512[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]59.3530769230769[/C][C]0.178068982358652[/C][C]333.315079004231[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]59.3652[/C][C]0.174859999976658[/C][C]339.501315383305[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]59.378125[/C][C]0.171384551699301[/C][C]346.461360789278[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]59.3945652173913[/C][C]0.167456305216286[/C][C]354.686944398287[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]59.4118181818182[/C][C]0.164079942592087[/C][C]362.090681184109[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]59.4307142857143[/C][C]0.160013934082984[/C][C]371.409618957892[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]59.45125[/C][C]0.155129056074165[/C][C]383.237360585609[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]59.4747368421053[/C][C]0.149059992906761[/C][C]398.998656059964[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]59.5008333333333[/C][C]0.140552975382554[/C][C]423.333858080095[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]59.5314705882353[/C][C]0.130364313567253[/C][C]456.654654630799[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]59.5584375[/C][C]0.121482035522282[/C][C]490.265389807991[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]59.5736666666667[/C][C]0.117097545871133[/C][C]508.752478316053[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]59.5867857142857[/C][C]0.112992079100844[/C][C]527.353653357465[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]59.5996153846154[/C][C]0.109185066278429[/C][C]545.858672949218[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]59.6058333333333[/C][C]0.106617827360677[/C][C]559.060663763979[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]59.6118181818182[/C][C]0.103201220595059[/C][C]577.627065242987[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]59.626[/C][C]0.100137799792927[/C][C]595.439485621806[/C][/ROW]
[ROW][C]Median[/C][C]59.685[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]58.43[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]59.5290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]59.5736666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]59.5290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]59.5736666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]59.5736666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]59.5290322580645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]59.5736666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]59.5584375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234436&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234436&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean59.27350.195359125338714303.407889942338
Geometric Mean59.2542993964588
Harmonic Mean59.2348942438741
Quadratic Mean59.2924915004702
Winsorized Mean ( 1 / 20 )59.28116666666670.192855891819296307.385821130175
Winsorized Mean ( 2 / 20 )59.29983333333330.188071012502936315.305546262254
Winsorized Mean ( 3 / 20 )59.30533333333330.186799004743757317.482062683824
Winsorized Mean ( 4 / 20 )59.31266666666670.184638273123617321.237117653046
Winsorized Mean ( 5 / 20 )59.31350.182530366640082324.951409958848
Winsorized Mean ( 6 / 20 )59.30250.180362570340027328.796046143058
Winsorized Mean ( 7 / 20 )59.3060.174058273247426340.7249703994
Winsorized Mean ( 8 / 20 )59.3060.172152245062985344.497395188206
Winsorized Mean ( 9 / 20 )59.30750.169723208531197349.43659451912
Winsorized Mean ( 10 / 20 )59.30250.167248525282107354.577117496082
Winsorized Mean ( 11 / 20 )59.30250.167248525282107354.577117496082
Winsorized Mean ( 12 / 20 )59.29250.161020163140686368.230281497077
Winsorized Mean ( 13 / 20 )59.34450.144813814812165409.798609870022
Winsorized Mean ( 14 / 20 )59.45183333333330.120975202125023491.43818145385
Winsorized Mean ( 15 / 20 )59.48183333333330.113384374930335524.603441787107
Winsorized Mean ( 16 / 20 )59.49783333333330.105710694547049562.836462178878
Winsorized Mean ( 17 / 20 )59.55733333333330.0960899021916534619.808449950807
Winsorized Mean ( 18 / 20 )59.56633333333330.0928877479002542641.272231051371
Winsorized Mean ( 19 / 20 )59.5220.0847911358761271701.983755553845
Winsorized Mean ( 20 / 20 )59.52533333333330.0823309659075446723.00054635796
Trimmed Mean ( 1 / 20 )59.30258620689650.188976701231336313.808981850632
Trimmed Mean ( 2 / 20 )59.32553571428570.184115456373196322.219203552551
Trimmed Mean ( 3 / 20 )59.33981481481480.181204620959111327.474070477512
Trimmed Mean ( 4 / 20 )59.35307692307690.178068982358652333.315079004231
Trimmed Mean ( 5 / 20 )59.36520.174859999976658339.501315383305
Trimmed Mean ( 6 / 20 )59.3781250.171384551699301346.461360789278
Trimmed Mean ( 7 / 20 )59.39456521739130.167456305216286354.686944398287
Trimmed Mean ( 8 / 20 )59.41181818181820.164079942592087362.090681184109
Trimmed Mean ( 9 / 20 )59.43071428571430.160013934082984371.409618957892
Trimmed Mean ( 10 / 20 )59.451250.155129056074165383.237360585609
Trimmed Mean ( 11 / 20 )59.47473684210530.149059992906761398.998656059964
Trimmed Mean ( 12 / 20 )59.50083333333330.140552975382554423.333858080095
Trimmed Mean ( 13 / 20 )59.53147058823530.130364313567253456.654654630799
Trimmed Mean ( 14 / 20 )59.55843750.121482035522282490.265389807991
Trimmed Mean ( 15 / 20 )59.57366666666670.117097545871133508.752478316053
Trimmed Mean ( 16 / 20 )59.58678571428570.112992079100844527.353653357465
Trimmed Mean ( 17 / 20 )59.59961538461540.109185066278429545.858672949218
Trimmed Mean ( 18 / 20 )59.60583333333330.106617827360677559.060663763979
Trimmed Mean ( 19 / 20 )59.61181818181820.103201220595059577.627065242987
Trimmed Mean ( 20 / 20 )59.6260.100137799792927595.439485621806
Median59.685
Midrange58.43
Midmean - Weighted Average at Xnp59.5290322580645
Midmean - Weighted Average at X(n+1)p59.5736666666667
Midmean - Empirical Distribution Function59.5290322580645
Midmean - Empirical Distribution Function - Averaging59.5736666666667
Midmean - Empirical Distribution Function - Interpolation59.5736666666667
Midmean - Closest Observation59.5290322580645
Midmean - True Basic - Statistics Graphics Toolkit59.5736666666667
Midmean - MS Excel (old versions)59.5584375
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')