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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 15 Oct 2011 10:14:35 -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/2011/Oct/15/t131868820916cxddilwfx0iqd.htm/, Retrieved Wed, 15 May 2024 02:33:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=129834, Retrieved Wed, 15 May 2024 02:33:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-15 14:14:35] [c81f0c87bb000ca3e7f952ee43cfaf8d] [Current]
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Dataseries X:
78,33
78,09
77,88
77,61
77,43
77,47
77,47
77,46
77,76
78,29
78,56
78,55
78,55
78,59
77,95
78,5
78,45
78,31
78,31
78,33
78,28
79,06
79,2
79,26
79,26
79,38
79,35
78,91
79,11
79,22
79,22
79,21
79,26
79,82
80,04
80,2
80,2
80,27
80,37
80,57
79,99
79,86
79,86
79,81
79,88
80,2
80,53
80,52
80,52
80,48
80,29
79,54
79,39
79,3
79,3
79,49
79,63
79,74
80,17
80,06




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129834&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=129834&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129834&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean79.17733333333330.119068623490035664.972274076553
Geometric Mean79.1720386907387
Harmonic Mean79.1667317864458
Quadratic Mean79.1826153689474
Winsorized Mean ( 1 / 20 )79.17716666666670.118814790036637666.391504308952
Winsorized Mean ( 2 / 20 )79.17716666666670.11866919591985667.209093757943
Winsorized Mean ( 3 / 20 )79.17716666666670.11866919591985667.209093757943
Winsorized Mean ( 4 / 20 )79.18383333333330.115948579014656682.921981504616
Winsorized Mean ( 5 / 20 )79.18716666666670.11145901723746710.459939710043
Winsorized Mean ( 6 / 20 )79.19116666666670.107502487598775736.644969205059
Winsorized Mean ( 7 / 20 )79.1970.105436220579882751.136559755554
Winsorized Mean ( 8 / 20 )79.20633333333330.100210503488488790.399514781729
Winsorized Mean ( 9 / 20 )79.23483333333330.0950876763616447833.28183383072
Winsorized Mean ( 10 / 20 )79.23650.0948048322327994835.785456646658
Winsorized Mean ( 11 / 20 )79.23466666666670.0932451560871125849.745659631297
Winsorized Mean ( 12 / 20 )79.21266666666670.0896099099981033883.97217080503
Winsorized Mean ( 13 / 20 )79.21266666666670.0881805629154345898.300759801589
Winsorized Mean ( 14 / 20 )79.2010.0863492775888308917.216706515267
Winsorized Mean ( 15 / 20 )79.20350.07711749968108471027.04963630229
Winsorized Mean ( 16 / 20 )79.21150.07413677427184851068.45085691944
Winsorized Mean ( 17 / 20 )79.22566666666670.07185530291800881102.57230085117
Winsorized Mean ( 18 / 20 )79.21366666666670.07007742556906551130.37352647318
Winsorized Mean ( 19 / 20 )79.21366666666670.06910565343804951146.26897693224
Winsorized Mean ( 20 / 20 )79.20033333333330.06412556831904881235.08197134849
Trimmed Mean ( 1 / 20 )79.1834482758620.116918633380083677.252598552446
Trimmed Mean ( 2 / 20 )79.19017857142860.11453873928434691.383361352011
Trimmed Mean ( 3 / 20 )79.19740740740740.111649591981344709.338977437918
Trimmed Mean ( 4 / 20 )79.20519230769230.108012865269358733.294058167735
Trimmed Mean ( 5 / 20 )79.21160.104527063188322757.809485733734
Trimmed Mean ( 6 / 20 )79.21770833333330.101665317795668779.20091188373
Trimmed Mean ( 7 / 20 )79.22347826086960.0992163582192486798.492100322825
Trimmed Mean ( 8 / 20 )79.22863636363640.0966093192255006820.09310280621
Trimmed Mean ( 9 / 20 )79.2326190476190.0946231964472835837.348789963581
Trimmed Mean ( 10 / 20 )79.232250.0932830593766449849.374479454919
Trimmed Mean ( 11 / 20 )79.23157894736840.0914180417991965866.695210135915
Trimmed Mean ( 12 / 20 )79.23111111111110.089177705393948888.463218033058
Trimmed Mean ( 13 / 20 )79.23382352941180.0869599603664289911.15293976146
Trimmed Mean ( 14 / 20 )79.2368750.084107551035142942.08990780023
Trimmed Mean ( 15 / 20 )79.2420.0804233053659011985.311404940066
Trimmed Mean ( 16 / 20 )79.24750.07793570983653671016.83169584539
Trimmed Mean ( 17 / 20 )79.25269230769230.07501088678381731056.54919846635
Trimmed Mean ( 18 / 20 )79.25666666666670.07114912555775241113.95138092503
Trimmed Mean ( 19 / 20 )79.26318181818180.06541041381416561211.7823018728
Trimmed Mean ( 20 / 20 )79.2710.05577162077804891421.35012205348
Median79.26
Midrange79
Midmean - Weighted Average at Xnp79.185
Midmean - Weighted Average at X(n+1)p79.242
Midmean - Empirical Distribution Function79.185
Midmean - Empirical Distribution Function - Averaging79.242
Midmean - Empirical Distribution Function - Interpolation79.242
Midmean - Closest Observation79.185
Midmean - True Basic - Statistics Graphics Toolkit79.242
Midmean - MS Excel (old versions)79.209393939394
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 79.1773333333333 & 0.119068623490035 & 664.972274076553 \tabularnewline
Geometric Mean & 79.1720386907387 &  &  \tabularnewline
Harmonic Mean & 79.1667317864458 &  &  \tabularnewline
Quadratic Mean & 79.1826153689474 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 79.1771666666667 & 0.118814790036637 & 666.391504308952 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 79.1771666666667 & 0.11866919591985 & 667.209093757943 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 79.1771666666667 & 0.11866919591985 & 667.209093757943 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 79.1838333333333 & 0.115948579014656 & 682.921981504616 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 79.1871666666667 & 0.11145901723746 & 710.459939710043 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 79.1911666666667 & 0.107502487598775 & 736.644969205059 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 79.197 & 0.105436220579882 & 751.136559755554 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 79.2063333333333 & 0.100210503488488 & 790.399514781729 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 79.2348333333333 & 0.0950876763616447 & 833.28183383072 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 79.2365 & 0.0948048322327994 & 835.785456646658 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 79.2346666666667 & 0.0932451560871125 & 849.745659631297 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 79.2126666666667 & 0.0896099099981033 & 883.97217080503 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 79.2126666666667 & 0.0881805629154345 & 898.300759801589 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 79.201 & 0.0863492775888308 & 917.216706515267 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 79.2035 & 0.0771174996810847 & 1027.04963630229 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 79.2115 & 0.0741367742718485 & 1068.45085691944 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 79.2256666666667 & 0.0718553029180088 & 1102.57230085117 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 79.2136666666667 & 0.0700774255690655 & 1130.37352647318 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 79.2136666666667 & 0.0691056534380495 & 1146.26897693224 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 79.2003333333333 & 0.0641255683190488 & 1235.08197134849 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 79.183448275862 & 0.116918633380083 & 677.252598552446 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 79.1901785714286 & 0.11453873928434 & 691.383361352011 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 79.1974074074074 & 0.111649591981344 & 709.338977437918 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 79.2051923076923 & 0.108012865269358 & 733.294058167735 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 79.2116 & 0.104527063188322 & 757.809485733734 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 79.2177083333333 & 0.101665317795668 & 779.20091188373 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 79.2234782608696 & 0.0992163582192486 & 798.492100322825 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 79.2286363636364 & 0.0966093192255006 & 820.09310280621 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 79.232619047619 & 0.0946231964472835 & 837.348789963581 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 79.23225 & 0.0932830593766449 & 849.374479454919 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 79.2315789473684 & 0.0914180417991965 & 866.695210135915 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 79.2311111111111 & 0.089177705393948 & 888.463218033058 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 79.2338235294118 & 0.0869599603664289 & 911.15293976146 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 79.236875 & 0.084107551035142 & 942.08990780023 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 79.242 & 0.0804233053659011 & 985.311404940066 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 79.2475 & 0.0779357098365367 & 1016.83169584539 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 79.2526923076923 & 0.0750108867838173 & 1056.54919846635 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 79.2566666666667 & 0.0711491255577524 & 1113.95138092503 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 79.2631818181818 & 0.0654104138141656 & 1211.7823018728 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 79.271 & 0.0557716207780489 & 1421.35012205348 \tabularnewline
Median & 79.26 &  &  \tabularnewline
Midrange & 79 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 79.185 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 79.242 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 79.185 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 79.242 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 79.242 &  &  \tabularnewline
Midmean - Closest Observation & 79.185 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 79.242 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 79.209393939394 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=129834&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]79.1773333333333[/C][C]0.119068623490035[/C][C]664.972274076553[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]79.1720386907387[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]79.1667317864458[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]79.1826153689474[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]79.1771666666667[/C][C]0.118814790036637[/C][C]666.391504308952[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]79.1771666666667[/C][C]0.11866919591985[/C][C]667.209093757943[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]79.1771666666667[/C][C]0.11866919591985[/C][C]667.209093757943[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]79.1838333333333[/C][C]0.115948579014656[/C][C]682.921981504616[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]79.1871666666667[/C][C]0.11145901723746[/C][C]710.459939710043[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]79.1911666666667[/C][C]0.107502487598775[/C][C]736.644969205059[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]79.197[/C][C]0.105436220579882[/C][C]751.136559755554[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]79.2063333333333[/C][C]0.100210503488488[/C][C]790.399514781729[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]79.2348333333333[/C][C]0.0950876763616447[/C][C]833.28183383072[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]79.2365[/C][C]0.0948048322327994[/C][C]835.785456646658[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]79.2346666666667[/C][C]0.0932451560871125[/C][C]849.745659631297[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]79.2126666666667[/C][C]0.0896099099981033[/C][C]883.97217080503[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]79.2126666666667[/C][C]0.0881805629154345[/C][C]898.300759801589[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]79.201[/C][C]0.0863492775888308[/C][C]917.216706515267[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]79.2035[/C][C]0.0771174996810847[/C][C]1027.04963630229[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]79.2115[/C][C]0.0741367742718485[/C][C]1068.45085691944[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]79.2256666666667[/C][C]0.0718553029180088[/C][C]1102.57230085117[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]79.2136666666667[/C][C]0.0700774255690655[/C][C]1130.37352647318[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]79.2136666666667[/C][C]0.0691056534380495[/C][C]1146.26897693224[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]79.2003333333333[/C][C]0.0641255683190488[/C][C]1235.08197134849[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]79.183448275862[/C][C]0.116918633380083[/C][C]677.252598552446[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]79.1901785714286[/C][C]0.11453873928434[/C][C]691.383361352011[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]79.1974074074074[/C][C]0.111649591981344[/C][C]709.338977437918[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]79.2051923076923[/C][C]0.108012865269358[/C][C]733.294058167735[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]79.2116[/C][C]0.104527063188322[/C][C]757.809485733734[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]79.2177083333333[/C][C]0.101665317795668[/C][C]779.20091188373[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]79.2234782608696[/C][C]0.0992163582192486[/C][C]798.492100322825[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]79.2286363636364[/C][C]0.0966093192255006[/C][C]820.09310280621[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]79.232619047619[/C][C]0.0946231964472835[/C][C]837.348789963581[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]79.23225[/C][C]0.0932830593766449[/C][C]849.374479454919[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]79.2315789473684[/C][C]0.0914180417991965[/C][C]866.695210135915[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]79.2311111111111[/C][C]0.089177705393948[/C][C]888.463218033058[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]79.2338235294118[/C][C]0.0869599603664289[/C][C]911.15293976146[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]79.236875[/C][C]0.084107551035142[/C][C]942.08990780023[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]79.242[/C][C]0.0804233053659011[/C][C]985.311404940066[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]79.2475[/C][C]0.0779357098365367[/C][C]1016.83169584539[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]79.2526923076923[/C][C]0.0750108867838173[/C][C]1056.54919846635[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]79.2566666666667[/C][C]0.0711491255577524[/C][C]1113.95138092503[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]79.2631818181818[/C][C]0.0654104138141656[/C][C]1211.7823018728[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]79.271[/C][C]0.0557716207780489[/C][C]1421.35012205348[/C][/ROW]
[ROW][C]Median[/C][C]79.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]79[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]79.185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]79.242[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]79.185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]79.242[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]79.242[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]79.185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]79.242[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]79.209393939394[/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=129834&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=129834&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 Mean79.17733333333330.119068623490035664.972274076553
Geometric Mean79.1720386907387
Harmonic Mean79.1667317864458
Quadratic Mean79.1826153689474
Winsorized Mean ( 1 / 20 )79.17716666666670.118814790036637666.391504308952
Winsorized Mean ( 2 / 20 )79.17716666666670.11866919591985667.209093757943
Winsorized Mean ( 3 / 20 )79.17716666666670.11866919591985667.209093757943
Winsorized Mean ( 4 / 20 )79.18383333333330.115948579014656682.921981504616
Winsorized Mean ( 5 / 20 )79.18716666666670.11145901723746710.459939710043
Winsorized Mean ( 6 / 20 )79.19116666666670.107502487598775736.644969205059
Winsorized Mean ( 7 / 20 )79.1970.105436220579882751.136559755554
Winsorized Mean ( 8 / 20 )79.20633333333330.100210503488488790.399514781729
Winsorized Mean ( 9 / 20 )79.23483333333330.0950876763616447833.28183383072
Winsorized Mean ( 10 / 20 )79.23650.0948048322327994835.785456646658
Winsorized Mean ( 11 / 20 )79.23466666666670.0932451560871125849.745659631297
Winsorized Mean ( 12 / 20 )79.21266666666670.0896099099981033883.97217080503
Winsorized Mean ( 13 / 20 )79.21266666666670.0881805629154345898.300759801589
Winsorized Mean ( 14 / 20 )79.2010.0863492775888308917.216706515267
Winsorized Mean ( 15 / 20 )79.20350.07711749968108471027.04963630229
Winsorized Mean ( 16 / 20 )79.21150.07413677427184851068.45085691944
Winsorized Mean ( 17 / 20 )79.22566666666670.07185530291800881102.57230085117
Winsorized Mean ( 18 / 20 )79.21366666666670.07007742556906551130.37352647318
Winsorized Mean ( 19 / 20 )79.21366666666670.06910565343804951146.26897693224
Winsorized Mean ( 20 / 20 )79.20033333333330.06412556831904881235.08197134849
Trimmed Mean ( 1 / 20 )79.1834482758620.116918633380083677.252598552446
Trimmed Mean ( 2 / 20 )79.19017857142860.11453873928434691.383361352011
Trimmed Mean ( 3 / 20 )79.19740740740740.111649591981344709.338977437918
Trimmed Mean ( 4 / 20 )79.20519230769230.108012865269358733.294058167735
Trimmed Mean ( 5 / 20 )79.21160.104527063188322757.809485733734
Trimmed Mean ( 6 / 20 )79.21770833333330.101665317795668779.20091188373
Trimmed Mean ( 7 / 20 )79.22347826086960.0992163582192486798.492100322825
Trimmed Mean ( 8 / 20 )79.22863636363640.0966093192255006820.09310280621
Trimmed Mean ( 9 / 20 )79.2326190476190.0946231964472835837.348789963581
Trimmed Mean ( 10 / 20 )79.232250.0932830593766449849.374479454919
Trimmed Mean ( 11 / 20 )79.23157894736840.0914180417991965866.695210135915
Trimmed Mean ( 12 / 20 )79.23111111111110.089177705393948888.463218033058
Trimmed Mean ( 13 / 20 )79.23382352941180.0869599603664289911.15293976146
Trimmed Mean ( 14 / 20 )79.2368750.084107551035142942.08990780023
Trimmed Mean ( 15 / 20 )79.2420.0804233053659011985.311404940066
Trimmed Mean ( 16 / 20 )79.24750.07793570983653671016.83169584539
Trimmed Mean ( 17 / 20 )79.25269230769230.07501088678381731056.54919846635
Trimmed Mean ( 18 / 20 )79.25666666666670.07114912555775241113.95138092503
Trimmed Mean ( 19 / 20 )79.26318181818180.06541041381416561211.7823018728
Trimmed Mean ( 20 / 20 )79.2710.05577162077804891421.35012205348
Median79.26
Midrange79
Midmean - Weighted Average at Xnp79.185
Midmean - Weighted Average at X(n+1)p79.242
Midmean - Empirical Distribution Function79.185
Midmean - Empirical Distribution Function - Averaging79.242
Midmean - Empirical Distribution Function - Interpolation79.242
Midmean - Closest Observation79.185
Midmean - True Basic - Statistics Graphics Toolkit79.242
Midmean - MS Excel (old versions)79.209393939394
Number of observations60



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')