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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 15 Dec 2009 12:59:30 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/15/t126090721034lgtpfkj2votht.htm/, Retrieved Wed, 08 May 2024 22:20:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=68103, Retrieved Wed, 08 May 2024 22:20:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper central ten...] [2009-12-15 19:59:30] [ba02bcb7e07025bbb7f8a074d38ad767] [Current]
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Dataseries X:
13.4
13.5
14.8
14.3
14.3
14
13.2
12.2
14.3
15.7
14.2
14.6
14.5
14.3
15.3
14.4
13.7
14.2
13.5
11.9
14.6
15.6
14.1
14.9
14.2
14.6
17.2
15.4
14.3
17.5
14.5
14.4
16.6
16.7
16.6
16.9
15.7
16.4
18.4
16.9
16.5
18.3
15.1
15.7
18.1
16.8
18.9
19
18.1
17.8
21.5
17.1
18.7
19
16.4
16.9
18.6
19.3
19.4
17.6




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68103&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=68103&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68103&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean15.910.26240629212519460.6311680682159
Geometric Mean15.7846892982549
Harmonic Mean15.6618190492545
Quadratic Mean16.0371651692769
Winsorized Mean ( 1 / 20 )15.880.25060153619541763.3675285518478
Winsorized Mean ( 2 / 20 )15.910.24248827800896265.6114189544949
Winsorized Mean ( 3 / 20 )15.9050.23720863781301867.0506780302718
Winsorized Mean ( 4 / 20 )15.91166666666670.23603470570564867.412402846002
Winsorized Mean ( 5 / 20 )15.90333333333330.23420700036658967.9028949110866
Winsorized Mean ( 6 / 20 )15.90333333333330.22655572226695670.1961229414195
Winsorized Mean ( 7 / 20 )15.92666666666670.21862263577640672.8500349934282
Winsorized Mean ( 8 / 20 )15.91333333333330.21123081154007775.3362315720408
Winsorized Mean ( 9 / 20 )15.91333333333330.20611371260433077.2065726838933
Winsorized Mean ( 10 / 20 )15.880.19970034048218579.5191433407528
Winsorized Mean ( 11 / 20 )15.880.19970034048218579.5191433407528
Winsorized Mean ( 12 / 20 )15.840.18584362541487685.2329476711344
Winsorized Mean ( 13 / 20 )15.79666666666670.17825213315839488.6197903316523
Winsorized Mean ( 14 / 20 )15.77333333333330.17429221949868590.4993543527188
Winsorized Mean ( 15 / 20 )15.69833333333330.16209245577279696.8480195977635
Winsorized Mean ( 16 / 20 )15.67166666666670.15795464676021799.2162433211415
Winsorized Mean ( 17 / 20 )15.64333333333330.145310240221985107.654720750827
Winsorized Mean ( 18 / 20 )15.64333333333330.145310240221985107.654720750827
Winsorized Mean ( 19 / 20 )15.6750.140773187771962111.349329002848
Winsorized Mean ( 20 / 20 )15.64166666666670.135906491338520115.091387560774
Trimmed Mean ( 1 / 20 )15.88275862068970.24372509792333765.1666929504548
Trimmed Mean ( 2 / 20 )15.88571428571430.23524549999737967.5282387373671
Trimmed Mean ( 3 / 20 )15.87222222222220.23012797865430368.9712842177498
Trimmed Mean ( 4 / 20 )15.85961538461540.22617648869321470.1205305478387
Trimmed Mean ( 5 / 20 )15.8440.22151905985163271.5243194450712
Trimmed Mean ( 6 / 20 )15.82916666666670.21612640635160473.2403177097901
Trimmed Mean ( 7 / 20 )15.81304347826090.2114959072856374.7676098379767
Trimmed Mean ( 8 / 20 )15.79090909090910.20756868451913576.0755849442858
Trimmed Mean ( 9 / 20 )15.76904761904760.20423757246748577.2093372856657
Trimmed Mean ( 10 / 20 )15.7450.20086192476552878.3871807381093
Trimmed Mean ( 11 / 20 )15.72368421052630.19776252733881579.5079048701064
Trimmed Mean ( 12 / 20 )15.70.19313618848260281.2897889481455
Trimmed Mean ( 13 / 20 )15.67941176470590.19026107458448982.4099821729069
Trimmed Mean ( 14 / 20 )15.66250.18787596714922983.366170977895
Trimmed Mean ( 15 / 20 )15.64666666666670.18499663453498884.5781151965088
Trimmed Mean ( 16 / 20 )15.63928571428570.18382612598761985.076512548271
Trimmed Mean ( 17 / 20 )15.63461538461540.18237259474386385.7289737340948
Trimmed Mean ( 18 / 20 )15.63333333333330.18303665058926685.4109452014311
Trimmed Mean ( 19 / 20 )15.63181818181820.18238278138381785.7088485174578
Trimmed Mean ( 20 / 20 )15.6250.18120575685057486.2279448046712
Median15.65
Midrange16.7
Midmean - Weighted Average at Xnp15.5242424242424
Midmean - Weighted Average at X(n+1)p15.5242424242424
Midmean - Empirical Distribution Function15.5242424242424
Midmean - Empirical Distribution Function - Averaging15.5242424242424
Midmean - Empirical Distribution Function - Interpolation15.5242424242424
Midmean - Closest Observation15.5242424242424
Midmean - True Basic - Statistics Graphics Toolkit15.5242424242424
Midmean - MS Excel (old versions)15.5823529411765
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 15.91 & 0.262406292125194 & 60.6311680682159 \tabularnewline
Geometric Mean & 15.7846892982549 &  &  \tabularnewline
Harmonic Mean & 15.6618190492545 &  &  \tabularnewline
Quadratic Mean & 16.0371651692769 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 15.88 & 0.250601536195417 & 63.3675285518478 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 15.91 & 0.242488278008962 & 65.6114189544949 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 15.905 & 0.237208637813018 & 67.0506780302718 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 15.9116666666667 & 0.236034705705648 & 67.412402846002 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 15.9033333333333 & 0.234207000366589 & 67.9028949110866 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 15.9033333333333 & 0.226555722266956 & 70.1961229414195 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 15.9266666666667 & 0.218622635776406 & 72.8500349934282 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 15.9133333333333 & 0.211230811540077 & 75.3362315720408 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 15.9133333333333 & 0.206113712604330 & 77.2065726838933 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 15.88 & 0.199700340482185 & 79.5191433407528 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 15.88 & 0.199700340482185 & 79.5191433407528 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 15.84 & 0.185843625414876 & 85.2329476711344 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 15.7966666666667 & 0.178252133158394 & 88.6197903316523 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 15.7733333333333 & 0.174292219498685 & 90.4993543527188 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 15.6983333333333 & 0.162092455772796 & 96.8480195977635 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 15.6716666666667 & 0.157954646760217 & 99.2162433211415 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 15.6433333333333 & 0.145310240221985 & 107.654720750827 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 15.6433333333333 & 0.145310240221985 & 107.654720750827 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 15.675 & 0.140773187771962 & 111.349329002848 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 15.6416666666667 & 0.135906491338520 & 115.091387560774 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 15.8827586206897 & 0.243725097923337 & 65.1666929504548 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 15.8857142857143 & 0.235245499997379 & 67.5282387373671 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 15.8722222222222 & 0.230127978654303 & 68.9712842177498 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 15.8596153846154 & 0.226176488693214 & 70.1205305478387 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 15.844 & 0.221519059851632 & 71.5243194450712 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 15.8291666666667 & 0.216126406351604 & 73.2403177097901 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 15.8130434782609 & 0.21149590728563 & 74.7676098379767 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 15.7909090909091 & 0.207568684519135 & 76.0755849442858 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 15.7690476190476 & 0.204237572467485 & 77.2093372856657 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 15.745 & 0.200861924765528 & 78.3871807381093 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 15.7236842105263 & 0.197762527338815 & 79.5079048701064 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 15.7 & 0.193136188482602 & 81.2897889481455 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 15.6794117647059 & 0.190261074584489 & 82.4099821729069 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 15.6625 & 0.187875967149229 & 83.366170977895 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 15.6466666666667 & 0.184996634534988 & 84.5781151965088 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 15.6392857142857 & 0.183826125987619 & 85.076512548271 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 15.6346153846154 & 0.182372594743863 & 85.7289737340948 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 15.6333333333333 & 0.183036650589266 & 85.4109452014311 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 15.6318181818182 & 0.182382781383817 & 85.7088485174578 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 15.625 & 0.181205756850574 & 86.2279448046712 \tabularnewline
Median & 15.65 &  &  \tabularnewline
Midrange & 16.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 15.5242424242424 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 15.5242424242424 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 15.5242424242424 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 15.5242424242424 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 15.5242424242424 &  &  \tabularnewline
Midmean - Closest Observation & 15.5242424242424 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 15.5242424242424 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 15.5823529411765 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=68103&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]15.91[/C][C]0.262406292125194[/C][C]60.6311680682159[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]15.7846892982549[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]15.6618190492545[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]16.0371651692769[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]15.88[/C][C]0.250601536195417[/C][C]63.3675285518478[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]15.91[/C][C]0.242488278008962[/C][C]65.6114189544949[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]15.905[/C][C]0.237208637813018[/C][C]67.0506780302718[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]15.9116666666667[/C][C]0.236034705705648[/C][C]67.412402846002[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]15.9033333333333[/C][C]0.234207000366589[/C][C]67.9028949110866[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]15.9033333333333[/C][C]0.226555722266956[/C][C]70.1961229414195[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]15.9266666666667[/C][C]0.218622635776406[/C][C]72.8500349934282[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]15.9133333333333[/C][C]0.211230811540077[/C][C]75.3362315720408[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]15.9133333333333[/C][C]0.206113712604330[/C][C]77.2065726838933[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]15.88[/C][C]0.199700340482185[/C][C]79.5191433407528[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]15.88[/C][C]0.199700340482185[/C][C]79.5191433407528[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]15.84[/C][C]0.185843625414876[/C][C]85.2329476711344[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]15.7966666666667[/C][C]0.178252133158394[/C][C]88.6197903316523[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]15.7733333333333[/C][C]0.174292219498685[/C][C]90.4993543527188[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]15.6983333333333[/C][C]0.162092455772796[/C][C]96.8480195977635[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]15.6716666666667[/C][C]0.157954646760217[/C][C]99.2162433211415[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]15.6433333333333[/C][C]0.145310240221985[/C][C]107.654720750827[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]15.6433333333333[/C][C]0.145310240221985[/C][C]107.654720750827[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]15.675[/C][C]0.140773187771962[/C][C]111.349329002848[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]15.6416666666667[/C][C]0.135906491338520[/C][C]115.091387560774[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]15.8827586206897[/C][C]0.243725097923337[/C][C]65.1666929504548[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]15.8857142857143[/C][C]0.235245499997379[/C][C]67.5282387373671[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]15.8722222222222[/C][C]0.230127978654303[/C][C]68.9712842177498[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]15.8596153846154[/C][C]0.226176488693214[/C][C]70.1205305478387[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]15.844[/C][C]0.221519059851632[/C][C]71.5243194450712[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]15.8291666666667[/C][C]0.216126406351604[/C][C]73.2403177097901[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]15.8130434782609[/C][C]0.21149590728563[/C][C]74.7676098379767[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]15.7909090909091[/C][C]0.207568684519135[/C][C]76.0755849442858[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]15.7690476190476[/C][C]0.204237572467485[/C][C]77.2093372856657[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]15.745[/C][C]0.200861924765528[/C][C]78.3871807381093[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]15.7236842105263[/C][C]0.197762527338815[/C][C]79.5079048701064[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]15.7[/C][C]0.193136188482602[/C][C]81.2897889481455[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]15.6794117647059[/C][C]0.190261074584489[/C][C]82.4099821729069[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]15.6625[/C][C]0.187875967149229[/C][C]83.366170977895[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]15.6466666666667[/C][C]0.184996634534988[/C][C]84.5781151965088[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]15.6392857142857[/C][C]0.183826125987619[/C][C]85.076512548271[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]15.6346153846154[/C][C]0.182372594743863[/C][C]85.7289737340948[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]15.6333333333333[/C][C]0.183036650589266[/C][C]85.4109452014311[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]15.6318181818182[/C][C]0.182382781383817[/C][C]85.7088485174578[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]15.625[/C][C]0.181205756850574[/C][C]86.2279448046712[/C][/ROW]
[ROW][C]Median[/C][C]15.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]15.5242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]15.5242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]15.5242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]15.5242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]15.5242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]15.5242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]15.5242424242424[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]15.5823529411765[/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=68103&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=68103&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 Mean15.910.26240629212519460.6311680682159
Geometric Mean15.7846892982549
Harmonic Mean15.6618190492545
Quadratic Mean16.0371651692769
Winsorized Mean ( 1 / 20 )15.880.25060153619541763.3675285518478
Winsorized Mean ( 2 / 20 )15.910.24248827800896265.6114189544949
Winsorized Mean ( 3 / 20 )15.9050.23720863781301867.0506780302718
Winsorized Mean ( 4 / 20 )15.91166666666670.23603470570564867.412402846002
Winsorized Mean ( 5 / 20 )15.90333333333330.23420700036658967.9028949110866
Winsorized Mean ( 6 / 20 )15.90333333333330.22655572226695670.1961229414195
Winsorized Mean ( 7 / 20 )15.92666666666670.21862263577640672.8500349934282
Winsorized Mean ( 8 / 20 )15.91333333333330.21123081154007775.3362315720408
Winsorized Mean ( 9 / 20 )15.91333333333330.20611371260433077.2065726838933
Winsorized Mean ( 10 / 20 )15.880.19970034048218579.5191433407528
Winsorized Mean ( 11 / 20 )15.880.19970034048218579.5191433407528
Winsorized Mean ( 12 / 20 )15.840.18584362541487685.2329476711344
Winsorized Mean ( 13 / 20 )15.79666666666670.17825213315839488.6197903316523
Winsorized Mean ( 14 / 20 )15.77333333333330.17429221949868590.4993543527188
Winsorized Mean ( 15 / 20 )15.69833333333330.16209245577279696.8480195977635
Winsorized Mean ( 16 / 20 )15.67166666666670.15795464676021799.2162433211415
Winsorized Mean ( 17 / 20 )15.64333333333330.145310240221985107.654720750827
Winsorized Mean ( 18 / 20 )15.64333333333330.145310240221985107.654720750827
Winsorized Mean ( 19 / 20 )15.6750.140773187771962111.349329002848
Winsorized Mean ( 20 / 20 )15.64166666666670.135906491338520115.091387560774
Trimmed Mean ( 1 / 20 )15.88275862068970.24372509792333765.1666929504548
Trimmed Mean ( 2 / 20 )15.88571428571430.23524549999737967.5282387373671
Trimmed Mean ( 3 / 20 )15.87222222222220.23012797865430368.9712842177498
Trimmed Mean ( 4 / 20 )15.85961538461540.22617648869321470.1205305478387
Trimmed Mean ( 5 / 20 )15.8440.22151905985163271.5243194450712
Trimmed Mean ( 6 / 20 )15.82916666666670.21612640635160473.2403177097901
Trimmed Mean ( 7 / 20 )15.81304347826090.2114959072856374.7676098379767
Trimmed Mean ( 8 / 20 )15.79090909090910.20756868451913576.0755849442858
Trimmed Mean ( 9 / 20 )15.76904761904760.20423757246748577.2093372856657
Trimmed Mean ( 10 / 20 )15.7450.20086192476552878.3871807381093
Trimmed Mean ( 11 / 20 )15.72368421052630.19776252733881579.5079048701064
Trimmed Mean ( 12 / 20 )15.70.19313618848260281.2897889481455
Trimmed Mean ( 13 / 20 )15.67941176470590.19026107458448982.4099821729069
Trimmed Mean ( 14 / 20 )15.66250.18787596714922983.366170977895
Trimmed Mean ( 15 / 20 )15.64666666666670.18499663453498884.5781151965088
Trimmed Mean ( 16 / 20 )15.63928571428570.18382612598761985.076512548271
Trimmed Mean ( 17 / 20 )15.63461538461540.18237259474386385.7289737340948
Trimmed Mean ( 18 / 20 )15.63333333333330.18303665058926685.4109452014311
Trimmed Mean ( 19 / 20 )15.63181818181820.18238278138381785.7088485174578
Trimmed Mean ( 20 / 20 )15.6250.18120575685057486.2279448046712
Median15.65
Midrange16.7
Midmean - Weighted Average at Xnp15.5242424242424
Midmean - Weighted Average at X(n+1)p15.5242424242424
Midmean - Empirical Distribution Function15.5242424242424
Midmean - Empirical Distribution Function - Averaging15.5242424242424
Midmean - Empirical Distribution Function - Interpolation15.5242424242424
Midmean - Closest Observation15.5242424242424
Midmean - True Basic - Statistics Graphics Toolkit15.5242424242424
Midmean - MS Excel (old versions)15.5823529411765
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')