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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Oct 2011 11:58:09 -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/18/t1318953683d6bpnyicy4n9iuy.htm/, Retrieved Thu, 16 May 2024 22:14:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132265, Retrieved Thu, 16 May 2024 22:14:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-18 15:58:09] [5143da885265528a100ac524801fc397] [Current]
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Dataseries X:
31.956
29.506
34.506
27.165
26.736
23.691
18.157
17.328
18.205
20.995
17.382
9.367
31.124
26.551
30.651
25.859
25.100
25.778
20.418
18.688
20.424
24.776
19.814
12.738
31.566
30.111
30.019
31.934
25.826
26.835
20.205
17.789
20.520
22.518
15.572
11.509
25.447
24.090
27.786
26.195
20.516
22.759
19.028
16.971
20.036
22.485
18.730
14.538
27.561
25.985
34.670
32.066
27.186
29.586
21.359
21.553
19.573
24.256
22.380
16.167




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132265&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132265&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132265&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean23.37070.74456096049840331.3885648588879
Geometric Mean22.6030208271498
Harmonic Mean21.7443947177942
Quadratic Mean24.0602890443984
Winsorized Mean ( 1 / 20 )23.40366666666670.73325473166328231.9175119587416
Winsorized Mean ( 2 / 20 )23.36330.70336612260570133.2164135421364
Winsorized Mean ( 3 / 20 )23.44780.68067627504741934.4477997244234
Winsorized Mean ( 4 / 20 )23.51526666666670.66573938839308935.3220300265334
Winsorized Mean ( 5 / 20 )23.53418333333330.64945479589898836.2368304644773
Winsorized Mean ( 6 / 20 )23.57038333333330.62536649958952237.6905116420603
Winsorized Mean ( 7 / 20 )23.556850.60689964770710338.8150661958677
Winsorized Mean ( 8 / 20 )23.492050.59168132285102139.7038897337563
Winsorized Mean ( 9 / 20 )23.53930.57857634662165140.6848640416216
Winsorized Mean ( 10 / 20 )23.52846666666670.55484582348096942.4054136679893
Winsorized Mean ( 11 / 20 )23.52260.55069625021421742.7142912101723
Winsorized Mean ( 12 / 20 )23.27520.47525027768606148.9746163081151
Winsorized Mean ( 13 / 20 )23.235550.46600348342882249.86132255715
Winsorized Mean ( 14 / 20 )23.21758333333330.44114797489958452.6299216008375
Winsorized Mean ( 15 / 20 )23.34858333333330.41895665963278255.7303071725808
Winsorized Mean ( 16 / 20 )23.324850.3958030589612158.9304439971141
Winsorized Mean ( 17 / 20 )23.35970.38222997580877961.1142544500129
Winsorized Mean ( 18 / 20 )23.35490.36654377013356663.7165378407321
Winsorized Mean ( 19 / 20 )23.30961666666670.34033432224688568.4903494680663
Winsorized Mean ( 20 / 20 )23.24161666666670.33008441318214470.4111304214831
Trimmed Mean ( 1 / 20 )23.41732758620690.70401354161717533.2626095975589
Trimmed Mean ( 2 / 20 )23.43196428571430.66785920145178935.0851859715012
Trimmed Mean ( 3 / 20 )23.47011111111110.64341109971243936.4776285668691
Trimmed Mean ( 4 / 20 )23.47869230769230.62411561533986437.619139355946
Trimmed Mean ( 5 / 20 )23.467720.60575262954106838.7414248911799
Trimmed Mean ( 6 / 20 )23.45110416666670.58803748029065439.8802881664538
Trimmed Mean ( 7 / 20 )23.42517391304350.57281485429315440.8948436610462
Trimmed Mean ( 8 / 20 )23.39952272727270.55832392778649541.9102989550195
Trimmed Mean ( 9 / 20 )23.3830.54342168716504243.0291991510055
Trimmed Mean ( 10 / 20 )23.356950.52694231785476744.3254398224998
Trimmed Mean ( 11 / 20 )23.32986842105260.51110984888374445.6455074618591
Trimmed Mean ( 12 / 20 )23.30066666666670.49026589157766747.5265913190199
Trimmed Mean ( 13 / 20 )23.30441176470590.48273122454148448.2761640016994
Trimmed Mean ( 14 / 20 )23.314343750.47350367374621249.237936351252
Trimmed Mean ( 15 / 20 )23.32816666666670.4661457102452850.0447953374744
Trimmed Mean ( 16 / 20 )23.325250.46036143100403750.6672549634061
Trimmed Mean ( 17 / 20 )23.32530769230770.45670030492732351.0735540148578
Trimmed Mean ( 18 / 20 )23.320250.45269098479800951.5147214835866
Trimmed Mean ( 19 / 20 )23.3150.44860954976296351.9716979103972
Trimmed Mean ( 20 / 20 )23.315850.44806813553180452.0363939121152
Median23.225
Midrange22.0185
Midmean - Weighted Average at Xnp23.1894516129032
Midmean - Weighted Average at X(n+1)p23.3281666666667
Midmean - Empirical Distribution Function23.1894516129032
Midmean - Empirical Distribution Function - Averaging23.3281666666667
Midmean - Empirical Distribution Function - Interpolation23.3281666666667
Midmean - Closest Observation23.1894516129032
Midmean - True Basic - Statistics Graphics Toolkit23.3281666666667
Midmean - MS Excel (old versions)23.31434375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 23.3707 & 0.744560960498403 & 31.3885648588879 \tabularnewline
Geometric Mean & 22.6030208271498 &  &  \tabularnewline
Harmonic Mean & 21.7443947177942 &  &  \tabularnewline
Quadratic Mean & 24.0602890443984 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 23.4036666666667 & 0.733254731663282 & 31.9175119587416 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 23.3633 & 0.703366122605701 & 33.2164135421364 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 23.4478 & 0.680676275047419 & 34.4477997244234 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 23.5152666666667 & 0.665739388393089 & 35.3220300265334 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 23.5341833333333 & 0.649454795898988 & 36.2368304644773 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 23.5703833333333 & 0.625366499589522 & 37.6905116420603 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 23.55685 & 0.606899647707103 & 38.8150661958677 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 23.49205 & 0.591681322851021 & 39.7038897337563 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 23.5393 & 0.578576346621651 & 40.6848640416216 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 23.5284666666667 & 0.554845823480969 & 42.4054136679893 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 23.5226 & 0.550696250214217 & 42.7142912101723 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 23.2752 & 0.475250277686061 & 48.9746163081151 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 23.23555 & 0.466003483428822 & 49.86132255715 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 23.2175833333333 & 0.441147974899584 & 52.6299216008375 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 23.3485833333333 & 0.418956659632782 & 55.7303071725808 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 23.32485 & 0.39580305896121 & 58.9304439971141 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 23.3597 & 0.382229975808779 & 61.1142544500129 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 23.3549 & 0.366543770133566 & 63.7165378407321 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 23.3096166666667 & 0.340334322246885 & 68.4903494680663 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 23.2416166666667 & 0.330084413182144 & 70.4111304214831 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 23.4173275862069 & 0.704013541617175 & 33.2626095975589 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 23.4319642857143 & 0.667859201451789 & 35.0851859715012 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 23.4701111111111 & 0.643411099712439 & 36.4776285668691 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 23.4786923076923 & 0.624115615339864 & 37.619139355946 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 23.46772 & 0.605752629541068 & 38.7414248911799 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 23.4511041666667 & 0.588037480290654 & 39.8802881664538 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 23.4251739130435 & 0.572814854293154 & 40.8948436610462 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 23.3995227272727 & 0.558323927786495 & 41.9102989550195 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 23.383 & 0.543421687165042 & 43.0291991510055 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 23.35695 & 0.526942317854767 & 44.3254398224998 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 23.3298684210526 & 0.511109848883744 & 45.6455074618591 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 23.3006666666667 & 0.490265891577667 & 47.5265913190199 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 23.3044117647059 & 0.482731224541484 & 48.2761640016994 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 23.31434375 & 0.473503673746212 & 49.237936351252 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 23.3281666666667 & 0.46614571024528 & 50.0447953374744 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 23.32525 & 0.460361431004037 & 50.6672549634061 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 23.3253076923077 & 0.456700304927323 & 51.0735540148578 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 23.32025 & 0.452690984798009 & 51.5147214835866 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 23.315 & 0.448609549762963 & 51.9716979103972 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 23.31585 & 0.448068135531804 & 52.0363939121152 \tabularnewline
Median & 23.225 &  &  \tabularnewline
Midrange & 22.0185 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 23.1894516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 23.3281666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 23.1894516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 23.3281666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 23.3281666666667 &  &  \tabularnewline
Midmean - Closest Observation & 23.1894516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 23.3281666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 23.31434375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132265&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]23.3707[/C][C]0.744560960498403[/C][C]31.3885648588879[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]22.6030208271498[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.7443947177942[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]24.0602890443984[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]23.4036666666667[/C][C]0.733254731663282[/C][C]31.9175119587416[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]23.3633[/C][C]0.703366122605701[/C][C]33.2164135421364[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]23.4478[/C][C]0.680676275047419[/C][C]34.4477997244234[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]23.5152666666667[/C][C]0.665739388393089[/C][C]35.3220300265334[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]23.5341833333333[/C][C]0.649454795898988[/C][C]36.2368304644773[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]23.5703833333333[/C][C]0.625366499589522[/C][C]37.6905116420603[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]23.55685[/C][C]0.606899647707103[/C][C]38.8150661958677[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]23.49205[/C][C]0.591681322851021[/C][C]39.7038897337563[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]23.5393[/C][C]0.578576346621651[/C][C]40.6848640416216[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]23.5284666666667[/C][C]0.554845823480969[/C][C]42.4054136679893[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]23.5226[/C][C]0.550696250214217[/C][C]42.7142912101723[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]23.2752[/C][C]0.475250277686061[/C][C]48.9746163081151[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]23.23555[/C][C]0.466003483428822[/C][C]49.86132255715[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]23.2175833333333[/C][C]0.441147974899584[/C][C]52.6299216008375[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]23.3485833333333[/C][C]0.418956659632782[/C][C]55.7303071725808[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]23.32485[/C][C]0.39580305896121[/C][C]58.9304439971141[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]23.3597[/C][C]0.382229975808779[/C][C]61.1142544500129[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]23.3549[/C][C]0.366543770133566[/C][C]63.7165378407321[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]23.3096166666667[/C][C]0.340334322246885[/C][C]68.4903494680663[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]23.2416166666667[/C][C]0.330084413182144[/C][C]70.4111304214831[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]23.4173275862069[/C][C]0.704013541617175[/C][C]33.2626095975589[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]23.4319642857143[/C][C]0.667859201451789[/C][C]35.0851859715012[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]23.4701111111111[/C][C]0.643411099712439[/C][C]36.4776285668691[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]23.4786923076923[/C][C]0.624115615339864[/C][C]37.619139355946[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]23.46772[/C][C]0.605752629541068[/C][C]38.7414248911799[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]23.4511041666667[/C][C]0.588037480290654[/C][C]39.8802881664538[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]23.4251739130435[/C][C]0.572814854293154[/C][C]40.8948436610462[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]23.3995227272727[/C][C]0.558323927786495[/C][C]41.9102989550195[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]23.383[/C][C]0.543421687165042[/C][C]43.0291991510055[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]23.35695[/C][C]0.526942317854767[/C][C]44.3254398224998[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]23.3298684210526[/C][C]0.511109848883744[/C][C]45.6455074618591[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]23.3006666666667[/C][C]0.490265891577667[/C][C]47.5265913190199[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]23.3044117647059[/C][C]0.482731224541484[/C][C]48.2761640016994[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]23.31434375[/C][C]0.473503673746212[/C][C]49.237936351252[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]23.3281666666667[/C][C]0.46614571024528[/C][C]50.0447953374744[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]23.32525[/C][C]0.460361431004037[/C][C]50.6672549634061[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]23.3253076923077[/C][C]0.456700304927323[/C][C]51.0735540148578[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]23.32025[/C][C]0.452690984798009[/C][C]51.5147214835866[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]23.315[/C][C]0.448609549762963[/C][C]51.9716979103972[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]23.31585[/C][C]0.448068135531804[/C][C]52.0363939121152[/C][/ROW]
[ROW][C]Median[/C][C]23.225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]22.0185[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]23.1894516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]23.3281666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]23.1894516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]23.3281666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]23.3281666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]23.1894516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]23.3281666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]23.31434375[/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=132265&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132265&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 Mean23.37070.74456096049840331.3885648588879
Geometric Mean22.6030208271498
Harmonic Mean21.7443947177942
Quadratic Mean24.0602890443984
Winsorized Mean ( 1 / 20 )23.40366666666670.73325473166328231.9175119587416
Winsorized Mean ( 2 / 20 )23.36330.70336612260570133.2164135421364
Winsorized Mean ( 3 / 20 )23.44780.68067627504741934.4477997244234
Winsorized Mean ( 4 / 20 )23.51526666666670.66573938839308935.3220300265334
Winsorized Mean ( 5 / 20 )23.53418333333330.64945479589898836.2368304644773
Winsorized Mean ( 6 / 20 )23.57038333333330.62536649958952237.6905116420603
Winsorized Mean ( 7 / 20 )23.556850.60689964770710338.8150661958677
Winsorized Mean ( 8 / 20 )23.492050.59168132285102139.7038897337563
Winsorized Mean ( 9 / 20 )23.53930.57857634662165140.6848640416216
Winsorized Mean ( 10 / 20 )23.52846666666670.55484582348096942.4054136679893
Winsorized Mean ( 11 / 20 )23.52260.55069625021421742.7142912101723
Winsorized Mean ( 12 / 20 )23.27520.47525027768606148.9746163081151
Winsorized Mean ( 13 / 20 )23.235550.46600348342882249.86132255715
Winsorized Mean ( 14 / 20 )23.21758333333330.44114797489958452.6299216008375
Winsorized Mean ( 15 / 20 )23.34858333333330.41895665963278255.7303071725808
Winsorized Mean ( 16 / 20 )23.324850.3958030589612158.9304439971141
Winsorized Mean ( 17 / 20 )23.35970.38222997580877961.1142544500129
Winsorized Mean ( 18 / 20 )23.35490.36654377013356663.7165378407321
Winsorized Mean ( 19 / 20 )23.30961666666670.34033432224688568.4903494680663
Winsorized Mean ( 20 / 20 )23.24161666666670.33008441318214470.4111304214831
Trimmed Mean ( 1 / 20 )23.41732758620690.70401354161717533.2626095975589
Trimmed Mean ( 2 / 20 )23.43196428571430.66785920145178935.0851859715012
Trimmed Mean ( 3 / 20 )23.47011111111110.64341109971243936.4776285668691
Trimmed Mean ( 4 / 20 )23.47869230769230.62411561533986437.619139355946
Trimmed Mean ( 5 / 20 )23.467720.60575262954106838.7414248911799
Trimmed Mean ( 6 / 20 )23.45110416666670.58803748029065439.8802881664538
Trimmed Mean ( 7 / 20 )23.42517391304350.57281485429315440.8948436610462
Trimmed Mean ( 8 / 20 )23.39952272727270.55832392778649541.9102989550195
Trimmed Mean ( 9 / 20 )23.3830.54342168716504243.0291991510055
Trimmed Mean ( 10 / 20 )23.356950.52694231785476744.3254398224998
Trimmed Mean ( 11 / 20 )23.32986842105260.51110984888374445.6455074618591
Trimmed Mean ( 12 / 20 )23.30066666666670.49026589157766747.5265913190199
Trimmed Mean ( 13 / 20 )23.30441176470590.48273122454148448.2761640016994
Trimmed Mean ( 14 / 20 )23.314343750.47350367374621249.237936351252
Trimmed Mean ( 15 / 20 )23.32816666666670.4661457102452850.0447953374744
Trimmed Mean ( 16 / 20 )23.325250.46036143100403750.6672549634061
Trimmed Mean ( 17 / 20 )23.32530769230770.45670030492732351.0735540148578
Trimmed Mean ( 18 / 20 )23.320250.45269098479800951.5147214835866
Trimmed Mean ( 19 / 20 )23.3150.44860954976296351.9716979103972
Trimmed Mean ( 20 / 20 )23.315850.44806813553180452.0363939121152
Median23.225
Midrange22.0185
Midmean - Weighted Average at Xnp23.1894516129032
Midmean - Weighted Average at X(n+1)p23.3281666666667
Midmean - Empirical Distribution Function23.1894516129032
Midmean - Empirical Distribution Function - Averaging23.3281666666667
Midmean - Empirical Distribution Function - Interpolation23.3281666666667
Midmean - Closest Observation23.1894516129032
Midmean - True Basic - Statistics Graphics Toolkit23.3281666666667
Midmean - MS Excel (old versions)23.31434375
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')