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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 computationMon, 20 Oct 2008 09:56:26 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t122451825482sfclv3iwhkdll.htm/, Retrieved Fri, 17 May 2024 08:55:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=17548, Retrieved Fri, 17 May 2024 08:55:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Pearson Correlation] [Q3 Clothing produ...] [2007-10-20 14:22:11] [b731da8b544846036771bbf9bf2f34ce]
- RMPD  [Harrell-Davis Quantiles] [Compute the 95% C...] [2008-10-19 19:58:52] [988ab43f527fc78aae41c84649095267]
- RMPD      [Central Tendency] [Frankrijk/Uitvoer ] [2008-10-20 15:56:26] [5d823194959040fa9b19b8c8302177e6] [Current]
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Dataseries X:
3258.1
3140.1
3627.4
3279.4
3204
3515.6
3146.6
2271.7
3627.9
3553.4
3018.3
3355.4
3242
3311.1
4125.2
3423
3120.3
3863
3240.8
2837.4
3945
3684.1
3659.6
3769.6
3592.7
3754
4507.8
3853.2
3817.2
3958.4
3428.9
3125.7
3977
3983.3
4299.6
4306.9
4259.5
3986
4755.6
3925.6
4206.5
4323.4
3816.1
3410.7
4227.4
4296.9
4351.7
3800
4277
4100.2
4672.5
4189.9
4231.9
4654.9
4298.5
3635.9
4505.1
4910.1
4908.7
4101.4




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' @ 72.249.76.132

\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' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17548&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' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=17548&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17548&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' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3827.8270.010311621455754.6750887311707
Geometric Mean3788.28221698916
Harmonic Mean3746.52857955473
Quadratic Mean3865.40956855372
Winsorized Mean ( 1 / 20 )3837.22567.023474832869757.2519555210848
Winsorized Mean ( 2 / 20 )3838.1516666666764.297222374202659.6938953961192
Winsorized Mean ( 3 / 20 )3839.0966666666762.272220909381561.65022879549
Winsorized Mean ( 4 / 20 )3838.2833333333361.937724335471661.9700412715221
Winsorized Mean ( 5 / 20 )3827.22559.13327313984664.722021913938
Winsorized Mean ( 6 / 20 )3827.60558.953002272805464.9263795300489
Winsorized Mean ( 7 / 20 )3816.40554.412968628292170.1377832566124
Winsorized Mean ( 8 / 20 )3817.5383333333352.870506505470672.2054428008615
Winsorized Mean ( 9 / 20 )3815.2433333333352.439841635650772.7546692425474
Winsorized Mean ( 10 / 20 )3816.7151.752907759679873.7487064055088
Winsorized Mean ( 11 / 20 )3820.4133333333351.01272990936774.8913720187287
Winsorized Mean ( 12 / 20 )3826.4333333333349.836145622892476.7802823735158
Winsorized Mean ( 13 / 20 )3831.7247.490985692380680.6831011009055
Winsorized Mean ( 14 / 20 )3840.5444.692312512781485.9328995093208
Winsorized Mean ( 15 / 20 )3836.71543.107125711961989.0041944720832
Winsorized Mean ( 16 / 20 )3837.0883333333342.665333252358989.934568438445
Winsorized Mean ( 17 / 20 )3855.7316666666737.8732496932307101.806200891069
Winsorized Mean ( 18 / 20 )3862.0916666666735.3892713554767109.131709095474
Winsorized Mean ( 19 / 20 )3854.0483333333330.4000978934332126.777497455555
Winsorized Mean ( 20 / 20 )3857.6816666666727.541843511659140.066211073839
Trimmed Mean ( 1 / 20 )3835.9896551724164.501439119257459.4713809110524
Trimmed Mean ( 2 / 20 )3834.6660714285761.386611144217262.4674664385640
Trimmed Mean ( 3 / 20 )3832.7296296296359.380796307881764.5449348600417
Trimmed Mean ( 4 / 20 )3830.2807692307757.860796442806966.1982033554766
Trimmed Mean ( 5 / 20 )3827.8856.067877230575268.2722476589957
Trimmed Mean ( 6 / 20 )3828.0437554.766197845695469.8979279296615
Trimmed Mean ( 7 / 20 )3828.1391304347853.132465077394972.0489652580312
Trimmed Mean ( 8 / 20 )3830.42552.323579863939173.206478034579
Trimmed Mean ( 9 / 20 )3832.7261904761951.622523541687974.2452311030681
Trimmed Mean ( 10 / 20 )3835.6450.73052244647575.608131259577
Trimmed Mean ( 11 / 20 )3838.6289473684249.647714841843477.3173339316154
Trimmed Mean ( 12 / 20 )3841.3888888888948.314040283712179.508748726691
Trimmed Mean ( 13 / 20 )3843.5882352941246.750841788432282.2143107644568
Trimmed Mean ( 14 / 20 )3845.345.192488849222485.0871482831855
Trimmed Mean ( 15 / 20 )3845.9843.754401919764887.8992702734827
Trimmed Mean ( 16 / 20 )3847.3035714285742.064357809674091.4623156458545
Trimmed Mean ( 17 / 20 )3848.7769230769239.576271565243797.249608688681
Trimmed Mean ( 18 / 20 )3847.7541666666737.5684172877437102.419916633591
Trimmed Mean ( 19 / 20 )3845.5818181818235.2871060642274108.979801607486
Trimmed Mean ( 20 / 20 )3844.24533.7600593001163113.869616336449
Median3835.2
Midrange3590.9
Midmean - Weighted Average at Xnp3831.93870967742
Midmean - Weighted Average at X(n+1)p3845.98
Midmean - Empirical Distribution Function3831.93870967742
Midmean - Empirical Distribution Function - Averaging3845.98
Midmean - Empirical Distribution Function - Interpolation3845.98
Midmean - Closest Observation3831.93870967742
Midmean - True Basic - Statistics Graphics Toolkit3845.98
Midmean - MS Excel (old versions)3845.3
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3827.82 & 70.0103116214557 & 54.6750887311707 \tabularnewline
Geometric Mean & 3788.28221698916 &  &  \tabularnewline
Harmonic Mean & 3746.52857955473 &  &  \tabularnewline
Quadratic Mean & 3865.40956855372 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3837.225 & 67.0234748328697 & 57.2519555210848 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3838.15166666667 & 64.2972223742026 & 59.6938953961192 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3839.09666666667 & 62.2722209093815 & 61.65022879549 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3838.28333333333 & 61.9377243354716 & 61.9700412715221 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3827.225 & 59.133273139846 & 64.722021913938 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3827.605 & 58.9530022728054 & 64.9263795300489 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3816.405 & 54.4129686282921 & 70.1377832566124 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3817.53833333333 & 52.8705065054706 & 72.2054428008615 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3815.24333333333 & 52.4398416356507 & 72.7546692425474 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3816.71 & 51.7529077596798 & 73.7487064055088 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3820.41333333333 & 51.012729909367 & 74.8913720187287 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3826.43333333333 & 49.8361456228924 & 76.7802823735158 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3831.72 & 47.4909856923806 & 80.6831011009055 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3840.54 & 44.6923125127814 & 85.9328995093208 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3836.715 & 43.1071257119619 & 89.0041944720832 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3837.08833333333 & 42.6653332523589 & 89.934568438445 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3855.73166666667 & 37.8732496932307 & 101.806200891069 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3862.09166666667 & 35.3892713554767 & 109.131709095474 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3854.04833333333 & 30.4000978934332 & 126.777497455555 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3857.68166666667 & 27.541843511659 & 140.066211073839 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3835.98965517241 & 64.5014391192574 & 59.4713809110524 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3834.66607142857 & 61.3866111442172 & 62.4674664385640 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3832.72962962963 & 59.3807963078817 & 64.5449348600417 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3830.28076923077 & 57.8607964428069 & 66.1982033554766 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3827.88 & 56.0678772305752 & 68.2722476589957 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3828.04375 & 54.7661978456954 & 69.8979279296615 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3828.13913043478 & 53.1324650773949 & 72.0489652580312 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3830.425 & 52.3235798639391 & 73.206478034579 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3832.72619047619 & 51.6225235416879 & 74.2452311030681 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3835.64 & 50.730522446475 & 75.608131259577 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3838.62894736842 & 49.6477148418434 & 77.3173339316154 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3841.38888888889 & 48.3140402837121 & 79.508748726691 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3843.58823529412 & 46.7508417884322 & 82.2143107644568 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3845.3 & 45.1924888492224 & 85.0871482831855 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3845.98 & 43.7544019197648 & 87.8992702734827 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3847.30357142857 & 42.0643578096740 & 91.4623156458545 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3848.77692307692 & 39.5762715652437 & 97.249608688681 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3847.75416666667 & 37.5684172877437 & 102.419916633591 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3845.58181818182 & 35.2871060642274 & 108.979801607486 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3844.245 & 33.7600593001163 & 113.869616336449 \tabularnewline
Median & 3835.2 &  &  \tabularnewline
Midrange & 3590.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3831.93870967742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3845.98 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3831.93870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3845.98 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3845.98 &  &  \tabularnewline
Midmean - Closest Observation & 3831.93870967742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3845.98 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3845.3 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=17548&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]3827.82[/C][C]70.0103116214557[/C][C]54.6750887311707[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]3788.28221698916[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]3746.52857955473[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3865.40956855372[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3837.225[/C][C]67.0234748328697[/C][C]57.2519555210848[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3838.15166666667[/C][C]64.2972223742026[/C][C]59.6938953961192[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3839.09666666667[/C][C]62.2722209093815[/C][C]61.65022879549[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3838.28333333333[/C][C]61.9377243354716[/C][C]61.9700412715221[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3827.225[/C][C]59.133273139846[/C][C]64.722021913938[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3827.605[/C][C]58.9530022728054[/C][C]64.9263795300489[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3816.405[/C][C]54.4129686282921[/C][C]70.1377832566124[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3817.53833333333[/C][C]52.8705065054706[/C][C]72.2054428008615[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3815.24333333333[/C][C]52.4398416356507[/C][C]72.7546692425474[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3816.71[/C][C]51.7529077596798[/C][C]73.7487064055088[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3820.41333333333[/C][C]51.012729909367[/C][C]74.8913720187287[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3826.43333333333[/C][C]49.8361456228924[/C][C]76.7802823735158[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3831.72[/C][C]47.4909856923806[/C][C]80.6831011009055[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3840.54[/C][C]44.6923125127814[/C][C]85.9328995093208[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3836.715[/C][C]43.1071257119619[/C][C]89.0041944720832[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3837.08833333333[/C][C]42.6653332523589[/C][C]89.934568438445[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3855.73166666667[/C][C]37.8732496932307[/C][C]101.806200891069[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3862.09166666667[/C][C]35.3892713554767[/C][C]109.131709095474[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3854.04833333333[/C][C]30.4000978934332[/C][C]126.777497455555[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3857.68166666667[/C][C]27.541843511659[/C][C]140.066211073839[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3835.98965517241[/C][C]64.5014391192574[/C][C]59.4713809110524[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3834.66607142857[/C][C]61.3866111442172[/C][C]62.4674664385640[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3832.72962962963[/C][C]59.3807963078817[/C][C]64.5449348600417[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3830.28076923077[/C][C]57.8607964428069[/C][C]66.1982033554766[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3827.88[/C][C]56.0678772305752[/C][C]68.2722476589957[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3828.04375[/C][C]54.7661978456954[/C][C]69.8979279296615[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3828.13913043478[/C][C]53.1324650773949[/C][C]72.0489652580312[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3830.425[/C][C]52.3235798639391[/C][C]73.206478034579[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3832.72619047619[/C][C]51.6225235416879[/C][C]74.2452311030681[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3835.64[/C][C]50.730522446475[/C][C]75.608131259577[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3838.62894736842[/C][C]49.6477148418434[/C][C]77.3173339316154[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3841.38888888889[/C][C]48.3140402837121[/C][C]79.508748726691[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3843.58823529412[/C][C]46.7508417884322[/C][C]82.2143107644568[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3845.3[/C][C]45.1924888492224[/C][C]85.0871482831855[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3845.98[/C][C]43.7544019197648[/C][C]87.8992702734827[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3847.30357142857[/C][C]42.0643578096740[/C][C]91.4623156458545[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3848.77692307692[/C][C]39.5762715652437[/C][C]97.249608688681[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3847.75416666667[/C][C]37.5684172877437[/C][C]102.419916633591[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3845.58181818182[/C][C]35.2871060642274[/C][C]108.979801607486[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3844.245[/C][C]33.7600593001163[/C][C]113.869616336449[/C][/ROW]
[ROW][C]Median[/C][C]3835.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]3590.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3831.93870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3845.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3831.93870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3845.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3845.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3831.93870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3845.98[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3845.3[/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=17548&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=17548&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 Mean3827.8270.010311621455754.6750887311707
Geometric Mean3788.28221698916
Harmonic Mean3746.52857955473
Quadratic Mean3865.40956855372
Winsorized Mean ( 1 / 20 )3837.22567.023474832869757.2519555210848
Winsorized Mean ( 2 / 20 )3838.1516666666764.297222374202659.6938953961192
Winsorized Mean ( 3 / 20 )3839.0966666666762.272220909381561.65022879549
Winsorized Mean ( 4 / 20 )3838.2833333333361.937724335471661.9700412715221
Winsorized Mean ( 5 / 20 )3827.22559.13327313984664.722021913938
Winsorized Mean ( 6 / 20 )3827.60558.953002272805464.9263795300489
Winsorized Mean ( 7 / 20 )3816.40554.412968628292170.1377832566124
Winsorized Mean ( 8 / 20 )3817.5383333333352.870506505470672.2054428008615
Winsorized Mean ( 9 / 20 )3815.2433333333352.439841635650772.7546692425474
Winsorized Mean ( 10 / 20 )3816.7151.752907759679873.7487064055088
Winsorized Mean ( 11 / 20 )3820.4133333333351.01272990936774.8913720187287
Winsorized Mean ( 12 / 20 )3826.4333333333349.836145622892476.7802823735158
Winsorized Mean ( 13 / 20 )3831.7247.490985692380680.6831011009055
Winsorized Mean ( 14 / 20 )3840.5444.692312512781485.9328995093208
Winsorized Mean ( 15 / 20 )3836.71543.107125711961989.0041944720832
Winsorized Mean ( 16 / 20 )3837.0883333333342.665333252358989.934568438445
Winsorized Mean ( 17 / 20 )3855.7316666666737.8732496932307101.806200891069
Winsorized Mean ( 18 / 20 )3862.0916666666735.3892713554767109.131709095474
Winsorized Mean ( 19 / 20 )3854.0483333333330.4000978934332126.777497455555
Winsorized Mean ( 20 / 20 )3857.6816666666727.541843511659140.066211073839
Trimmed Mean ( 1 / 20 )3835.9896551724164.501439119257459.4713809110524
Trimmed Mean ( 2 / 20 )3834.6660714285761.386611144217262.4674664385640
Trimmed Mean ( 3 / 20 )3832.7296296296359.380796307881764.5449348600417
Trimmed Mean ( 4 / 20 )3830.2807692307757.860796442806966.1982033554766
Trimmed Mean ( 5 / 20 )3827.8856.067877230575268.2722476589957
Trimmed Mean ( 6 / 20 )3828.0437554.766197845695469.8979279296615
Trimmed Mean ( 7 / 20 )3828.1391304347853.132465077394972.0489652580312
Trimmed Mean ( 8 / 20 )3830.42552.323579863939173.206478034579
Trimmed Mean ( 9 / 20 )3832.7261904761951.622523541687974.2452311030681
Trimmed Mean ( 10 / 20 )3835.6450.73052244647575.608131259577
Trimmed Mean ( 11 / 20 )3838.6289473684249.647714841843477.3173339316154
Trimmed Mean ( 12 / 20 )3841.3888888888948.314040283712179.508748726691
Trimmed Mean ( 13 / 20 )3843.5882352941246.750841788432282.2143107644568
Trimmed Mean ( 14 / 20 )3845.345.192488849222485.0871482831855
Trimmed Mean ( 15 / 20 )3845.9843.754401919764887.8992702734827
Trimmed Mean ( 16 / 20 )3847.3035714285742.064357809674091.4623156458545
Trimmed Mean ( 17 / 20 )3848.7769230769239.576271565243797.249608688681
Trimmed Mean ( 18 / 20 )3847.7541666666737.5684172877437102.419916633591
Trimmed Mean ( 19 / 20 )3845.5818181818235.2871060642274108.979801607486
Trimmed Mean ( 20 / 20 )3844.24533.7600593001163113.869616336449
Median3835.2
Midrange3590.9
Midmean - Weighted Average at Xnp3831.93870967742
Midmean - Weighted Average at X(n+1)p3845.98
Midmean - Empirical Distribution Function3831.93870967742
Midmean - Empirical Distribution Function - Averaging3845.98
Midmean - Empirical Distribution Function - Interpolation3845.98
Midmean - Closest Observation3831.93870967742
Midmean - True Basic - Statistics Graphics Toolkit3845.98
Midmean - MS Excel (old versions)3845.3
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')