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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 computationSat, 17 Oct 2009 06:20:40 -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/2009/Oct/17/t12557824578byz9qi8y5dhled.htm/, Retrieved Sun, 05 May 2024 21:07:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47141, Retrieved Sun, 05 May 2024 21:07:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [WS 3 deel 2] [2009-10-17 12:01:58] [023d83ebdf42a2acf423907b4076e8a1]
- RMPD    [Central Tendency] [central tendensy ...] [2009-10-17 12:20:40] [9f6463b67b1eb7bae5c03a796abf0348] [Current]
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Dataseries X:
5560
3922
3759
4138
4634
3996
4308
4143
4429
5219
4929
5755
5592
4163
4962
5208
4755
4491
5732
5731
5040
6102
4904
5369
5578
4619
4731
5011
5299
4146
4625
4736
4219
5116
4205
4121
5103
4300
4578
3809
5526
4247
3830
4394
4826
4409
4569
4106
4794
3914
3793
4405
4022
4100
4788
3163
3585
3903
4178
3863




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47141&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47141&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4590.8666666666782.183061703036655.8614703751909
Geometric Mean4547.98818579046
Harmonic Mean4505.62289151181
Quadratic Mean4634.06366306434
Winsorized Mean ( 1 / 20 )4592.1166666666778.750679637159358.3120893410021
Winsorized Mean ( 2 / 20 )4597.1577.397757690260259.3964235811254
Winsorized Mean ( 3 / 20 )4598.877.078684575044559.6637063197746
Winsorized Mean ( 4 / 20 )4590.674.681437199259261.4690902071384
Winsorized Mean ( 5 / 20 )4591.1833333333374.109658754548561.9512140588766
Winsorized Mean ( 6 / 20 )4592.6833333333373.13847438913362.7943551146278
Winsorized Mean ( 7 / 20 )4593.3833333333371.478522283510364.2624271821719
Winsorized Mean ( 8 / 20 )4573.9166666666766.802848021371668.4688872127634
Winsorized Mean ( 9 / 20 )4564.6166666666764.528560188785170.7379283423092
Winsorized Mean ( 10 / 20 )4563.6166666666759.973968419200676.093291588916
Winsorized Mean ( 11 / 20 )4566.3666666666758.844758737589677.6002275245919
Winsorized Mean ( 12 / 20 )4563.5666666666753.139574061617185.8788717684311
Winsorized Mean ( 13 / 20 )4562.0552.453344483051186.9734817667176
Winsorized Mean ( 14 / 20 )4550.8549.418093080660492.088741517648
Winsorized Mean ( 15 / 20 )4547.8547.588245860378195.5666660490743
Winsorized Mean ( 16 / 20 )4536.1166666666745.2725275051474100.195790176524
Winsorized Mean ( 17 / 20 )4527.6166666666743.6730992695924103.670605988319
Winsorized Mean ( 18 / 20 )4525.2166666666741.7596505417729108.363374883609
Winsorized Mean ( 19 / 20 )4505.2666666666737.3565343565715120.601836981543
Winsorized Mean ( 20 / 20 )4503.634.4898838849231130.57741844033
Trimmed Mean ( 1 / 20 )4589.4310344827676.971782103645759.6248509395677
Trimmed Mean ( 2 / 20 )4586.5535714285774.77024079711861.3419660353075
Trimmed Mean ( 3 / 20 )4580.6666666666772.924939632510662.8134447522335
Trimmed Mean ( 4 / 20 )4573.6923076923170.748090159969864.6475727804192
Trimmed Mean ( 5 / 20 )4568.6268.960336958786666.2499663064348
Trimmed Mean ( 6 / 20 )4562.9791666666766.86067397811668.2460839111518
Trimmed Mean ( 7 / 20 )4556.5217391304364.452991813795770.6952712496916
Trimmed Mean ( 8 / 20 )4549.3409090909161.816759695587173.5939724355314
Trimmed Mean ( 9 / 20 )4544.9523809523859.778986596777476.0292644572431
Trimmed Mean ( 10 / 20 )4541.67557.715742281038778.6904026614602
Trimmed Mean ( 11 / 20 )4538.2105263157956.192239608053580.7622290545858
Trimmed Mean ( 12 / 20 )4533.9444444444454.363516951248183.4004990609856
Trimmed Mean ( 13 / 20 )4529.5882352941253.371634826052184.8688306074355
Trimmed Mean ( 14 / 20 )4524.9062552.046066741455686.9404074755151
Trimmed Mean ( 15 / 20 )4521.250.947897658903288.7416401412575
Trimmed Mean ( 16 / 20 )4517.3928571428649.749327699738590.8030935494754
Trimmed Mean ( 17 / 20 )4514.6923076923148.564968990186292.9619106439585
Trimmed Mean ( 18 / 20 )4512.7916666666747.115913923076695.7806246533695
Trimmed Mean ( 19 / 20 )4510.9090909090945.344134301418399.4816454301123
Trimmed Mean ( 20 / 20 )4511.844.122652017446102.255866175407
Median4530
Midrange4632.5
Midmean - Weighted Average at Xnp4508.29032258064
Midmean - Weighted Average at X(n+1)p4521.2
Midmean - Empirical Distribution Function4508.29032258064
Midmean - Empirical Distribution Function - Averaging4521.2
Midmean - Empirical Distribution Function - Interpolation4521.2
Midmean - Closest Observation4508.29032258064
Midmean - True Basic - Statistics Graphics Toolkit4521.2
Midmean - MS Excel (old versions)4524.90625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4590.86666666667 & 82.1830617030366 & 55.8614703751909 \tabularnewline
Geometric Mean & 4547.98818579046 &  &  \tabularnewline
Harmonic Mean & 4505.62289151181 &  &  \tabularnewline
Quadratic Mean & 4634.06366306434 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 4592.11666666667 & 78.7506796371593 & 58.3120893410021 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 4597.15 & 77.3977576902602 & 59.3964235811254 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 4598.8 & 77.0786845750445 & 59.6637063197746 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 4590.6 & 74.6814371992592 & 61.4690902071384 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 4591.18333333333 & 74.1096587545485 & 61.9512140588766 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 4592.68333333333 & 73.138474389133 & 62.7943551146278 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 4593.38333333333 & 71.4785222835103 & 64.2624271821719 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 4573.91666666667 & 66.8028480213716 & 68.4688872127634 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 4564.61666666667 & 64.5285601887851 & 70.7379283423092 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 4563.61666666667 & 59.9739684192006 & 76.093291588916 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 4566.36666666667 & 58.8447587375896 & 77.6002275245919 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 4563.56666666667 & 53.1395740616171 & 85.8788717684311 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 4562.05 & 52.4533444830511 & 86.9734817667176 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 4550.85 & 49.4180930806604 & 92.088741517648 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 4547.85 & 47.5882458603781 & 95.5666660490743 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 4536.11666666667 & 45.2725275051474 & 100.195790176524 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4527.61666666667 & 43.6730992695924 & 103.670605988319 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 4525.21666666667 & 41.7596505417729 & 108.363374883609 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 4505.26666666667 & 37.3565343565715 & 120.601836981543 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 4503.6 & 34.4898838849231 & 130.57741844033 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 4589.43103448276 & 76.9717821036457 & 59.6248509395677 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 4586.55357142857 & 74.770240797118 & 61.3419660353075 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 4580.66666666667 & 72.9249396325106 & 62.8134447522335 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 4573.69230769231 & 70.7480901599698 & 64.6475727804192 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 4568.62 & 68.9603369587866 & 66.2499663064348 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 4562.97916666667 & 66.860673978116 & 68.2460839111518 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 4556.52173913043 & 64.4529918137957 & 70.6952712496916 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 4549.34090909091 & 61.8167596955871 & 73.5939724355314 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 4544.95238095238 & 59.7789865967774 & 76.0292644572431 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 4541.675 & 57.7157422810387 & 78.6904026614602 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 4538.21052631579 & 56.1922396080535 & 80.7622290545858 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 4533.94444444444 & 54.3635169512481 & 83.4004990609856 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 4529.58823529412 & 53.3716348260521 & 84.8688306074355 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 4524.90625 & 52.0460667414556 & 86.9404074755151 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 4521.2 & 50.9478976589032 & 88.7416401412575 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 4517.39285714286 & 49.7493276997385 & 90.8030935494754 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 4514.69230769231 & 48.5649689901862 & 92.9619106439585 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 4512.79166666667 & 47.1159139230766 & 95.7806246533695 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 4510.90909090909 & 45.3441343014183 & 99.4816454301123 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 4511.8 & 44.122652017446 & 102.255866175407 \tabularnewline
Median & 4530 &  &  \tabularnewline
Midrange & 4632.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4508.29032258064 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4521.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4508.29032258064 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4521.2 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4521.2 &  &  \tabularnewline
Midmean - Closest Observation & 4508.29032258064 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4521.2 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4524.90625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47141&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]4590.86666666667[/C][C]82.1830617030366[/C][C]55.8614703751909[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4547.98818579046[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4505.62289151181[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4634.06366306434[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]4592.11666666667[/C][C]78.7506796371593[/C][C]58.3120893410021[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]4597.15[/C][C]77.3977576902602[/C][C]59.3964235811254[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]4598.8[/C][C]77.0786845750445[/C][C]59.6637063197746[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]4590.6[/C][C]74.6814371992592[/C][C]61.4690902071384[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]4591.18333333333[/C][C]74.1096587545485[/C][C]61.9512140588766[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]4592.68333333333[/C][C]73.138474389133[/C][C]62.7943551146278[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]4593.38333333333[/C][C]71.4785222835103[/C][C]64.2624271821719[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]4573.91666666667[/C][C]66.8028480213716[/C][C]68.4688872127634[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]4564.61666666667[/C][C]64.5285601887851[/C][C]70.7379283423092[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]4563.61666666667[/C][C]59.9739684192006[/C][C]76.093291588916[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]4566.36666666667[/C][C]58.8447587375896[/C][C]77.6002275245919[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]4563.56666666667[/C][C]53.1395740616171[/C][C]85.8788717684311[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]4562.05[/C][C]52.4533444830511[/C][C]86.9734817667176[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]4550.85[/C][C]49.4180930806604[/C][C]92.088741517648[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]4547.85[/C][C]47.5882458603781[/C][C]95.5666660490743[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]4536.11666666667[/C][C]45.2725275051474[/C][C]100.195790176524[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4527.61666666667[/C][C]43.6730992695924[/C][C]103.670605988319[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]4525.21666666667[/C][C]41.7596505417729[/C][C]108.363374883609[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]4505.26666666667[/C][C]37.3565343565715[/C][C]120.601836981543[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]4503.6[/C][C]34.4898838849231[/C][C]130.57741844033[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]4589.43103448276[/C][C]76.9717821036457[/C][C]59.6248509395677[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]4586.55357142857[/C][C]74.770240797118[/C][C]61.3419660353075[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]4580.66666666667[/C][C]72.9249396325106[/C][C]62.8134447522335[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]4573.69230769231[/C][C]70.7480901599698[/C][C]64.6475727804192[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]4568.62[/C][C]68.9603369587866[/C][C]66.2499663064348[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]4562.97916666667[/C][C]66.860673978116[/C][C]68.2460839111518[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]4556.52173913043[/C][C]64.4529918137957[/C][C]70.6952712496916[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]4549.34090909091[/C][C]61.8167596955871[/C][C]73.5939724355314[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]4544.95238095238[/C][C]59.7789865967774[/C][C]76.0292644572431[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]4541.675[/C][C]57.7157422810387[/C][C]78.6904026614602[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]4538.21052631579[/C][C]56.1922396080535[/C][C]80.7622290545858[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]4533.94444444444[/C][C]54.3635169512481[/C][C]83.4004990609856[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]4529.58823529412[/C][C]53.3716348260521[/C][C]84.8688306074355[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]4524.90625[/C][C]52.0460667414556[/C][C]86.9404074755151[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]4521.2[/C][C]50.9478976589032[/C][C]88.7416401412575[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]4517.39285714286[/C][C]49.7493276997385[/C][C]90.8030935494754[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]4514.69230769231[/C][C]48.5649689901862[/C][C]92.9619106439585[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]4512.79166666667[/C][C]47.1159139230766[/C][C]95.7806246533695[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]4510.90909090909[/C][C]45.3441343014183[/C][C]99.4816454301123[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]4511.8[/C][C]44.122652017446[/C][C]102.255866175407[/C][/ROW]
[ROW][C]Median[/C][C]4530[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4632.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4508.29032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4521.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4508.29032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4521.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4521.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4508.29032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4521.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4524.90625[/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=47141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47141&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 Mean4590.8666666666782.183061703036655.8614703751909
Geometric Mean4547.98818579046
Harmonic Mean4505.62289151181
Quadratic Mean4634.06366306434
Winsorized Mean ( 1 / 20 )4592.1166666666778.750679637159358.3120893410021
Winsorized Mean ( 2 / 20 )4597.1577.397757690260259.3964235811254
Winsorized Mean ( 3 / 20 )4598.877.078684575044559.6637063197746
Winsorized Mean ( 4 / 20 )4590.674.681437199259261.4690902071384
Winsorized Mean ( 5 / 20 )4591.1833333333374.109658754548561.9512140588766
Winsorized Mean ( 6 / 20 )4592.6833333333373.13847438913362.7943551146278
Winsorized Mean ( 7 / 20 )4593.3833333333371.478522283510364.2624271821719
Winsorized Mean ( 8 / 20 )4573.9166666666766.802848021371668.4688872127634
Winsorized Mean ( 9 / 20 )4564.6166666666764.528560188785170.7379283423092
Winsorized Mean ( 10 / 20 )4563.6166666666759.973968419200676.093291588916
Winsorized Mean ( 11 / 20 )4566.3666666666758.844758737589677.6002275245919
Winsorized Mean ( 12 / 20 )4563.5666666666753.139574061617185.8788717684311
Winsorized Mean ( 13 / 20 )4562.0552.453344483051186.9734817667176
Winsorized Mean ( 14 / 20 )4550.8549.418093080660492.088741517648
Winsorized Mean ( 15 / 20 )4547.8547.588245860378195.5666660490743
Winsorized Mean ( 16 / 20 )4536.1166666666745.2725275051474100.195790176524
Winsorized Mean ( 17 / 20 )4527.6166666666743.6730992695924103.670605988319
Winsorized Mean ( 18 / 20 )4525.2166666666741.7596505417729108.363374883609
Winsorized Mean ( 19 / 20 )4505.2666666666737.3565343565715120.601836981543
Winsorized Mean ( 20 / 20 )4503.634.4898838849231130.57741844033
Trimmed Mean ( 1 / 20 )4589.4310344827676.971782103645759.6248509395677
Trimmed Mean ( 2 / 20 )4586.5535714285774.77024079711861.3419660353075
Trimmed Mean ( 3 / 20 )4580.6666666666772.924939632510662.8134447522335
Trimmed Mean ( 4 / 20 )4573.6923076923170.748090159969864.6475727804192
Trimmed Mean ( 5 / 20 )4568.6268.960336958786666.2499663064348
Trimmed Mean ( 6 / 20 )4562.9791666666766.86067397811668.2460839111518
Trimmed Mean ( 7 / 20 )4556.5217391304364.452991813795770.6952712496916
Trimmed Mean ( 8 / 20 )4549.3409090909161.816759695587173.5939724355314
Trimmed Mean ( 9 / 20 )4544.9523809523859.778986596777476.0292644572431
Trimmed Mean ( 10 / 20 )4541.67557.715742281038778.6904026614602
Trimmed Mean ( 11 / 20 )4538.2105263157956.192239608053580.7622290545858
Trimmed Mean ( 12 / 20 )4533.9444444444454.363516951248183.4004990609856
Trimmed Mean ( 13 / 20 )4529.5882352941253.371634826052184.8688306074355
Trimmed Mean ( 14 / 20 )4524.9062552.046066741455686.9404074755151
Trimmed Mean ( 15 / 20 )4521.250.947897658903288.7416401412575
Trimmed Mean ( 16 / 20 )4517.3928571428649.749327699738590.8030935494754
Trimmed Mean ( 17 / 20 )4514.6923076923148.564968990186292.9619106439585
Trimmed Mean ( 18 / 20 )4512.7916666666747.115913923076695.7806246533695
Trimmed Mean ( 19 / 20 )4510.9090909090945.344134301418399.4816454301123
Trimmed Mean ( 20 / 20 )4511.844.122652017446102.255866175407
Median4530
Midrange4632.5
Midmean - Weighted Average at Xnp4508.29032258064
Midmean - Weighted Average at X(n+1)p4521.2
Midmean - Empirical Distribution Function4508.29032258064
Midmean - Empirical Distribution Function - Averaging4521.2
Midmean - Empirical Distribution Function - Interpolation4521.2
Midmean - Closest Observation4508.29032258064
Midmean - True Basic - Statistics Graphics Toolkit4521.2
Midmean - MS Excel (old versions)4524.90625
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')