Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 28 Jul 2009 05:03:28 -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/Jul/28/t1248779047j1ua4d9onju3twy.htm/, Retrieved Sat, 18 May 2024 14:21:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42412, Retrieved Sat, 18 May 2024 14:21:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact227
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [Decielen Aantal O...] [2009-07-28 08:12:34] [3277f4fd1367f73c9bc433502ffbb1d3]
- RMPD  [Mean versus Median] [] [2009-07-28 10:02:32] [3277f4fd1367f73c9bc433502ffbb1d3]
- RM D      [Central Tendency] [] [2009-07-28 11:03:28] [b5b38cb8cda4101c154c09cb859ab89a] [Current]
- RM          [Mean versus Median] [] [2009-07-28 11:20:43] [3277f4fd1367f73c9bc433502ffbb1d3]
-               [Mean versus Median] [] [2009-07-28 11:23:03] [3277f4fd1367f73c9bc433502ffbb1d3]
-    D        [Central Tendency] [] [2009-08-19 18:13:42] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
6430
5124
4836
4629
4597
4490
4517
4560
4135
4559
4739
4886
5605
4616
4997
4607
4882
4555
4462
4476
4277
4369
4492
5183
6039
4923
4953
4892
4614
4363
4675
4556
4217
4664
4601
5428
5607
4869
5174
5031
4671
4491
4504
4615
4582
4800
4775
5791
5818
4714
4915
4598
4407
4383
4412
4274
4236
4637
4534
5271
5467
5204
5752
4724
4623
4451
4138
4140
4169
4603
4434
5185




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42412&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42412&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42412&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4777.0416666666755.649481609479185.8416202362784
Geometric Mean4755.59859075243
Harmonic Mean4735.58504480271
Quadratic Mean4800.00046730322
Winsorized Mean ( 1 / 24 )4771.6527777777853.598056190820689.0266012780327
Winsorized Mean ( 2 / 24 )4765.5694444444451.683564654488792.2066710433557
Winsorized Mean ( 3 / 24 )4765.6527777777851.161192224924593.1497600139206
Winsorized Mean ( 4 / 24 )4766.1527777777850.130411539111595.075077810986
Winsorized Mean ( 5 / 24 )4757.4027777777847.2530921549181100.679184383971
Winsorized Mean ( 6 / 24 )4760.4027777777846.7325225283544101.864879536290
Winsorized Mean ( 7 / 24 )4747.2777777777843.4096034382482109.360081681717
Winsorized Mean ( 8 / 24 )4752.541.0307911402674115.827647187040
Winsorized Mean ( 9 / 24 )4733.62536.6102555685347129.297786275723
Winsorized Mean ( 10 / 24 )4726.2638888888934.4656277543382137.129778182961
Winsorized Mean ( 11 / 24 )4727.0277777777833.3971453301907141.539875071436
Winsorized Mean ( 12 / 24 )4727.5277777777833.2207957819708142.306277333171
Winsorized Mean ( 13 / 24 )4729.87532.3855812884567146.048791215796
Winsorized Mean ( 14 / 24 )4723.4583333333330.1115163754207156.86550867923
Winsorized Mean ( 15 / 24 )4706.37526.3084169093061178.892368029001
Winsorized Mean ( 16 / 24 )4701.9305555555624.608517985225191.069228889712
Winsorized Mean ( 17 / 24 )4694.8472222222222.4627378786640209.006010201525
Winsorized Mean ( 18 / 24 )4687.5972222222221.2373469622411220.724237851203
Winsorized Mean ( 19 / 24 )4685.7520.8748201945158224.468999317706
Winsorized Mean ( 20 / 24 )4682.6944444444419.4630246015065240.594385524334
Winsorized Mean ( 21 / 24 )4684.7361111111118.7133365389294250.34210769231
Winsorized Mean ( 22 / 24 )4688.7083333333317.8831347697783262.186042530812
Winsorized Mean ( 23 / 24 )4691.2638888888916.4503211085901285.177648382753
Winsorized Mean ( 24 / 24 )4680.5972222222214.7572117024496317.173549895287
Trimmed Mean ( 1 / 24 )4762.651.221285042527792.9808769156366
Trimmed Mean ( 2 / 24 )4753.0147058823548.340582259345598.3234889555654
Trimmed Mean ( 3 / 24 )4746.1666666666746.1411616537425102.861880727741
Trimmed Mean ( 4 / 24 )4738.85937543.7151894799009108.403038654992
Trimmed Mean ( 5 / 24 )4730.9354838709741.1448401304978114.982473351847
Trimmed Mean ( 6 / 24 )4724.5833333333339.0120529808132121.10573457021
Trimmed Mean ( 7 / 24 )4717.1724137931036.5078958545736129.209649128605
Trimmed Mean ( 8 / 24 )4711.6428571428634.4182584111888136.893703360981
Trimmed Mean ( 9 / 24 )4704.8333333333332.4376276187793145.042460830568
Trimmed Mean ( 10 / 24 )4700.4038461538531.1726963575762150.785924715539
Trimmed Mean ( 11 / 24 )4696.6830.115416622842155.956002828055
Trimmed Mean ( 12 / 24 )4692.5416666666729.0115371757961161.747433037832
Trimmed Mean ( 13 / 24 )4687.9782608695727.6153267170831169.760014389746
Trimmed Mean ( 14 / 24 )4682.7045454545525.9761758539066180.269204050307
Trimmed Mean ( 15 / 24 )4677.7142857142924.4233681657577191.526175012691
Trimmed Mean ( 16 / 24 )4674.27523.4159431633827199.619334885879
Trimmed Mean ( 17 / 24 )467122.4952342036634207.643981730109
Trimmed Mean ( 18 / 24 )4668.1944444444421.8020975925626214.116757556250
Trimmed Mean ( 19 / 24 )4665.9117647058821.1609723689398220.496094572409
Trimmed Mean ( 20 / 24 )4663.562520.3286970162633229.407841352010
Trimmed Mean ( 21 / 24 )4661.2666666666719.5391698157348238.560118501707
Trimmed Mean ( 22 / 24 )4658.3928571428618.5662932969294250.905917656342
Trimmed Mean ( 23 / 24 )4654.5769230769217.3092392471076268.907076540335
Trimmed Mean ( 24 / 24 )4649.7916666666715.8287917781045293.75531195619
Median4619.5
Midrange5282.5
Midmean - Weighted Average at Xnp4663.37837837838
Midmean - Weighted Average at X(n+1)p4668.19444444444
Midmean - Empirical Distribution Function4663.37837837838
Midmean - Empirical Distribution Function - Averaging4668.19444444444
Midmean - Empirical Distribution Function - Interpolation4668.19444444444
Midmean - Closest Observation4663.37837837838
Midmean - True Basic - Statistics Graphics Toolkit4668.19444444444
Midmean - MS Excel (old versions)4671
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4777.04166666667 & 55.6494816094791 & 85.8416202362784 \tabularnewline
Geometric Mean & 4755.59859075243 &  &  \tabularnewline
Harmonic Mean & 4735.58504480271 &  &  \tabularnewline
Quadratic Mean & 4800.00046730322 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 4771.65277777778 & 53.5980561908206 & 89.0266012780327 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 4765.56944444444 & 51.6835646544887 & 92.2066710433557 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 4765.65277777778 & 51.1611922249245 & 93.1497600139206 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 4766.15277777778 & 50.1304115391115 & 95.075077810986 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 4757.40277777778 & 47.2530921549181 & 100.679184383971 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 4760.40277777778 & 46.7325225283544 & 101.864879536290 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 4747.27777777778 & 43.4096034382482 & 109.360081681717 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 4752.5 & 41.0307911402674 & 115.827647187040 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 4733.625 & 36.6102555685347 & 129.297786275723 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 4726.26388888889 & 34.4656277543382 & 137.129778182961 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 4727.02777777778 & 33.3971453301907 & 141.539875071436 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 4727.52777777778 & 33.2207957819708 & 142.306277333171 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 4729.875 & 32.3855812884567 & 146.048791215796 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 4723.45833333333 & 30.1115163754207 & 156.86550867923 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 4706.375 & 26.3084169093061 & 178.892368029001 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 4701.93055555556 & 24.608517985225 & 191.069228889712 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 4694.84722222222 & 22.4627378786640 & 209.006010201525 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 4687.59722222222 & 21.2373469622411 & 220.724237851203 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 4685.75 & 20.8748201945158 & 224.468999317706 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 4682.69444444444 & 19.4630246015065 & 240.594385524334 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 4684.73611111111 & 18.7133365389294 & 250.34210769231 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 4688.70833333333 & 17.8831347697783 & 262.186042530812 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 4691.26388888889 & 16.4503211085901 & 285.177648382753 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 4680.59722222222 & 14.7572117024496 & 317.173549895287 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 4762.6 & 51.2212850425277 & 92.9808769156366 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 4753.01470588235 & 48.3405822593455 & 98.3234889555654 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 4746.16666666667 & 46.1411616537425 & 102.861880727741 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 4738.859375 & 43.7151894799009 & 108.403038654992 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 4730.93548387097 & 41.1448401304978 & 114.982473351847 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 4724.58333333333 & 39.0120529808132 & 121.10573457021 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 4717.17241379310 & 36.5078958545736 & 129.209649128605 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 4711.64285714286 & 34.4182584111888 & 136.893703360981 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 4704.83333333333 & 32.4376276187793 & 145.042460830568 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 4700.40384615385 & 31.1726963575762 & 150.785924715539 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 4696.68 & 30.115416622842 & 155.956002828055 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 4692.54166666667 & 29.0115371757961 & 161.747433037832 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 4687.97826086957 & 27.6153267170831 & 169.760014389746 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 4682.70454545455 & 25.9761758539066 & 180.269204050307 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 4677.71428571429 & 24.4233681657577 & 191.526175012691 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 4674.275 & 23.4159431633827 & 199.619334885879 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 4671 & 22.4952342036634 & 207.643981730109 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 4668.19444444444 & 21.8020975925626 & 214.116757556250 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 4665.91176470588 & 21.1609723689398 & 220.496094572409 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 4663.5625 & 20.3286970162633 & 229.407841352010 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 4661.26666666667 & 19.5391698157348 & 238.560118501707 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 4658.39285714286 & 18.5662932969294 & 250.905917656342 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 4654.57692307692 & 17.3092392471076 & 268.907076540335 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 4649.79166666667 & 15.8287917781045 & 293.75531195619 \tabularnewline
Median & 4619.5 &  &  \tabularnewline
Midrange & 5282.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4663.37837837838 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4668.19444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4663.37837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4668.19444444444 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4668.19444444444 &  &  \tabularnewline
Midmean - Closest Observation & 4663.37837837838 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4668.19444444444 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4671 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42412&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]4777.04166666667[/C][C]55.6494816094791[/C][C]85.8416202362784[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4755.59859075243[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4735.58504480271[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4800.00046730322[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]4771.65277777778[/C][C]53.5980561908206[/C][C]89.0266012780327[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]4765.56944444444[/C][C]51.6835646544887[/C][C]92.2066710433557[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]4765.65277777778[/C][C]51.1611922249245[/C][C]93.1497600139206[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]4766.15277777778[/C][C]50.1304115391115[/C][C]95.075077810986[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]4757.40277777778[/C][C]47.2530921549181[/C][C]100.679184383971[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]4760.40277777778[/C][C]46.7325225283544[/C][C]101.864879536290[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]4747.27777777778[/C][C]43.4096034382482[/C][C]109.360081681717[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]4752.5[/C][C]41.0307911402674[/C][C]115.827647187040[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]4733.625[/C][C]36.6102555685347[/C][C]129.297786275723[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]4726.26388888889[/C][C]34.4656277543382[/C][C]137.129778182961[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]4727.02777777778[/C][C]33.3971453301907[/C][C]141.539875071436[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]4727.52777777778[/C][C]33.2207957819708[/C][C]142.306277333171[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]4729.875[/C][C]32.3855812884567[/C][C]146.048791215796[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]4723.45833333333[/C][C]30.1115163754207[/C][C]156.86550867923[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]4706.375[/C][C]26.3084169093061[/C][C]178.892368029001[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]4701.93055555556[/C][C]24.608517985225[/C][C]191.069228889712[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]4694.84722222222[/C][C]22.4627378786640[/C][C]209.006010201525[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]4687.59722222222[/C][C]21.2373469622411[/C][C]220.724237851203[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]4685.75[/C][C]20.8748201945158[/C][C]224.468999317706[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]4682.69444444444[/C][C]19.4630246015065[/C][C]240.594385524334[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]4684.73611111111[/C][C]18.7133365389294[/C][C]250.34210769231[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]4688.70833333333[/C][C]17.8831347697783[/C][C]262.186042530812[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]4691.26388888889[/C][C]16.4503211085901[/C][C]285.177648382753[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]4680.59722222222[/C][C]14.7572117024496[/C][C]317.173549895287[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]4762.6[/C][C]51.2212850425277[/C][C]92.9808769156366[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]4753.01470588235[/C][C]48.3405822593455[/C][C]98.3234889555654[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]4746.16666666667[/C][C]46.1411616537425[/C][C]102.861880727741[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]4738.859375[/C][C]43.7151894799009[/C][C]108.403038654992[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]4730.93548387097[/C][C]41.1448401304978[/C][C]114.982473351847[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]4724.58333333333[/C][C]39.0120529808132[/C][C]121.10573457021[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]4717.17241379310[/C][C]36.5078958545736[/C][C]129.209649128605[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]4711.64285714286[/C][C]34.4182584111888[/C][C]136.893703360981[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]4704.83333333333[/C][C]32.4376276187793[/C][C]145.042460830568[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]4700.40384615385[/C][C]31.1726963575762[/C][C]150.785924715539[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]4696.68[/C][C]30.115416622842[/C][C]155.956002828055[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]4692.54166666667[/C][C]29.0115371757961[/C][C]161.747433037832[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]4687.97826086957[/C][C]27.6153267170831[/C][C]169.760014389746[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]4682.70454545455[/C][C]25.9761758539066[/C][C]180.269204050307[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]4677.71428571429[/C][C]24.4233681657577[/C][C]191.526175012691[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]4674.275[/C][C]23.4159431633827[/C][C]199.619334885879[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]4671[/C][C]22.4952342036634[/C][C]207.643981730109[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]4668.19444444444[/C][C]21.8020975925626[/C][C]214.116757556250[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]4665.91176470588[/C][C]21.1609723689398[/C][C]220.496094572409[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]4663.5625[/C][C]20.3286970162633[/C][C]229.407841352010[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]4661.26666666667[/C][C]19.5391698157348[/C][C]238.560118501707[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]4658.39285714286[/C][C]18.5662932969294[/C][C]250.905917656342[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]4654.57692307692[/C][C]17.3092392471076[/C][C]268.907076540335[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]4649.79166666667[/C][C]15.8287917781045[/C][C]293.75531195619[/C][/ROW]
[ROW][C]Median[/C][C]4619.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]5282.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4663.37837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4668.19444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4663.37837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4668.19444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4668.19444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4663.37837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4668.19444444444[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4671[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42412&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42412&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 Mean4777.0416666666755.649481609479185.8416202362784
Geometric Mean4755.59859075243
Harmonic Mean4735.58504480271
Quadratic Mean4800.00046730322
Winsorized Mean ( 1 / 24 )4771.6527777777853.598056190820689.0266012780327
Winsorized Mean ( 2 / 24 )4765.5694444444451.683564654488792.2066710433557
Winsorized Mean ( 3 / 24 )4765.6527777777851.161192224924593.1497600139206
Winsorized Mean ( 4 / 24 )4766.1527777777850.130411539111595.075077810986
Winsorized Mean ( 5 / 24 )4757.4027777777847.2530921549181100.679184383971
Winsorized Mean ( 6 / 24 )4760.4027777777846.7325225283544101.864879536290
Winsorized Mean ( 7 / 24 )4747.2777777777843.4096034382482109.360081681717
Winsorized Mean ( 8 / 24 )4752.541.0307911402674115.827647187040
Winsorized Mean ( 9 / 24 )4733.62536.6102555685347129.297786275723
Winsorized Mean ( 10 / 24 )4726.2638888888934.4656277543382137.129778182961
Winsorized Mean ( 11 / 24 )4727.0277777777833.3971453301907141.539875071436
Winsorized Mean ( 12 / 24 )4727.5277777777833.2207957819708142.306277333171
Winsorized Mean ( 13 / 24 )4729.87532.3855812884567146.048791215796
Winsorized Mean ( 14 / 24 )4723.4583333333330.1115163754207156.86550867923
Winsorized Mean ( 15 / 24 )4706.37526.3084169093061178.892368029001
Winsorized Mean ( 16 / 24 )4701.9305555555624.608517985225191.069228889712
Winsorized Mean ( 17 / 24 )4694.8472222222222.4627378786640209.006010201525
Winsorized Mean ( 18 / 24 )4687.5972222222221.2373469622411220.724237851203
Winsorized Mean ( 19 / 24 )4685.7520.8748201945158224.468999317706
Winsorized Mean ( 20 / 24 )4682.6944444444419.4630246015065240.594385524334
Winsorized Mean ( 21 / 24 )4684.7361111111118.7133365389294250.34210769231
Winsorized Mean ( 22 / 24 )4688.7083333333317.8831347697783262.186042530812
Winsorized Mean ( 23 / 24 )4691.2638888888916.4503211085901285.177648382753
Winsorized Mean ( 24 / 24 )4680.5972222222214.7572117024496317.173549895287
Trimmed Mean ( 1 / 24 )4762.651.221285042527792.9808769156366
Trimmed Mean ( 2 / 24 )4753.0147058823548.340582259345598.3234889555654
Trimmed Mean ( 3 / 24 )4746.1666666666746.1411616537425102.861880727741
Trimmed Mean ( 4 / 24 )4738.85937543.7151894799009108.403038654992
Trimmed Mean ( 5 / 24 )4730.9354838709741.1448401304978114.982473351847
Trimmed Mean ( 6 / 24 )4724.5833333333339.0120529808132121.10573457021
Trimmed Mean ( 7 / 24 )4717.1724137931036.5078958545736129.209649128605
Trimmed Mean ( 8 / 24 )4711.6428571428634.4182584111888136.893703360981
Trimmed Mean ( 9 / 24 )4704.8333333333332.4376276187793145.042460830568
Trimmed Mean ( 10 / 24 )4700.4038461538531.1726963575762150.785924715539
Trimmed Mean ( 11 / 24 )4696.6830.115416622842155.956002828055
Trimmed Mean ( 12 / 24 )4692.5416666666729.0115371757961161.747433037832
Trimmed Mean ( 13 / 24 )4687.9782608695727.6153267170831169.760014389746
Trimmed Mean ( 14 / 24 )4682.7045454545525.9761758539066180.269204050307
Trimmed Mean ( 15 / 24 )4677.7142857142924.4233681657577191.526175012691
Trimmed Mean ( 16 / 24 )4674.27523.4159431633827199.619334885879
Trimmed Mean ( 17 / 24 )467122.4952342036634207.643981730109
Trimmed Mean ( 18 / 24 )4668.1944444444421.8020975925626214.116757556250
Trimmed Mean ( 19 / 24 )4665.9117647058821.1609723689398220.496094572409
Trimmed Mean ( 20 / 24 )4663.562520.3286970162633229.407841352010
Trimmed Mean ( 21 / 24 )4661.2666666666719.5391698157348238.560118501707
Trimmed Mean ( 22 / 24 )4658.3928571428618.5662932969294250.905917656342
Trimmed Mean ( 23 / 24 )4654.5769230769217.3092392471076268.907076540335
Trimmed Mean ( 24 / 24 )4649.7916666666715.8287917781045293.75531195619
Median4619.5
Midrange5282.5
Midmean - Weighted Average at Xnp4663.37837837838
Midmean - Weighted Average at X(n+1)p4668.19444444444
Midmean - Empirical Distribution Function4663.37837837838
Midmean - Empirical Distribution Function - Averaging4668.19444444444
Midmean - Empirical Distribution Function - Interpolation4668.19444444444
Midmean - Closest Observation4663.37837837838
Midmean - True Basic - Statistics Graphics Toolkit4668.19444444444
Midmean - MS Excel (old versions)4671
Number of observations72



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')