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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 12 Oct 2012 11:21:04 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/12/t1350055520hwkekrkgk6mudud.htm/, Retrieved Mon, 13 May 2024 10:42:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175544, Retrieved Mon, 13 May 2024 10:42:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centurmmaten gem....] [2012-10-12 15:21:04] [a5163a6b16cb463ddc5e8265592a0086] [Current]
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Dataseries X:
299,81
299,01
296,82
296,67
296,95
296,80
296,80
295,93
293,77
291,02
288,61
284,55
284,55
278,14
273,28
270,14
268,36
267,15
267,15
265,47
261,75
256,51
252,98
251,17
251,17
244,27
240,54
238,92
237,47
235,91
235,91
231,41
224,94
222,19
219,06
217,83
217,83
216,89
213,84
212,90
213,98
215,31
215,31
214,09
213,71
211,54
209,40
207,33
207,33
202,75
200,26
198,99
198,82
198,43
198,43
195,68
195,45
193,65
191,38
189,71
189,71
185,49
183,01
182,38
181,60
182,13
182,13
180,81
180,25
179,84
178,50
178,11




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' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175544&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175544&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175544&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' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean231.2497222222224.6945644032556949.2590371242644
Geometric Mean227.958210701376
Harmonic Mean224.793029070067
Quadratic Mean234.608606850502
Winsorized Mean ( 1 / 24 )231.2440277777784.6914307667564849.2907258519885
Winsorized Mean ( 2 / 24 )231.2240277777784.6741143983884649.4690561825999
Winsorized Mean ( 3 / 24 )231.2356944444444.6704064484618149.5108288745622
Winsorized Mean ( 4 / 24 )231.2656944444444.6654254252456549.5701191992084
Winsorized Mean ( 5 / 24 )231.3205555555564.6571223991899149.6702761335612
Winsorized Mean ( 6 / 24 )231.3538888888894.648363370570949.7710420733469
Winsorized Mean ( 7 / 24 )231.2819444444444.6341762019132549.9078874793234
Winsorized Mean ( 8 / 24 )231.0697222222224.5833215705022950.4153415089527
Winsorized Mean ( 9 / 24 )230.8047222222224.5060757539136751.2207816350537
Winsorized Mean ( 10 / 24 )230.8144444444444.3927914697901852.5439110942977
Winsorized Mean ( 11 / 24 )230.8388888888894.1877694272773655.1221582031957
Winsorized Mean ( 12 / 24 )230.8388888888894.1877694272773655.1221582031957
Winsorized Mean ( 13 / 24 )229.9830555555563.9418605478867858.3437827801516
Winsorized Mean ( 14 / 24 )229.4794444444443.7217731446100961.6586330031369
Winsorized Mean ( 15 / 24 )229.2002777777783.5641734680919164.3067122937988
Winsorized Mean ( 16 / 24 )228.8558333333333.4938495521243565.5024865607574
Winsorized Mean ( 17 / 24 )229.2194444444443.3630976520537168.1572372138732
Winsorized Mean ( 18 / 24 )229.2194444444443.3630976520537168.1572372138732
Winsorized Mean ( 19 / 24 )228.8790277777783.2797716207356969.7850503769033
Winsorized Mean ( 20 / 24 )227.8929166666673.1132596830913973.2007413015977
Winsorized Mean ( 21 / 24 )226.7352.8343850920023779.9944230019294
Winsorized Mean ( 22 / 24 )226.4172222222222.5769264123813787.8632859418702
Winsorized Mean ( 23 / 24 )227.3020833333332.3088121309633998.4497960163123
Winsorized Mean ( 24 / 24 )227.3020833333332.3088121309633998.4497960163123
Trimmed Mean ( 1 / 24 )231.0294285714294.6655269957933849.5183992675927
Trimmed Mean ( 2 / 24 )230.8022058823534.6320041468461449.8277200463006
Trimmed Mean ( 3 / 24 )230.5721212121214.5999623922408750.1247839767225
Trimmed Mean ( 4 / 24 )230.323281254.5602735764423650.5064613754344
Trimmed Mean ( 5 / 24 )230.0496774193554.5114137815304750.9928125771057
Trimmed Mean ( 6 / 24 )229.7446666666674.4520653587485451.6040642159951
Trimmed Mean ( 7 / 24 )229.4117241379314.3796451522796852.3813496667688
Trimmed Mean ( 8 / 24 )229.0682142857144.2923406497749653.3667369335478
Trimmed Mean ( 9 / 24 )228.734629629634.1953678302164454.5207569124705
Trimmed Mean ( 10 / 24 )228.4161538461544.0916580437577255.8248395646426
Trimmed Mean ( 11 / 24 )228.07083.9860460572617957.2173017380218
Trimmed Mean ( 12 / 24 )227.6933333333333.8968691781034958.4298119661657
Trimmed Mean ( 13 / 24 )227.2830434782613.7799069572881160.1292693303024
Trimmed Mean ( 14 / 24 )226.9431818181823.6852221279623861.5819546116918
Trimmed Mean ( 15 / 24 )226.6326190476193.6095276242322462.7873346989066
Trimmed Mean ( 16 / 24 )226.32453.541544479641963.9055929696764
Trimmed Mean ( 17 / 24 )226.0247368421053.4625485548324365.2769869542072
Trimmed Mean ( 18 / 24 )225.6488888888893.3805034794022166.7500833126761
Trimmed Mean ( 19 / 24 )225.2288235294123.2607730611429569.0722167124583
Trimmed Mean ( 20 / 24 )224.79656253.1119996880368972.2354065021792
Trimmed Mean ( 21 / 24 )224.4252.9500416420205376.0751973135837
Trimmed Mean ( 22 / 24 )224.1421428571432.8067742296030479.8575605024147
Trimmed Mean ( 23 / 24 )223.8557692307692.6787988222667183.5657263136132
Trimmed Mean ( 24 / 24 )223.406252.5680443422299886.9947011140795
Median217.83
Midrange238.96
Midmean - Weighted Average at Xnp226.024736842105
Midmean - Weighted Average at X(n+1)p226.024736842105
Midmean - Empirical Distribution Function226.024736842105
Midmean - Empirical Distribution Function - Averaging226.024736842105
Midmean - Empirical Distribution Function - Interpolation226.024736842105
Midmean - Closest Observation226.024736842105
Midmean - True Basic - Statistics Graphics Toolkit226.024736842105
Midmean - MS Excel (old versions)226.024736842105
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 231.249722222222 & 4.69456440325569 & 49.2590371242644 \tabularnewline
Geometric Mean & 227.958210701376 &  &  \tabularnewline
Harmonic Mean & 224.793029070067 &  &  \tabularnewline
Quadratic Mean & 234.608606850502 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 231.244027777778 & 4.69143076675648 & 49.2907258519885 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 231.224027777778 & 4.67411439838846 & 49.4690561825999 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 231.235694444444 & 4.67040644846181 & 49.5108288745622 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 231.265694444444 & 4.66542542524565 & 49.5701191992084 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 231.320555555556 & 4.65712239918991 & 49.6702761335612 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 231.353888888889 & 4.6483633705709 & 49.7710420733469 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 231.281944444444 & 4.63417620191325 & 49.9078874793234 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 231.069722222222 & 4.58332157050229 & 50.4153415089527 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 230.804722222222 & 4.50607575391367 & 51.2207816350537 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 230.814444444444 & 4.39279146979018 & 52.5439110942977 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 230.838888888889 & 4.18776942727736 & 55.1221582031957 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 230.838888888889 & 4.18776942727736 & 55.1221582031957 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 229.983055555556 & 3.94186054788678 & 58.3437827801516 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 229.479444444444 & 3.72177314461009 & 61.6586330031369 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 229.200277777778 & 3.56417346809191 & 64.3067122937988 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 228.855833333333 & 3.49384955212435 & 65.5024865607574 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 229.219444444444 & 3.36309765205371 & 68.1572372138732 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 229.219444444444 & 3.36309765205371 & 68.1572372138732 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 228.879027777778 & 3.27977162073569 & 69.7850503769033 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 227.892916666667 & 3.11325968309139 & 73.2007413015977 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 226.735 & 2.83438509200237 & 79.9944230019294 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 226.417222222222 & 2.57692641238137 & 87.8632859418702 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 227.302083333333 & 2.30881213096339 & 98.4497960163123 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 227.302083333333 & 2.30881213096339 & 98.4497960163123 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 231.029428571429 & 4.66552699579338 & 49.5183992675927 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 230.802205882353 & 4.63200414684614 & 49.8277200463006 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 230.572121212121 & 4.59996239224087 & 50.1247839767225 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 230.32328125 & 4.56027357644236 & 50.5064613754344 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 230.049677419355 & 4.51141378153047 & 50.9928125771057 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 229.744666666667 & 4.45206535874854 & 51.6040642159951 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 229.411724137931 & 4.37964515227968 & 52.3813496667688 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 229.068214285714 & 4.29234064977496 & 53.3667369335478 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 228.73462962963 & 4.19536783021644 & 54.5207569124705 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 228.416153846154 & 4.09165804375772 & 55.8248395646426 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 228.0708 & 3.98604605726179 & 57.2173017380218 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 227.693333333333 & 3.89686917810349 & 58.4298119661657 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 227.283043478261 & 3.77990695728811 & 60.1292693303024 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 226.943181818182 & 3.68522212796238 & 61.5819546116918 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 226.632619047619 & 3.60952762423224 & 62.7873346989066 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 226.3245 & 3.5415444796419 & 63.9055929696764 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 226.024736842105 & 3.46254855483243 & 65.2769869542072 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 225.648888888889 & 3.38050347940221 & 66.7500833126761 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 225.228823529412 & 3.26077306114295 & 69.0722167124583 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 224.7965625 & 3.11199968803689 & 72.2354065021792 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 224.425 & 2.95004164202053 & 76.0751973135837 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 224.142142857143 & 2.80677422960304 & 79.8575605024147 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 223.855769230769 & 2.67879882226671 & 83.5657263136132 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 223.40625 & 2.56804434222998 & 86.9947011140795 \tabularnewline
Median & 217.83 &  &  \tabularnewline
Midrange & 238.96 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 226.024736842105 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 226.024736842105 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 226.024736842105 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 226.024736842105 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 226.024736842105 &  &  \tabularnewline
Midmean - Closest Observation & 226.024736842105 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 226.024736842105 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 226.024736842105 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175544&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]231.249722222222[/C][C]4.69456440325569[/C][C]49.2590371242644[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]227.958210701376[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]224.793029070067[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]234.608606850502[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]231.244027777778[/C][C]4.69143076675648[/C][C]49.2907258519885[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]231.224027777778[/C][C]4.67411439838846[/C][C]49.4690561825999[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]231.235694444444[/C][C]4.67040644846181[/C][C]49.5108288745622[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]231.265694444444[/C][C]4.66542542524565[/C][C]49.5701191992084[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]231.320555555556[/C][C]4.65712239918991[/C][C]49.6702761335612[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]231.353888888889[/C][C]4.6483633705709[/C][C]49.7710420733469[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]231.281944444444[/C][C]4.63417620191325[/C][C]49.9078874793234[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]231.069722222222[/C][C]4.58332157050229[/C][C]50.4153415089527[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]230.804722222222[/C][C]4.50607575391367[/C][C]51.2207816350537[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]230.814444444444[/C][C]4.39279146979018[/C][C]52.5439110942977[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]230.838888888889[/C][C]4.18776942727736[/C][C]55.1221582031957[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]230.838888888889[/C][C]4.18776942727736[/C][C]55.1221582031957[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]229.983055555556[/C][C]3.94186054788678[/C][C]58.3437827801516[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]229.479444444444[/C][C]3.72177314461009[/C][C]61.6586330031369[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]229.200277777778[/C][C]3.56417346809191[/C][C]64.3067122937988[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]228.855833333333[/C][C]3.49384955212435[/C][C]65.5024865607574[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]229.219444444444[/C][C]3.36309765205371[/C][C]68.1572372138732[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]229.219444444444[/C][C]3.36309765205371[/C][C]68.1572372138732[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]228.879027777778[/C][C]3.27977162073569[/C][C]69.7850503769033[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]227.892916666667[/C][C]3.11325968309139[/C][C]73.2007413015977[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]226.735[/C][C]2.83438509200237[/C][C]79.9944230019294[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]226.417222222222[/C][C]2.57692641238137[/C][C]87.8632859418702[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]227.302083333333[/C][C]2.30881213096339[/C][C]98.4497960163123[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]227.302083333333[/C][C]2.30881213096339[/C][C]98.4497960163123[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]231.029428571429[/C][C]4.66552699579338[/C][C]49.5183992675927[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]230.802205882353[/C][C]4.63200414684614[/C][C]49.8277200463006[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]230.572121212121[/C][C]4.59996239224087[/C][C]50.1247839767225[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]230.32328125[/C][C]4.56027357644236[/C][C]50.5064613754344[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]230.049677419355[/C][C]4.51141378153047[/C][C]50.9928125771057[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]229.744666666667[/C][C]4.45206535874854[/C][C]51.6040642159951[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]229.411724137931[/C][C]4.37964515227968[/C][C]52.3813496667688[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]229.068214285714[/C][C]4.29234064977496[/C][C]53.3667369335478[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]228.73462962963[/C][C]4.19536783021644[/C][C]54.5207569124705[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]228.416153846154[/C][C]4.09165804375772[/C][C]55.8248395646426[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]228.0708[/C][C]3.98604605726179[/C][C]57.2173017380218[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]227.693333333333[/C][C]3.89686917810349[/C][C]58.4298119661657[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]227.283043478261[/C][C]3.77990695728811[/C][C]60.1292693303024[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]226.943181818182[/C][C]3.68522212796238[/C][C]61.5819546116918[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]226.632619047619[/C][C]3.60952762423224[/C][C]62.7873346989066[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]226.3245[/C][C]3.5415444796419[/C][C]63.9055929696764[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]226.024736842105[/C][C]3.46254855483243[/C][C]65.2769869542072[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]225.648888888889[/C][C]3.38050347940221[/C][C]66.7500833126761[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]225.228823529412[/C][C]3.26077306114295[/C][C]69.0722167124583[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]224.7965625[/C][C]3.11199968803689[/C][C]72.2354065021792[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]224.425[/C][C]2.95004164202053[/C][C]76.0751973135837[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]224.142142857143[/C][C]2.80677422960304[/C][C]79.8575605024147[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]223.855769230769[/C][C]2.67879882226671[/C][C]83.5657263136132[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]223.40625[/C][C]2.56804434222998[/C][C]86.9947011140795[/C][/ROW]
[ROW][C]Median[/C][C]217.83[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]238.96[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]226.024736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]226.024736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]226.024736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]226.024736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]226.024736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]226.024736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]226.024736842105[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]226.024736842105[/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=175544&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175544&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 Mean231.2497222222224.6945644032556949.2590371242644
Geometric Mean227.958210701376
Harmonic Mean224.793029070067
Quadratic Mean234.608606850502
Winsorized Mean ( 1 / 24 )231.2440277777784.6914307667564849.2907258519885
Winsorized Mean ( 2 / 24 )231.2240277777784.6741143983884649.4690561825999
Winsorized Mean ( 3 / 24 )231.2356944444444.6704064484618149.5108288745622
Winsorized Mean ( 4 / 24 )231.2656944444444.6654254252456549.5701191992084
Winsorized Mean ( 5 / 24 )231.3205555555564.6571223991899149.6702761335612
Winsorized Mean ( 6 / 24 )231.3538888888894.648363370570949.7710420733469
Winsorized Mean ( 7 / 24 )231.2819444444444.6341762019132549.9078874793234
Winsorized Mean ( 8 / 24 )231.0697222222224.5833215705022950.4153415089527
Winsorized Mean ( 9 / 24 )230.8047222222224.5060757539136751.2207816350537
Winsorized Mean ( 10 / 24 )230.8144444444444.3927914697901852.5439110942977
Winsorized Mean ( 11 / 24 )230.8388888888894.1877694272773655.1221582031957
Winsorized Mean ( 12 / 24 )230.8388888888894.1877694272773655.1221582031957
Winsorized Mean ( 13 / 24 )229.9830555555563.9418605478867858.3437827801516
Winsorized Mean ( 14 / 24 )229.4794444444443.7217731446100961.6586330031369
Winsorized Mean ( 15 / 24 )229.2002777777783.5641734680919164.3067122937988
Winsorized Mean ( 16 / 24 )228.8558333333333.4938495521243565.5024865607574
Winsorized Mean ( 17 / 24 )229.2194444444443.3630976520537168.1572372138732
Winsorized Mean ( 18 / 24 )229.2194444444443.3630976520537168.1572372138732
Winsorized Mean ( 19 / 24 )228.8790277777783.2797716207356969.7850503769033
Winsorized Mean ( 20 / 24 )227.8929166666673.1132596830913973.2007413015977
Winsorized Mean ( 21 / 24 )226.7352.8343850920023779.9944230019294
Winsorized Mean ( 22 / 24 )226.4172222222222.5769264123813787.8632859418702
Winsorized Mean ( 23 / 24 )227.3020833333332.3088121309633998.4497960163123
Winsorized Mean ( 24 / 24 )227.3020833333332.3088121309633998.4497960163123
Trimmed Mean ( 1 / 24 )231.0294285714294.6655269957933849.5183992675927
Trimmed Mean ( 2 / 24 )230.8022058823534.6320041468461449.8277200463006
Trimmed Mean ( 3 / 24 )230.5721212121214.5999623922408750.1247839767225
Trimmed Mean ( 4 / 24 )230.323281254.5602735764423650.5064613754344
Trimmed Mean ( 5 / 24 )230.0496774193554.5114137815304750.9928125771057
Trimmed Mean ( 6 / 24 )229.7446666666674.4520653587485451.6040642159951
Trimmed Mean ( 7 / 24 )229.4117241379314.3796451522796852.3813496667688
Trimmed Mean ( 8 / 24 )229.0682142857144.2923406497749653.3667369335478
Trimmed Mean ( 9 / 24 )228.734629629634.1953678302164454.5207569124705
Trimmed Mean ( 10 / 24 )228.4161538461544.0916580437577255.8248395646426
Trimmed Mean ( 11 / 24 )228.07083.9860460572617957.2173017380218
Trimmed Mean ( 12 / 24 )227.6933333333333.8968691781034958.4298119661657
Trimmed Mean ( 13 / 24 )227.2830434782613.7799069572881160.1292693303024
Trimmed Mean ( 14 / 24 )226.9431818181823.6852221279623861.5819546116918
Trimmed Mean ( 15 / 24 )226.6326190476193.6095276242322462.7873346989066
Trimmed Mean ( 16 / 24 )226.32453.541544479641963.9055929696764
Trimmed Mean ( 17 / 24 )226.0247368421053.4625485548324365.2769869542072
Trimmed Mean ( 18 / 24 )225.6488888888893.3805034794022166.7500833126761
Trimmed Mean ( 19 / 24 )225.2288235294123.2607730611429569.0722167124583
Trimmed Mean ( 20 / 24 )224.79656253.1119996880368972.2354065021792
Trimmed Mean ( 21 / 24 )224.4252.9500416420205376.0751973135837
Trimmed Mean ( 22 / 24 )224.1421428571432.8067742296030479.8575605024147
Trimmed Mean ( 23 / 24 )223.8557692307692.6787988222667183.5657263136132
Trimmed Mean ( 24 / 24 )223.406252.5680443422299886.9947011140795
Median217.83
Midrange238.96
Midmean - Weighted Average at Xnp226.024736842105
Midmean - Weighted Average at X(n+1)p226.024736842105
Midmean - Empirical Distribution Function226.024736842105
Midmean - Empirical Distribution Function - Averaging226.024736842105
Midmean - Empirical Distribution Function - Interpolation226.024736842105
Midmean - Closest Observation226.024736842105
Midmean - True Basic - Statistics Graphics Toolkit226.024736842105
Midmean - MS Excel (old versions)226.024736842105
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')