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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Oct 2012 08:46:36 -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/21/t1350823621h9z4c4ui3uktjsw.htm/, Retrieved Sun, 28 Apr 2024 22:16:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=180885, Retrieved Sun, 28 Apr 2024 22:16:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact62
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-21 12:46:36] [606ba890a58836132a627f58687546e9] [Current]
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Dataseries X:
46,83
45,93
45,93
45,93
45,9
45,91
45,85
45,58
45,56
45,5
45,5
45,5
45,51
45,49
45,4
45,38
45,38
45,38
45,49
45,41
44,99
44,98
44,93
44,93
44,91
44,86
44,76
44,89
44,89
45
45,01
45,11
45,05
44,67
44,48
44,48
44,48
44,58
44,79
44,79
44,41
44,41
44,44
44,43
44,36
44,39
44,39
44,41
44,32
44,43
44,82
44,97
44,91
44,79
44,76
44,8
44,65
44,49
44,56
44,4
44,45
44,46
44,39
44,5
44,44
44,41
44,4
44,42
44,49
44,46
44,49
44,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180885&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=180885&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180885&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean44.92347222222220.0632990887534698709.701720939224
Geometric Mean44.9203315955034
Harmonic Mean44.9172163735875
Quadratic Mean44.9266383952773
Winsorized Mean ( 1 / 24 )44.91152777777780.0590150174921758761.018630278847
Winsorized Mean ( 2 / 24 )44.91236111111110.0589081315263013762.413608230956
Winsorized Mean ( 3 / 24 )44.91236111111110.0589081315263013762.413608230956
Winsorized Mean ( 4 / 24 )44.911250.0586396843293623765.884920999001
Winsorized Mean ( 5 / 24 )44.911250.0583872780414467769.195816392046
Winsorized Mean ( 6 / 24 )44.90708333333330.0574083052982267782.240184587376
Winsorized Mean ( 7 / 24 )44.88180555555560.0517258204415142867.686682829959
Winsorized Mean ( 8 / 24 )44.87958333333330.0513070315140685874.725783366112
Winsorized Mean ( 9 / 24 )44.87333333333330.0501644400797348894.524752235021
Winsorized Mean ( 10 / 24 )44.87194444444440.0499172393662778898.926803928147
Winsorized Mean ( 11 / 24 )44.87347222222220.0497195419627141902.531890898631
Winsorized Mean ( 12 / 24 )44.87513888888890.049506956030888906.441083973952
Winsorized Mean ( 13 / 24 )44.87333333333330.0491870531459561912.299689924047
Winsorized Mean ( 14 / 24 )44.87527777777780.0489418438307318916.910240100097
Winsorized Mean ( 15 / 24 )44.85861111111110.0460604936463287973.906433907415
Winsorized Mean ( 16 / 24 )44.85861111111110.0454034709931946987.99959848521
Winsorized Mean ( 17 / 24 )44.856250.04431553770233011012.20141570439
Winsorized Mean ( 18 / 24 )44.856250.04431553770233011012.20141570439
Winsorized Mean ( 19 / 24 )44.86152777777780.0436583422710051027.55912030063
Winsorized Mean ( 20 / 24 )44.78652777777780.0318853087734761404.61326863592
Winsorized Mean ( 21 / 24 )44.76902777777780.02945658041893861519.83112571323
Winsorized Mean ( 22 / 24 )44.75986111111110.02742645098150931631.99610264149
Winsorized Mean ( 23 / 24 )44.75666666666670.02701865697487811656.50967434397
Winsorized Mean ( 24 / 24 )44.75333333333330.02659835734511681682.56004506796
Trimmed Mean ( 1 / 24 )44.90485714285710.0583757879902634769.237704343227
Trimmed Mean ( 2 / 24 )44.89779411764710.0575856218596452779.670213982885
Trimmed Mean ( 3 / 24 )44.88984848484850.0566770149981649792.029158315799
Trimmed Mean ( 4 / 24 )44.881406250.0555553970576856807.867617315337
Trimmed Mean ( 5 / 24 )44.87274193548390.0542733203585458826.791905102564
Trimmed Mean ( 6 / 24 )44.86350.0527663140488806850.229939473132
Trimmed Mean ( 7 / 24 )44.85448275862070.0511915920185475876.208005845359
Trimmed Mean ( 8 / 24 )44.84946428571430.0507677546467622883.424224643637
Trimmed Mean ( 9 / 24 )44.84444444444440.0502924130569196891.674145634863
Trimmed Mean ( 10 / 24 )44.840.0499101757262549898.413987679314
Trimmed Mean ( 11 / 24 )44.83540.0494237900247256907.162319554406
Trimmed Mean ( 12 / 24 )44.83020833333330.0487844164595889918.945261351419
Trimmed Mean ( 13 / 24 )44.8243478260870.047946883023638934.87511594838
Trimmed Mean ( 14 / 24 )44.81818181818180.0468819225780745955.980031397906
Trimmed Mean ( 15 / 24 )44.81119047619050.0454812980938439985.266304047198
Trimmed Mean ( 16 / 24 )44.80550.04432101718262531010.93122063012
Trimmed Mean ( 17 / 24 )44.79921052631580.04286234803344171045.18796990223
Trimmed Mean ( 18 / 24 )44.79250.04110647228225821089.67025174118
Trimmed Mean ( 19 / 24 )44.7850.03859670818027031160.33211409705
Trimmed Mean ( 20 / 24 )44.77593750.03509451344572151275.86716850348
Trimmed Mean ( 21 / 24 )44.77466666666670.03428324658150941306.02177831127
Trimmed Mean ( 22 / 24 )44.77535714285710.03372579336831061327.62946904991
Trimmed Mean ( 23 / 24 )44.77730769230770.03335846192869981342.30732184279
Trimmed Mean ( 24 / 24 )44.780.03272082171818181368.54753788525
Median44.795
Midrange45.575
Midmean - Weighted Average at Xnp44.7992105263158
Midmean - Weighted Average at X(n+1)p44.7992105263158
Midmean - Empirical Distribution Function44.7992105263158
Midmean - Empirical Distribution Function - Averaging44.7992105263158
Midmean - Empirical Distribution Function - Interpolation44.7992105263158
Midmean - Closest Observation44.7992105263158
Midmean - True Basic - Statistics Graphics Toolkit44.7992105263158
Midmean - MS Excel (old versions)44.7992105263158
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 44.9234722222222 & 0.0632990887534698 & 709.701720939224 \tabularnewline
Geometric Mean & 44.9203315955034 &  &  \tabularnewline
Harmonic Mean & 44.9172163735875 &  &  \tabularnewline
Quadratic Mean & 44.9266383952773 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 44.9115277777778 & 0.0590150174921758 & 761.018630278847 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 44.9123611111111 & 0.0589081315263013 & 762.413608230956 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 44.9123611111111 & 0.0589081315263013 & 762.413608230956 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 44.91125 & 0.0586396843293623 & 765.884920999001 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 44.91125 & 0.0583872780414467 & 769.195816392046 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 44.9070833333333 & 0.0574083052982267 & 782.240184587376 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 44.8818055555556 & 0.0517258204415142 & 867.686682829959 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 44.8795833333333 & 0.0513070315140685 & 874.725783366112 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 44.8733333333333 & 0.0501644400797348 & 894.524752235021 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 44.8719444444444 & 0.0499172393662778 & 898.926803928147 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 44.8734722222222 & 0.0497195419627141 & 902.531890898631 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 44.8751388888889 & 0.049506956030888 & 906.441083973952 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 44.8733333333333 & 0.0491870531459561 & 912.299689924047 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 44.8752777777778 & 0.0489418438307318 & 916.910240100097 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 44.8586111111111 & 0.0460604936463287 & 973.906433907415 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 44.8586111111111 & 0.0454034709931946 & 987.99959848521 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 44.85625 & 0.0443155377023301 & 1012.20141570439 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 44.85625 & 0.0443155377023301 & 1012.20141570439 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 44.8615277777778 & 0.043658342271005 & 1027.55912030063 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 44.7865277777778 & 0.031885308773476 & 1404.61326863592 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 44.7690277777778 & 0.0294565804189386 & 1519.83112571323 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 44.7598611111111 & 0.0274264509815093 & 1631.99610264149 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 44.7566666666667 & 0.0270186569748781 & 1656.50967434397 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 44.7533333333333 & 0.0265983573451168 & 1682.56004506796 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 44.9048571428571 & 0.0583757879902634 & 769.237704343227 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 44.8977941176471 & 0.0575856218596452 & 779.670213982885 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 44.8898484848485 & 0.0566770149981649 & 792.029158315799 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 44.88140625 & 0.0555553970576856 & 807.867617315337 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 44.8727419354839 & 0.0542733203585458 & 826.791905102564 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 44.8635 & 0.0527663140488806 & 850.229939473132 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 44.8544827586207 & 0.0511915920185475 & 876.208005845359 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 44.8494642857143 & 0.0507677546467622 & 883.424224643637 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 44.8444444444444 & 0.0502924130569196 & 891.674145634863 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 44.84 & 0.0499101757262549 & 898.413987679314 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 44.8354 & 0.0494237900247256 & 907.162319554406 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 44.8302083333333 & 0.0487844164595889 & 918.945261351419 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 44.824347826087 & 0.047946883023638 & 934.87511594838 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 44.8181818181818 & 0.0468819225780745 & 955.980031397906 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 44.8111904761905 & 0.0454812980938439 & 985.266304047198 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 44.8055 & 0.0443210171826253 & 1010.93122063012 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 44.7992105263158 & 0.0428623480334417 & 1045.18796990223 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 44.7925 & 0.0411064722822582 & 1089.67025174118 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 44.785 & 0.0385967081802703 & 1160.33211409705 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 44.7759375 & 0.0350945134457215 & 1275.86716850348 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 44.7746666666667 & 0.0342832465815094 & 1306.02177831127 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 44.7753571428571 & 0.0337257933683106 & 1327.62946904991 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 44.7773076923077 & 0.0333584619286998 & 1342.30732184279 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 44.78 & 0.0327208217181818 & 1368.54753788525 \tabularnewline
Median & 44.795 &  &  \tabularnewline
Midrange & 45.575 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 44.7992105263158 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 44.7992105263158 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 44.7992105263158 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 44.7992105263158 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 44.7992105263158 &  &  \tabularnewline
Midmean - Closest Observation & 44.7992105263158 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 44.7992105263158 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 44.7992105263158 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180885&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]44.9234722222222[/C][C]0.0632990887534698[/C][C]709.701720939224[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]44.9203315955034[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]44.9172163735875[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]44.9266383952773[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]44.9115277777778[/C][C]0.0590150174921758[/C][C]761.018630278847[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]44.9123611111111[/C][C]0.0589081315263013[/C][C]762.413608230956[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]44.9123611111111[/C][C]0.0589081315263013[/C][C]762.413608230956[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]44.91125[/C][C]0.0586396843293623[/C][C]765.884920999001[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]44.91125[/C][C]0.0583872780414467[/C][C]769.195816392046[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]44.9070833333333[/C][C]0.0574083052982267[/C][C]782.240184587376[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]44.8818055555556[/C][C]0.0517258204415142[/C][C]867.686682829959[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]44.8795833333333[/C][C]0.0513070315140685[/C][C]874.725783366112[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]44.8733333333333[/C][C]0.0501644400797348[/C][C]894.524752235021[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]44.8719444444444[/C][C]0.0499172393662778[/C][C]898.926803928147[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]44.8734722222222[/C][C]0.0497195419627141[/C][C]902.531890898631[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]44.8751388888889[/C][C]0.049506956030888[/C][C]906.441083973952[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]44.8733333333333[/C][C]0.0491870531459561[/C][C]912.299689924047[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]44.8752777777778[/C][C]0.0489418438307318[/C][C]916.910240100097[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]44.8586111111111[/C][C]0.0460604936463287[/C][C]973.906433907415[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]44.8586111111111[/C][C]0.0454034709931946[/C][C]987.99959848521[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]44.85625[/C][C]0.0443155377023301[/C][C]1012.20141570439[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]44.85625[/C][C]0.0443155377023301[/C][C]1012.20141570439[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]44.8615277777778[/C][C]0.043658342271005[/C][C]1027.55912030063[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]44.7865277777778[/C][C]0.031885308773476[/C][C]1404.61326863592[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]44.7690277777778[/C][C]0.0294565804189386[/C][C]1519.83112571323[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]44.7598611111111[/C][C]0.0274264509815093[/C][C]1631.99610264149[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]44.7566666666667[/C][C]0.0270186569748781[/C][C]1656.50967434397[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]44.7533333333333[/C][C]0.0265983573451168[/C][C]1682.56004506796[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]44.9048571428571[/C][C]0.0583757879902634[/C][C]769.237704343227[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]44.8977941176471[/C][C]0.0575856218596452[/C][C]779.670213982885[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]44.8898484848485[/C][C]0.0566770149981649[/C][C]792.029158315799[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]44.88140625[/C][C]0.0555553970576856[/C][C]807.867617315337[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]44.8727419354839[/C][C]0.0542733203585458[/C][C]826.791905102564[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]44.8635[/C][C]0.0527663140488806[/C][C]850.229939473132[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]44.8544827586207[/C][C]0.0511915920185475[/C][C]876.208005845359[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]44.8494642857143[/C][C]0.0507677546467622[/C][C]883.424224643637[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]44.8444444444444[/C][C]0.0502924130569196[/C][C]891.674145634863[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]44.84[/C][C]0.0499101757262549[/C][C]898.413987679314[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]44.8354[/C][C]0.0494237900247256[/C][C]907.162319554406[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]44.8302083333333[/C][C]0.0487844164595889[/C][C]918.945261351419[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]44.824347826087[/C][C]0.047946883023638[/C][C]934.87511594838[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]44.8181818181818[/C][C]0.0468819225780745[/C][C]955.980031397906[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]44.8111904761905[/C][C]0.0454812980938439[/C][C]985.266304047198[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]44.8055[/C][C]0.0443210171826253[/C][C]1010.93122063012[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]44.7992105263158[/C][C]0.0428623480334417[/C][C]1045.18796990223[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]44.7925[/C][C]0.0411064722822582[/C][C]1089.67025174118[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]44.785[/C][C]0.0385967081802703[/C][C]1160.33211409705[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]44.7759375[/C][C]0.0350945134457215[/C][C]1275.86716850348[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]44.7746666666667[/C][C]0.0342832465815094[/C][C]1306.02177831127[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]44.7753571428571[/C][C]0.0337257933683106[/C][C]1327.62946904991[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]44.7773076923077[/C][C]0.0333584619286998[/C][C]1342.30732184279[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]44.78[/C][C]0.0327208217181818[/C][C]1368.54753788525[/C][/ROW]
[ROW][C]Median[/C][C]44.795[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]45.575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]44.7992105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]44.7992105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]44.7992105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]44.7992105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]44.7992105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]44.7992105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]44.7992105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]44.7992105263158[/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=180885&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180885&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 Mean44.92347222222220.0632990887534698709.701720939224
Geometric Mean44.9203315955034
Harmonic Mean44.9172163735875
Quadratic Mean44.9266383952773
Winsorized Mean ( 1 / 24 )44.91152777777780.0590150174921758761.018630278847
Winsorized Mean ( 2 / 24 )44.91236111111110.0589081315263013762.413608230956
Winsorized Mean ( 3 / 24 )44.91236111111110.0589081315263013762.413608230956
Winsorized Mean ( 4 / 24 )44.911250.0586396843293623765.884920999001
Winsorized Mean ( 5 / 24 )44.911250.0583872780414467769.195816392046
Winsorized Mean ( 6 / 24 )44.90708333333330.0574083052982267782.240184587376
Winsorized Mean ( 7 / 24 )44.88180555555560.0517258204415142867.686682829959
Winsorized Mean ( 8 / 24 )44.87958333333330.0513070315140685874.725783366112
Winsorized Mean ( 9 / 24 )44.87333333333330.0501644400797348894.524752235021
Winsorized Mean ( 10 / 24 )44.87194444444440.0499172393662778898.926803928147
Winsorized Mean ( 11 / 24 )44.87347222222220.0497195419627141902.531890898631
Winsorized Mean ( 12 / 24 )44.87513888888890.049506956030888906.441083973952
Winsorized Mean ( 13 / 24 )44.87333333333330.0491870531459561912.299689924047
Winsorized Mean ( 14 / 24 )44.87527777777780.0489418438307318916.910240100097
Winsorized Mean ( 15 / 24 )44.85861111111110.0460604936463287973.906433907415
Winsorized Mean ( 16 / 24 )44.85861111111110.0454034709931946987.99959848521
Winsorized Mean ( 17 / 24 )44.856250.04431553770233011012.20141570439
Winsorized Mean ( 18 / 24 )44.856250.04431553770233011012.20141570439
Winsorized Mean ( 19 / 24 )44.86152777777780.0436583422710051027.55912030063
Winsorized Mean ( 20 / 24 )44.78652777777780.0318853087734761404.61326863592
Winsorized Mean ( 21 / 24 )44.76902777777780.02945658041893861519.83112571323
Winsorized Mean ( 22 / 24 )44.75986111111110.02742645098150931631.99610264149
Winsorized Mean ( 23 / 24 )44.75666666666670.02701865697487811656.50967434397
Winsorized Mean ( 24 / 24 )44.75333333333330.02659835734511681682.56004506796
Trimmed Mean ( 1 / 24 )44.90485714285710.0583757879902634769.237704343227
Trimmed Mean ( 2 / 24 )44.89779411764710.0575856218596452779.670213982885
Trimmed Mean ( 3 / 24 )44.88984848484850.0566770149981649792.029158315799
Trimmed Mean ( 4 / 24 )44.881406250.0555553970576856807.867617315337
Trimmed Mean ( 5 / 24 )44.87274193548390.0542733203585458826.791905102564
Trimmed Mean ( 6 / 24 )44.86350.0527663140488806850.229939473132
Trimmed Mean ( 7 / 24 )44.85448275862070.0511915920185475876.208005845359
Trimmed Mean ( 8 / 24 )44.84946428571430.0507677546467622883.424224643637
Trimmed Mean ( 9 / 24 )44.84444444444440.0502924130569196891.674145634863
Trimmed Mean ( 10 / 24 )44.840.0499101757262549898.413987679314
Trimmed Mean ( 11 / 24 )44.83540.0494237900247256907.162319554406
Trimmed Mean ( 12 / 24 )44.83020833333330.0487844164595889918.945261351419
Trimmed Mean ( 13 / 24 )44.8243478260870.047946883023638934.87511594838
Trimmed Mean ( 14 / 24 )44.81818181818180.0468819225780745955.980031397906
Trimmed Mean ( 15 / 24 )44.81119047619050.0454812980938439985.266304047198
Trimmed Mean ( 16 / 24 )44.80550.04432101718262531010.93122063012
Trimmed Mean ( 17 / 24 )44.79921052631580.04286234803344171045.18796990223
Trimmed Mean ( 18 / 24 )44.79250.04110647228225821089.67025174118
Trimmed Mean ( 19 / 24 )44.7850.03859670818027031160.33211409705
Trimmed Mean ( 20 / 24 )44.77593750.03509451344572151275.86716850348
Trimmed Mean ( 21 / 24 )44.77466666666670.03428324658150941306.02177831127
Trimmed Mean ( 22 / 24 )44.77535714285710.03372579336831061327.62946904991
Trimmed Mean ( 23 / 24 )44.77730769230770.03335846192869981342.30732184279
Trimmed Mean ( 24 / 24 )44.780.03272082171818181368.54753788525
Median44.795
Midrange45.575
Midmean - Weighted Average at Xnp44.7992105263158
Midmean - Weighted Average at X(n+1)p44.7992105263158
Midmean - Empirical Distribution Function44.7992105263158
Midmean - Empirical Distribution Function - Averaging44.7992105263158
Midmean - Empirical Distribution Function - Interpolation44.7992105263158
Midmean - Closest Observation44.7992105263158
Midmean - True Basic - Statistics Graphics Toolkit44.7992105263158
Midmean - MS Excel (old versions)44.7992105263158
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')