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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 08 Oct 2012 03:46:11 -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/08/t13496824640pepdiihg0kkdmz.htm/, Retrieved Thu, 02 May 2024 05:13:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173245, Retrieved Thu, 02 May 2024 05:13:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [robuustheid gem. ...] [2012-10-08 07:46:11] [2393b4ba43587e8aaa64ad8cc48ac424] [Current]
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Dataseries X:
31,5
31,29
31,3
31,06
31,09
31,11
31,13
31,1
31,03
30,74
30,83
30,82
30,8
30,74
30,71
30,58
30,71
30,7
30,7
30,72
30,68
30,78
30,84
30,8
30,8
30,88
30,87
30,92
30,82
30,75
30,75
30,75
30,63
30,52
30,58
30,6
30,6
30,63
30,56
30,61
30,53
30,6
30,6
30,63
30,66
30,34
30,32
30,3
30,3
30,08
29,96
29,91
29,83
29,89
29,85
30,06
29,83
29,95
30,02
30,03
30,03
29,96
29,85
30,12
29,91
29,9
29,92
29,89
29,96
29,72
29,6
29,54




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173245&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173245&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173245&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean30.48777777777780.0541321566564736563.210107649236
Geometric Mean30.4843583086435
Harmonic Mean30.4809315522025
Quadratic Mean30.491189620027
Winsorized Mean ( 1 / 24 )30.48583333333330.0532664449982754572.32716270666
Winsorized Mean ( 2 / 24 )30.48888888888890.0524719746181416581.050915479512
Winsorized Mean ( 3 / 24 )30.48680555555560.050255928102309606.631032531958
Winsorized Mean ( 4 / 24 )30.48569444444440.0500581924231516609.005099240159
Winsorized Mean ( 5 / 24 )30.48638888888890.0496833894223175613.613307050154
Winsorized Mean ( 6 / 24 )30.48555555555560.0495393051806467615.381169444928
Winsorized Mean ( 7 / 24 )30.48652777777780.0483556528206512630.464609605228
Winsorized Mean ( 8 / 24 )30.48319444444440.0478087226233531637.607381493901
Winsorized Mean ( 9 / 24 )30.47069444444440.0455222375918764669.358451085499
Winsorized Mean ( 10 / 24 )30.46652777777780.0445276723415428684.215593936482
Winsorized Mean ( 11 / 24 )30.4650.0443294678677711687.240372270496
Winsorized Mean ( 12 / 24 )30.46166666666670.0434073041458247701.763614813124
Winsorized Mean ( 13 / 24 )30.46527777777780.0422452654152947721.152476574286
Winsorized Mean ( 14 / 24 )30.46527777777780.0416774503520677730.977483517447
Winsorized Mean ( 15 / 24 )30.46527777777780.0416774503520677730.977483517447
Winsorized Mean ( 16 / 24 )30.46083333333330.0411530550951199740.184009739426
Winsorized Mean ( 17 / 24 )30.4750.0387666870526632786.113086181462
Winsorized Mean ( 18 / 24 )30.47750.0383546327843852794.623694387393
Winsorized Mean ( 19 / 24 )30.47222222222220.0377389218384242807.44813942185
Winsorized Mean ( 20 / 24 )30.47222222222220.0354289731296245860.093294568067
Winsorized Mean ( 21 / 24 )30.47805555555560.0344766590482186884.019983285775
Winsorized Mean ( 22 / 24 )30.49027777777780.0325019394041673938.106412624361
Winsorized Mean ( 23 / 24 )30.54458333333330.02319369475796851316.93478128746
Winsorized Mean ( 24 / 24 )30.54458333333330.02319369475796851316.93478128746
Trimmed Mean ( 1 / 24 )30.48685714285710.0519928100050501586.366790713869
Trimmed Mean ( 2 / 24 )30.48794117647060.0504782043489083603.982284427873
Trimmed Mean ( 3 / 24 )30.48742424242420.0491794253633613619.922335756639
Trimmed Mean ( 4 / 24 )30.487656250.0486186887340787627.076892524871
Trimmed Mean ( 5 / 24 )30.48822580645160.0479922236085503635.274290583607
Trimmed Mean ( 6 / 24 )30.48866666666670.0473277230700793644.203115825398
Trimmed Mean ( 7 / 24 )30.48931034482760.0465369786868182655.163081170627
Trimmed Mean ( 8 / 24 )30.48982142857140.0458501873492671664.9879355195
Trimmed Mean ( 9 / 24 )30.49092592592590.0451074255590732675.962450705475
Trimmed Mean ( 10 / 24 )30.49403846153850.0446599854433783682.804487256272
Trimmed Mean ( 11 / 24 )30.4980.0442562113708116689.123606728668
Trimmed Mean ( 12 / 24 )30.50250.0437265641383761697.573674059377
Trimmed Mean ( 13 / 24 )30.50782608695650.0431768781425101706.57785832181
Trimmed Mean ( 14 / 24 )30.51318181818180.0426572116882249715.311212584593
Trimmed Mean ( 15 / 24 )30.51904761904760.0420245621500515726.219288378956
Trimmed Mean ( 16 / 24 )30.52550.0411095316166894742.54069067543
Trimmed Mean ( 17 / 24 )30.53315789473680.0399058373594233765.130114166789
Trimmed Mean ( 18 / 24 )30.540.0388607608026236785.882709685348
Trimmed Mean ( 19 / 24 )30.54735294117650.0374458820992459815.773356873108
Trimmed Mean ( 20 / 24 )30.556250.0354827025100873861.159039149097
Trimmed Mean ( 21 / 24 )30.56633333333330.0332544468838062919.165290589093
Trimmed Mean ( 22 / 24 )30.57714285714290.03017960847909761013.1722841375
Trimmed Mean ( 23 / 24 )30.58807692307690.02621226507260831166.93757057421
Trimmed Mean ( 24 / 24 )30.593750.02480950977674321233.14609096706
Median30.605
Midrange30.52
Midmean - Weighted Average at Xnp30.54
Midmean - Weighted Average at X(n+1)p30.5536842105263
Midmean - Empirical Distribution Function30.54
Midmean - Empirical Distribution Function - Averaging30.5536842105263
Midmean - Empirical Distribution Function - Interpolation30.5536842105263
Midmean - Closest Observation30.54
Midmean - True Basic - Statistics Graphics Toolkit30.5536842105263
Midmean - MS Excel (old versions)30.54
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 30.4877777777778 & 0.0541321566564736 & 563.210107649236 \tabularnewline
Geometric Mean & 30.4843583086435 &  &  \tabularnewline
Harmonic Mean & 30.4809315522025 &  &  \tabularnewline
Quadratic Mean & 30.491189620027 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 30.4858333333333 & 0.0532664449982754 & 572.32716270666 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 30.4888888888889 & 0.0524719746181416 & 581.050915479512 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 30.4868055555556 & 0.050255928102309 & 606.631032531958 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 30.4856944444444 & 0.0500581924231516 & 609.005099240159 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 30.4863888888889 & 0.0496833894223175 & 613.613307050154 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 30.4855555555556 & 0.0495393051806467 & 615.381169444928 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 30.4865277777778 & 0.0483556528206512 & 630.464609605228 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 30.4831944444444 & 0.0478087226233531 & 637.607381493901 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 30.4706944444444 & 0.0455222375918764 & 669.358451085499 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 30.4665277777778 & 0.0445276723415428 & 684.215593936482 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 30.465 & 0.0443294678677711 & 687.240372270496 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 30.4616666666667 & 0.0434073041458247 & 701.763614813124 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 30.4652777777778 & 0.0422452654152947 & 721.152476574286 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 30.4652777777778 & 0.0416774503520677 & 730.977483517447 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 30.4652777777778 & 0.0416774503520677 & 730.977483517447 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 30.4608333333333 & 0.0411530550951199 & 740.184009739426 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 30.475 & 0.0387666870526632 & 786.113086181462 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 30.4775 & 0.0383546327843852 & 794.623694387393 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 30.4722222222222 & 0.0377389218384242 & 807.44813942185 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 30.4722222222222 & 0.0354289731296245 & 860.093294568067 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 30.4780555555556 & 0.0344766590482186 & 884.019983285775 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 30.4902777777778 & 0.0325019394041673 & 938.106412624361 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 30.5445833333333 & 0.0231936947579685 & 1316.93478128746 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 30.5445833333333 & 0.0231936947579685 & 1316.93478128746 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 30.4868571428571 & 0.0519928100050501 & 586.366790713869 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 30.4879411764706 & 0.0504782043489083 & 603.982284427873 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 30.4874242424242 & 0.0491794253633613 & 619.922335756639 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 30.48765625 & 0.0486186887340787 & 627.076892524871 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 30.4882258064516 & 0.0479922236085503 & 635.274290583607 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 30.4886666666667 & 0.0473277230700793 & 644.203115825398 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 30.4893103448276 & 0.0465369786868182 & 655.163081170627 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 30.4898214285714 & 0.0458501873492671 & 664.9879355195 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 30.4909259259259 & 0.0451074255590732 & 675.962450705475 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 30.4940384615385 & 0.0446599854433783 & 682.804487256272 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 30.498 & 0.0442562113708116 & 689.123606728668 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 30.5025 & 0.0437265641383761 & 697.573674059377 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 30.5078260869565 & 0.0431768781425101 & 706.57785832181 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 30.5131818181818 & 0.0426572116882249 & 715.311212584593 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 30.5190476190476 & 0.0420245621500515 & 726.219288378956 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 30.5255 & 0.0411095316166894 & 742.54069067543 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 30.5331578947368 & 0.0399058373594233 & 765.130114166789 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 30.54 & 0.0388607608026236 & 785.882709685348 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 30.5473529411765 & 0.0374458820992459 & 815.773356873108 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 30.55625 & 0.0354827025100873 & 861.159039149097 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 30.5663333333333 & 0.0332544468838062 & 919.165290589093 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 30.5771428571429 & 0.0301796084790976 & 1013.1722841375 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 30.5880769230769 & 0.0262122650726083 & 1166.93757057421 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 30.59375 & 0.0248095097767432 & 1233.14609096706 \tabularnewline
Median & 30.605 &  &  \tabularnewline
Midrange & 30.52 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 30.54 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 30.5536842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 30.54 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 30.5536842105263 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 30.5536842105263 &  &  \tabularnewline
Midmean - Closest Observation & 30.54 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 30.5536842105263 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 30.54 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173245&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]30.4877777777778[/C][C]0.0541321566564736[/C][C]563.210107649236[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]30.4843583086435[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]30.4809315522025[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]30.491189620027[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]30.4858333333333[/C][C]0.0532664449982754[/C][C]572.32716270666[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]30.4888888888889[/C][C]0.0524719746181416[/C][C]581.050915479512[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]30.4868055555556[/C][C]0.050255928102309[/C][C]606.631032531958[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]30.4856944444444[/C][C]0.0500581924231516[/C][C]609.005099240159[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]30.4863888888889[/C][C]0.0496833894223175[/C][C]613.613307050154[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]30.4855555555556[/C][C]0.0495393051806467[/C][C]615.381169444928[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]30.4865277777778[/C][C]0.0483556528206512[/C][C]630.464609605228[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]30.4831944444444[/C][C]0.0478087226233531[/C][C]637.607381493901[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]30.4706944444444[/C][C]0.0455222375918764[/C][C]669.358451085499[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]30.4665277777778[/C][C]0.0445276723415428[/C][C]684.215593936482[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]30.465[/C][C]0.0443294678677711[/C][C]687.240372270496[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]30.4616666666667[/C][C]0.0434073041458247[/C][C]701.763614813124[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]30.4652777777778[/C][C]0.0422452654152947[/C][C]721.152476574286[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]30.4652777777778[/C][C]0.0416774503520677[/C][C]730.977483517447[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]30.4652777777778[/C][C]0.0416774503520677[/C][C]730.977483517447[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]30.4608333333333[/C][C]0.0411530550951199[/C][C]740.184009739426[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]30.475[/C][C]0.0387666870526632[/C][C]786.113086181462[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]30.4775[/C][C]0.0383546327843852[/C][C]794.623694387393[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]30.4722222222222[/C][C]0.0377389218384242[/C][C]807.44813942185[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]30.4722222222222[/C][C]0.0354289731296245[/C][C]860.093294568067[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]30.4780555555556[/C][C]0.0344766590482186[/C][C]884.019983285775[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]30.4902777777778[/C][C]0.0325019394041673[/C][C]938.106412624361[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]30.5445833333333[/C][C]0.0231936947579685[/C][C]1316.93478128746[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]30.5445833333333[/C][C]0.0231936947579685[/C][C]1316.93478128746[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]30.4868571428571[/C][C]0.0519928100050501[/C][C]586.366790713869[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]30.4879411764706[/C][C]0.0504782043489083[/C][C]603.982284427873[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]30.4874242424242[/C][C]0.0491794253633613[/C][C]619.922335756639[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]30.48765625[/C][C]0.0486186887340787[/C][C]627.076892524871[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]30.4882258064516[/C][C]0.0479922236085503[/C][C]635.274290583607[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]30.4886666666667[/C][C]0.0473277230700793[/C][C]644.203115825398[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]30.4893103448276[/C][C]0.0465369786868182[/C][C]655.163081170627[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]30.4898214285714[/C][C]0.0458501873492671[/C][C]664.9879355195[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]30.4909259259259[/C][C]0.0451074255590732[/C][C]675.962450705475[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]30.4940384615385[/C][C]0.0446599854433783[/C][C]682.804487256272[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]30.498[/C][C]0.0442562113708116[/C][C]689.123606728668[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]30.5025[/C][C]0.0437265641383761[/C][C]697.573674059377[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]30.5078260869565[/C][C]0.0431768781425101[/C][C]706.57785832181[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]30.5131818181818[/C][C]0.0426572116882249[/C][C]715.311212584593[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]30.5190476190476[/C][C]0.0420245621500515[/C][C]726.219288378956[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]30.5255[/C][C]0.0411095316166894[/C][C]742.54069067543[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]30.5331578947368[/C][C]0.0399058373594233[/C][C]765.130114166789[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]30.54[/C][C]0.0388607608026236[/C][C]785.882709685348[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]30.5473529411765[/C][C]0.0374458820992459[/C][C]815.773356873108[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]30.55625[/C][C]0.0354827025100873[/C][C]861.159039149097[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]30.5663333333333[/C][C]0.0332544468838062[/C][C]919.165290589093[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]30.5771428571429[/C][C]0.0301796084790976[/C][C]1013.1722841375[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]30.5880769230769[/C][C]0.0262122650726083[/C][C]1166.93757057421[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]30.59375[/C][C]0.0248095097767432[/C][C]1233.14609096706[/C][/ROW]
[ROW][C]Median[/C][C]30.605[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]30.52[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]30.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]30.5536842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]30.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]30.5536842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]30.5536842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]30.54[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]30.5536842105263[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]30.54[/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=173245&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173245&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 Mean30.48777777777780.0541321566564736563.210107649236
Geometric Mean30.4843583086435
Harmonic Mean30.4809315522025
Quadratic Mean30.491189620027
Winsorized Mean ( 1 / 24 )30.48583333333330.0532664449982754572.32716270666
Winsorized Mean ( 2 / 24 )30.48888888888890.0524719746181416581.050915479512
Winsorized Mean ( 3 / 24 )30.48680555555560.050255928102309606.631032531958
Winsorized Mean ( 4 / 24 )30.48569444444440.0500581924231516609.005099240159
Winsorized Mean ( 5 / 24 )30.48638888888890.0496833894223175613.613307050154
Winsorized Mean ( 6 / 24 )30.48555555555560.0495393051806467615.381169444928
Winsorized Mean ( 7 / 24 )30.48652777777780.0483556528206512630.464609605228
Winsorized Mean ( 8 / 24 )30.48319444444440.0478087226233531637.607381493901
Winsorized Mean ( 9 / 24 )30.47069444444440.0455222375918764669.358451085499
Winsorized Mean ( 10 / 24 )30.46652777777780.0445276723415428684.215593936482
Winsorized Mean ( 11 / 24 )30.4650.0443294678677711687.240372270496
Winsorized Mean ( 12 / 24 )30.46166666666670.0434073041458247701.763614813124
Winsorized Mean ( 13 / 24 )30.46527777777780.0422452654152947721.152476574286
Winsorized Mean ( 14 / 24 )30.46527777777780.0416774503520677730.977483517447
Winsorized Mean ( 15 / 24 )30.46527777777780.0416774503520677730.977483517447
Winsorized Mean ( 16 / 24 )30.46083333333330.0411530550951199740.184009739426
Winsorized Mean ( 17 / 24 )30.4750.0387666870526632786.113086181462
Winsorized Mean ( 18 / 24 )30.47750.0383546327843852794.623694387393
Winsorized Mean ( 19 / 24 )30.47222222222220.0377389218384242807.44813942185
Winsorized Mean ( 20 / 24 )30.47222222222220.0354289731296245860.093294568067
Winsorized Mean ( 21 / 24 )30.47805555555560.0344766590482186884.019983285775
Winsorized Mean ( 22 / 24 )30.49027777777780.0325019394041673938.106412624361
Winsorized Mean ( 23 / 24 )30.54458333333330.02319369475796851316.93478128746
Winsorized Mean ( 24 / 24 )30.54458333333330.02319369475796851316.93478128746
Trimmed Mean ( 1 / 24 )30.48685714285710.0519928100050501586.366790713869
Trimmed Mean ( 2 / 24 )30.48794117647060.0504782043489083603.982284427873
Trimmed Mean ( 3 / 24 )30.48742424242420.0491794253633613619.922335756639
Trimmed Mean ( 4 / 24 )30.487656250.0486186887340787627.076892524871
Trimmed Mean ( 5 / 24 )30.48822580645160.0479922236085503635.274290583607
Trimmed Mean ( 6 / 24 )30.48866666666670.0473277230700793644.203115825398
Trimmed Mean ( 7 / 24 )30.48931034482760.0465369786868182655.163081170627
Trimmed Mean ( 8 / 24 )30.48982142857140.0458501873492671664.9879355195
Trimmed Mean ( 9 / 24 )30.49092592592590.0451074255590732675.962450705475
Trimmed Mean ( 10 / 24 )30.49403846153850.0446599854433783682.804487256272
Trimmed Mean ( 11 / 24 )30.4980.0442562113708116689.123606728668
Trimmed Mean ( 12 / 24 )30.50250.0437265641383761697.573674059377
Trimmed Mean ( 13 / 24 )30.50782608695650.0431768781425101706.57785832181
Trimmed Mean ( 14 / 24 )30.51318181818180.0426572116882249715.311212584593
Trimmed Mean ( 15 / 24 )30.51904761904760.0420245621500515726.219288378956
Trimmed Mean ( 16 / 24 )30.52550.0411095316166894742.54069067543
Trimmed Mean ( 17 / 24 )30.53315789473680.0399058373594233765.130114166789
Trimmed Mean ( 18 / 24 )30.540.0388607608026236785.882709685348
Trimmed Mean ( 19 / 24 )30.54735294117650.0374458820992459815.773356873108
Trimmed Mean ( 20 / 24 )30.556250.0354827025100873861.159039149097
Trimmed Mean ( 21 / 24 )30.56633333333330.0332544468838062919.165290589093
Trimmed Mean ( 22 / 24 )30.57714285714290.03017960847909761013.1722841375
Trimmed Mean ( 23 / 24 )30.58807692307690.02621226507260831166.93757057421
Trimmed Mean ( 24 / 24 )30.593750.02480950977674321233.14609096706
Median30.605
Midrange30.52
Midmean - Weighted Average at Xnp30.54
Midmean - Weighted Average at X(n+1)p30.5536842105263
Midmean - Empirical Distribution Function30.54
Midmean - Empirical Distribution Function - Averaging30.5536842105263
Midmean - Empirical Distribution Function - Interpolation30.5536842105263
Midmean - Closest Observation30.54
Midmean - True Basic - Statistics Graphics Toolkit30.5536842105263
Midmean - MS Excel (old versions)30.54
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')