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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 computationMon, 13 Oct 2014 15:33:56 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/13/t1413210860x1p683jjxfcpqkz.htm/, Retrieved Thu, 09 May 2024 21:48:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=240763, Retrieved Thu, 09 May 2024 21:48:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-10-13 14:33:56] [fa76cbd0c9542d7a6f5f3c5daec42b95] [Current]
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Dataseries X:
75
84,3
84
79,1
78,8
82,7
85,3
84,5
80,8
70,1
68,2
68,1
72,3
73,1
71,5
74,1
80,3
80,6
81,4
87,4
89,3
93,2
92,8
96,8
100,3
95,6
89
87,4
86,7
92,8
98,6
100,8
105,5
107,8
113,7
120,3
126,5
134,8
134,5
133,1
128,8
127,1
129,1
128,4
126,5
117,1
114,2
109,1
110,3
109,2
103,6
98,9
95,9
91,2
98,7
94,5
95,6
93,8
89,5
87,1
87,1
84,5
84,2
83,7
82,2
77,7
78,5
79,1
78,6
79
76,2
77,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240763&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=240763&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240763&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean94.14305555555552.1318435107343444.1603968966402
Geometric Mean92.5461093375482
Harmonic Mean91.0682908600956
Quadratic Mean95.8414974783308
Winsorized Mean ( 1 / 24 )94.14027777777782.1304894664549244.1871594579742
Winsorized Mean ( 2 / 24 )94.15416666666672.1114885624910544.5913694912879
Winsorized Mean ( 3 / 24 )94.04583333333332.0606767442678145.6383242034156
Winsorized Mean ( 4 / 24 )94.07361111111112.0499427384799745.8908482394325
Winsorized Mean ( 5 / 24 )94.10138888888892.0351387861603246.2383153074436
Winsorized Mean ( 6 / 24 )94.07638888888891.9977417738669447.0913659210266
Winsorized Mean ( 7 / 24 )94.10555555555561.9720701301314947.7191729227605
Winsorized Mean ( 8 / 24 )94.23888888888891.9543044217595848.2211920720313
Winsorized Mean ( 9 / 24 )93.65138888888891.7568477615712353.3064907144441
Winsorized Mean ( 10 / 24 )93.22083333333331.6625535367378656.0708760791213
Winsorized Mean ( 11 / 24 )92.88472222222221.5611425680728459.4979114155372
Winsorized Mean ( 12 / 24 )92.81805555555551.5430244957989960.1533260218878
Winsorized Mean ( 13 / 24 )92.24027777777781.424835135456964.7375092615183
Winsorized Mean ( 14 / 24 )92.06527777777781.3818875862195466.6228416087324
Winsorized Mean ( 15 / 24 )92.06527777777781.3754813636319666.9331335283812
Winsorized Mean ( 16 / 24 )91.77638888888891.3256844764887669.2294362018708
Winsorized Mean ( 17 / 24 )91.51666666666671.1969036081745976.4611837090539
Winsorized Mean ( 18 / 24 )91.11666666666671.1102048338405682.0719419419789
Winsorized Mean ( 19 / 24 )90.43055555555560.98982428154141991.3602113445138
Winsorized Mean ( 20 / 24 )90.45833333333330.94675491802492595.5456703853657
Winsorized Mean ( 21 / 24 )90.28333333333330.856652600311984105.390835562109
Winsorized Mean ( 22 / 24 )90.3750.82786645763341109.166157375613
Winsorized Mean ( 23 / 24 )90.66250.782424899024474115.873740870258
Winsorized Mean ( 24 / 24 )90.16250.685954658148768131.440903460482
Trimmed Mean ( 1 / 24 )93.93428571428572.080099820142545.1585471065761
Trimmed Mean ( 2 / 24 )93.71617647058822.0198451447242246.3977036632596
Trimmed Mean ( 3 / 24 )93.47727272727271.9596676796606447.7005737745598
Trimmed Mean ( 4 / 24 )93.26406251.910704192658548.8113559693587
Trimmed Mean ( 5 / 24 )93.02903225806451.8550221784046750.1498221105205
Trimmed Mean ( 6 / 24 )92.77166666666671.7915386368656151.7832352357052
Trimmed Mean ( 7 / 24 )92.5017241379311.7244136651868353.6424211924285
Trimmed Mean ( 8 / 24 )92.20714285714291.6478712303565355.9553083751534
Trimmed Mean ( 9 / 24 )91.86851851851851.5555469243712559.0586610273115
Trimmed Mean ( 10 / 24 )91.59423076923081.4931023243542361.344912050047
Trimmed Mean ( 11 / 24 )91.361.438349394129263.5172513527639
Trimmed Mean ( 12 / 24 )91.15208333333331.3933033531484865.4215631702564
Trimmed Mean ( 13 / 24 )90.93478260869571.339014048521667.9117464892145
Trimmed Mean ( 14 / 24 )90.77045454545451.298065643101269.9274763397909
Trimmed Mean ( 15 / 24 )90.61190476190481.2541971458327572.2469390581664
Trimmed Mean ( 16 / 24 )90.43751.1964621325455275.5874319294923
Trimmed Mean ( 17 / 24 )90.27894736842111.1321699472247279.739748957055
Trimmed Mean ( 18 / 24 )90.13333333333331.0801969250212783.4415755549007
Trimmed Mean ( 19 / 24 )90.01764705882351.0331016121208887.1333913360411
Trimmed Mean ( 20 / 24 )89.968751.0021191004727289.7785003374945
Trimmed Mean ( 21 / 24 )89.910.9684369442263892.8403243350274
Trimmed Mean ( 22 / 24 )89.86428571428570.9453480404652595.0594721390222
Trimmed Mean ( 23 / 24 )89.80.91661584940727297.9690674758341
Trimmed Mean ( 24 / 24 )89.68750.88379764594929101.479677402474
Median89.15
Midrange101.45
Midmean - Weighted Average at Xnp89.8675675675676
Midmean - Weighted Average at X(n+1)p90.1333333333333
Midmean - Empirical Distribution Function89.8675675675676
Midmean - Empirical Distribution Function - Averaging90.1333333333333
Midmean - Empirical Distribution Function - Interpolation90.1333333333333
Midmean - Closest Observation89.8675675675676
Midmean - True Basic - Statistics Graphics Toolkit90.1333333333333
Midmean - MS Excel (old versions)90.2789473684211
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 94.1430555555555 & 2.13184351073434 & 44.1603968966402 \tabularnewline
Geometric Mean & 92.5461093375482 &  &  \tabularnewline
Harmonic Mean & 91.0682908600956 &  &  \tabularnewline
Quadratic Mean & 95.8414974783308 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 94.1402777777778 & 2.13048946645492 & 44.1871594579742 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 94.1541666666667 & 2.11148856249105 & 44.5913694912879 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 94.0458333333333 & 2.06067674426781 & 45.6383242034156 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 94.0736111111111 & 2.04994273847997 & 45.8908482394325 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 94.1013888888889 & 2.03513878616032 & 46.2383153074436 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 94.0763888888889 & 1.99774177386694 & 47.0913659210266 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 94.1055555555556 & 1.97207013013149 & 47.7191729227605 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 94.2388888888889 & 1.95430442175958 & 48.2211920720313 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 93.6513888888889 & 1.75684776157123 & 53.3064907144441 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 93.2208333333333 & 1.66255353673786 & 56.0708760791213 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 92.8847222222222 & 1.56114256807284 & 59.4979114155372 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 92.8180555555555 & 1.54302449579899 & 60.1533260218878 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 92.2402777777778 & 1.4248351354569 & 64.7375092615183 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 92.0652777777778 & 1.38188758621954 & 66.6228416087324 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 92.0652777777778 & 1.37548136363196 & 66.9331335283812 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 91.7763888888889 & 1.32568447648876 & 69.2294362018708 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 91.5166666666667 & 1.19690360817459 & 76.4611837090539 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 91.1166666666667 & 1.11020483384056 & 82.0719419419789 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 90.4305555555556 & 0.989824281541419 & 91.3602113445138 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 90.4583333333333 & 0.946754918024925 & 95.5456703853657 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 90.2833333333333 & 0.856652600311984 & 105.390835562109 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 90.375 & 0.82786645763341 & 109.166157375613 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 90.6625 & 0.782424899024474 & 115.873740870258 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 90.1625 & 0.685954658148768 & 131.440903460482 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 93.9342857142857 & 2.0800998201425 & 45.1585471065761 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 93.7161764705882 & 2.01984514472422 & 46.3977036632596 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 93.4772727272727 & 1.95966767966064 & 47.7005737745598 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 93.2640625 & 1.9107041926585 & 48.8113559693587 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 93.0290322580645 & 1.85502217840467 & 50.1498221105205 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 92.7716666666667 & 1.79153863686561 & 51.7832352357052 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 92.501724137931 & 1.72441366518683 & 53.6424211924285 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 92.2071428571429 & 1.64787123035653 & 55.9553083751534 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 91.8685185185185 & 1.55554692437125 & 59.0586610273115 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 91.5942307692308 & 1.49310232435423 & 61.344912050047 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 91.36 & 1.4383493941292 & 63.5172513527639 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 91.1520833333333 & 1.39330335314848 & 65.4215631702564 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 90.9347826086957 & 1.3390140485216 & 67.9117464892145 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 90.7704545454545 & 1.2980656431012 & 69.9274763397909 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 90.6119047619048 & 1.25419714583275 & 72.2469390581664 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 90.4375 & 1.19646213254552 & 75.5874319294923 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 90.2789473684211 & 1.13216994722472 & 79.739748957055 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 90.1333333333333 & 1.08019692502127 & 83.4415755549007 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 90.0176470588235 & 1.03310161212088 & 87.1333913360411 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 89.96875 & 1.00211910047272 & 89.7785003374945 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 89.91 & 0.96843694422638 & 92.8403243350274 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 89.8642857142857 & 0.94534804046525 & 95.0594721390222 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 89.8 & 0.916615849407272 & 97.9690674758341 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 89.6875 & 0.88379764594929 & 101.479677402474 \tabularnewline
Median & 89.15 &  &  \tabularnewline
Midrange & 101.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 89.8675675675676 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 90.1333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 89.8675675675676 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 90.1333333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 90.1333333333333 &  &  \tabularnewline
Midmean - Closest Observation & 89.8675675675676 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 90.1333333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 90.2789473684211 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=240763&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]94.1430555555555[/C][C]2.13184351073434[/C][C]44.1603968966402[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]92.5461093375482[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]91.0682908600956[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]95.8414974783308[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]94.1402777777778[/C][C]2.13048946645492[/C][C]44.1871594579742[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]94.1541666666667[/C][C]2.11148856249105[/C][C]44.5913694912879[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]94.0458333333333[/C][C]2.06067674426781[/C][C]45.6383242034156[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]94.0736111111111[/C][C]2.04994273847997[/C][C]45.8908482394325[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]94.1013888888889[/C][C]2.03513878616032[/C][C]46.2383153074436[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]94.0763888888889[/C][C]1.99774177386694[/C][C]47.0913659210266[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]94.1055555555556[/C][C]1.97207013013149[/C][C]47.7191729227605[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]94.2388888888889[/C][C]1.95430442175958[/C][C]48.2211920720313[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]93.6513888888889[/C][C]1.75684776157123[/C][C]53.3064907144441[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]93.2208333333333[/C][C]1.66255353673786[/C][C]56.0708760791213[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]92.8847222222222[/C][C]1.56114256807284[/C][C]59.4979114155372[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]92.8180555555555[/C][C]1.54302449579899[/C][C]60.1533260218878[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]92.2402777777778[/C][C]1.4248351354569[/C][C]64.7375092615183[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]92.0652777777778[/C][C]1.38188758621954[/C][C]66.6228416087324[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]92.0652777777778[/C][C]1.37548136363196[/C][C]66.9331335283812[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]91.7763888888889[/C][C]1.32568447648876[/C][C]69.2294362018708[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]91.5166666666667[/C][C]1.19690360817459[/C][C]76.4611837090539[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]91.1166666666667[/C][C]1.11020483384056[/C][C]82.0719419419789[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]90.4305555555556[/C][C]0.989824281541419[/C][C]91.3602113445138[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]90.4583333333333[/C][C]0.946754918024925[/C][C]95.5456703853657[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]90.2833333333333[/C][C]0.856652600311984[/C][C]105.390835562109[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]90.375[/C][C]0.82786645763341[/C][C]109.166157375613[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]90.6625[/C][C]0.782424899024474[/C][C]115.873740870258[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]90.1625[/C][C]0.685954658148768[/C][C]131.440903460482[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]93.9342857142857[/C][C]2.0800998201425[/C][C]45.1585471065761[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]93.7161764705882[/C][C]2.01984514472422[/C][C]46.3977036632596[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]93.4772727272727[/C][C]1.95966767966064[/C][C]47.7005737745598[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]93.2640625[/C][C]1.9107041926585[/C][C]48.8113559693587[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]93.0290322580645[/C][C]1.85502217840467[/C][C]50.1498221105205[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]92.7716666666667[/C][C]1.79153863686561[/C][C]51.7832352357052[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]92.501724137931[/C][C]1.72441366518683[/C][C]53.6424211924285[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]92.2071428571429[/C][C]1.64787123035653[/C][C]55.9553083751534[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]91.8685185185185[/C][C]1.55554692437125[/C][C]59.0586610273115[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]91.5942307692308[/C][C]1.49310232435423[/C][C]61.344912050047[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]91.36[/C][C]1.4383493941292[/C][C]63.5172513527639[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]91.1520833333333[/C][C]1.39330335314848[/C][C]65.4215631702564[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]90.9347826086957[/C][C]1.3390140485216[/C][C]67.9117464892145[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]90.7704545454545[/C][C]1.2980656431012[/C][C]69.9274763397909[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]90.6119047619048[/C][C]1.25419714583275[/C][C]72.2469390581664[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]90.4375[/C][C]1.19646213254552[/C][C]75.5874319294923[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]90.2789473684211[/C][C]1.13216994722472[/C][C]79.739748957055[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]90.1333333333333[/C][C]1.08019692502127[/C][C]83.4415755549007[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]90.0176470588235[/C][C]1.03310161212088[/C][C]87.1333913360411[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]89.96875[/C][C]1.00211910047272[/C][C]89.7785003374945[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]89.91[/C][C]0.96843694422638[/C][C]92.8403243350274[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]89.8642857142857[/C][C]0.94534804046525[/C][C]95.0594721390222[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]89.8[/C][C]0.916615849407272[/C][C]97.9690674758341[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]89.6875[/C][C]0.88379764594929[/C][C]101.479677402474[/C][/ROW]
[ROW][C]Median[/C][C]89.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]89.8675675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]90.1333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]89.8675675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]90.1333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]90.1333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]89.8675675675676[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]90.1333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]90.2789473684211[/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=240763&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=240763&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 Mean94.14305555555552.1318435107343444.1603968966402
Geometric Mean92.5461093375482
Harmonic Mean91.0682908600956
Quadratic Mean95.8414974783308
Winsorized Mean ( 1 / 24 )94.14027777777782.1304894664549244.1871594579742
Winsorized Mean ( 2 / 24 )94.15416666666672.1114885624910544.5913694912879
Winsorized Mean ( 3 / 24 )94.04583333333332.0606767442678145.6383242034156
Winsorized Mean ( 4 / 24 )94.07361111111112.0499427384799745.8908482394325
Winsorized Mean ( 5 / 24 )94.10138888888892.0351387861603246.2383153074436
Winsorized Mean ( 6 / 24 )94.07638888888891.9977417738669447.0913659210266
Winsorized Mean ( 7 / 24 )94.10555555555561.9720701301314947.7191729227605
Winsorized Mean ( 8 / 24 )94.23888888888891.9543044217595848.2211920720313
Winsorized Mean ( 9 / 24 )93.65138888888891.7568477615712353.3064907144441
Winsorized Mean ( 10 / 24 )93.22083333333331.6625535367378656.0708760791213
Winsorized Mean ( 11 / 24 )92.88472222222221.5611425680728459.4979114155372
Winsorized Mean ( 12 / 24 )92.81805555555551.5430244957989960.1533260218878
Winsorized Mean ( 13 / 24 )92.24027777777781.424835135456964.7375092615183
Winsorized Mean ( 14 / 24 )92.06527777777781.3818875862195466.6228416087324
Winsorized Mean ( 15 / 24 )92.06527777777781.3754813636319666.9331335283812
Winsorized Mean ( 16 / 24 )91.77638888888891.3256844764887669.2294362018708
Winsorized Mean ( 17 / 24 )91.51666666666671.1969036081745976.4611837090539
Winsorized Mean ( 18 / 24 )91.11666666666671.1102048338405682.0719419419789
Winsorized Mean ( 19 / 24 )90.43055555555560.98982428154141991.3602113445138
Winsorized Mean ( 20 / 24 )90.45833333333330.94675491802492595.5456703853657
Winsorized Mean ( 21 / 24 )90.28333333333330.856652600311984105.390835562109
Winsorized Mean ( 22 / 24 )90.3750.82786645763341109.166157375613
Winsorized Mean ( 23 / 24 )90.66250.782424899024474115.873740870258
Winsorized Mean ( 24 / 24 )90.16250.685954658148768131.440903460482
Trimmed Mean ( 1 / 24 )93.93428571428572.080099820142545.1585471065761
Trimmed Mean ( 2 / 24 )93.71617647058822.0198451447242246.3977036632596
Trimmed Mean ( 3 / 24 )93.47727272727271.9596676796606447.7005737745598
Trimmed Mean ( 4 / 24 )93.26406251.910704192658548.8113559693587
Trimmed Mean ( 5 / 24 )93.02903225806451.8550221784046750.1498221105205
Trimmed Mean ( 6 / 24 )92.77166666666671.7915386368656151.7832352357052
Trimmed Mean ( 7 / 24 )92.5017241379311.7244136651868353.6424211924285
Trimmed Mean ( 8 / 24 )92.20714285714291.6478712303565355.9553083751534
Trimmed Mean ( 9 / 24 )91.86851851851851.5555469243712559.0586610273115
Trimmed Mean ( 10 / 24 )91.59423076923081.4931023243542361.344912050047
Trimmed Mean ( 11 / 24 )91.361.438349394129263.5172513527639
Trimmed Mean ( 12 / 24 )91.15208333333331.3933033531484865.4215631702564
Trimmed Mean ( 13 / 24 )90.93478260869571.339014048521667.9117464892145
Trimmed Mean ( 14 / 24 )90.77045454545451.298065643101269.9274763397909
Trimmed Mean ( 15 / 24 )90.61190476190481.2541971458327572.2469390581664
Trimmed Mean ( 16 / 24 )90.43751.1964621325455275.5874319294923
Trimmed Mean ( 17 / 24 )90.27894736842111.1321699472247279.739748957055
Trimmed Mean ( 18 / 24 )90.13333333333331.0801969250212783.4415755549007
Trimmed Mean ( 19 / 24 )90.01764705882351.0331016121208887.1333913360411
Trimmed Mean ( 20 / 24 )89.968751.0021191004727289.7785003374945
Trimmed Mean ( 21 / 24 )89.910.9684369442263892.8403243350274
Trimmed Mean ( 22 / 24 )89.86428571428570.9453480404652595.0594721390222
Trimmed Mean ( 23 / 24 )89.80.91661584940727297.9690674758341
Trimmed Mean ( 24 / 24 )89.68750.88379764594929101.479677402474
Median89.15
Midrange101.45
Midmean - Weighted Average at Xnp89.8675675675676
Midmean - Weighted Average at X(n+1)p90.1333333333333
Midmean - Empirical Distribution Function89.8675675675676
Midmean - Empirical Distribution Function - Averaging90.1333333333333
Midmean - Empirical Distribution Function - Interpolation90.1333333333333
Midmean - Closest Observation89.8675675675676
Midmean - True Basic - Statistics Graphics Toolkit90.1333333333333
Midmean - MS Excel (old versions)90.2789473684211
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')