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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 16 Oct 2008 08:20:24 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/16/t1224167360f2rhtt6m93hxv5h.htm/, Retrieved Wed, 15 May 2024 05:29:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16349, Retrieved Wed, 15 May 2024 05:29:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Q1 central tenden...] [2007-10-18 09:35:57] [b731da8b544846036771bbf9bf2f34ce]
-    D    [Central Tendency] [] [2008-10-16 14:20:24] [1e28c3a908c2cc51d131d1d2a5af4149] [Current]
-    D      [Central Tendency] [] [2008-10-16 14:30:25] [7c33e759a6f7358dc2f6505c3a7a1eae]
-    D        [Central Tendency] [] [2008-10-16 14:31:36] [7c33e759a6f7358dc2f6505c3a7a1eae]
-    D          [Central Tendency] [] [2008-10-16 14:32:46] [7c33e759a6f7358dc2f6505c3a7a1eae]
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Dataseries X:
2.9
4.5
4.4
1.7
0.1
2.7
4
4
8.1
7.1
9.1
11.1
13.7
14.2
5.8
3.8
6.4
6.1
8.2
6.8
5.6
8.8
7.9
6.5
3.6
3.8
11.5
18
16.6
17.5
17.9
18.4
24
20.7
18.2
16.9
20.6
21.6
22.8
17.5
21.7
25
22.7
25.4
17
17.1
20.2
23.9
20.9
18.9
18.6
21.2
17.6
14.4
13.8
7
7.8
10.7
11.6
7.1
8.3
6.9
5.5
4.6
4.5
4.1
3.4
7.9
12.3
18.2
16.7
21.3
23
28.7
28.7
34.4
39.2
39.4
34.6
34.6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16349&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16349&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16349&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean14.2751.0430519059380613.6858002163967
Geometric Mean10.7546924177666
Harmonic Mean4.17001164811969
Quadratic Mean17.0212881416184
Winsorized Mean ( 1 / 26 )14.29251.0390367602931613.7555287225521
Winsorized Mean ( 2 / 26 )14.20251.0030065168207114.1599279384730
Winsorized Mean ( 3 / 26 )14.211.0019263092233514.1826797731412
Winsorized Mean ( 4 / 26 )14.2250.99584977388755714.2842830043221
Winsorized Mean ( 5 / 26 )13.881250.911357822969315.2313939159192
Winsorized Mean ( 6 / 26 )13.896250.90923260825694215.2834927760015
Winsorized Mean ( 7 / 26 )13.60750.85410359960648815.9319080334861
Winsorized Mean ( 8 / 26 )13.58750.8442946554313116.0933151863419
Winsorized Mean ( 9 / 26 )13.4750.8255866728759516.3217266493166
Winsorized Mean ( 10 / 26 )13.4750.82176388705999316.3976541342176
Winsorized Mean ( 11 / 26 )13.39250.79644537624483216.8153402599239
Winsorized Mean ( 12 / 26 )13.37750.78975035111648316.9388971857854
Winsorized Mean ( 13 / 26 )13.361250.78730330826744316.9709054435489
Winsorized Mean ( 14 / 26 )13.203750.75925605608551617.3903782448234
Winsorized Mean ( 15 / 26 )13.353750.73303587507404418.2170483793186
Winsorized Mean ( 16 / 26 )13.313750.72185315258188418.4438482430673
Winsorized Mean ( 17 / 26 )13.3350.71316530119982918.6983297947407
Winsorized Mean ( 18 / 26 )13.3350.69483879379830919.1915018548472
Winsorized Mean ( 19 / 26 )13.358750.67899705856356619.6742383954663
Winsorized Mean ( 20 / 26 )13.358750.67234638674259519.8688507343973
Winsorized Mean ( 21 / 26 )13.33250.64803445515133820.5737517411577
Winsorized Mean ( 22 / 26 )13.00250.59815109379876421.7378186461604
Winsorized Mean ( 23 / 26 )12.9450.58377021012368222.1748211462475
Winsorized Mean ( 24 / 26 )12.9150.57259154372848322.5553453267975
Winsorized Mean ( 25 / 26 )12.85250.56505845726489422.7454342727851
Winsorized Mean ( 26 / 26 )13.080.53620915057891124.3934665901885
Trimmed Mean ( 1 / 26 )14.13461538461541.0030055182669314.0922608372467
Trimmed Mean ( 2 / 26 )13.96842105263160.9603694656842514.5448408677584
Trimmed Mean ( 3 / 26 )13.84189189189190.93309508886300714.8343851094088
Trimmed Mean ( 4 / 26 )13.70555555555560.90115750832352315.2088346698157
Trimmed Mean ( 5 / 26 )13.55714285714290.86517287595849415.6698657966171
Trimmed Mean ( 6 / 26 )13.48088235294120.84933030828798515.8723669947855
Trimmed Mean ( 7 / 26 )13.39696969696970.83074928881802416.1263691432474
Trimmed Mean ( 8 / 26 )13.3593750.82201455601925916.2519932307464
Trimmed Mean ( 9 / 26 )13.32258064516130.81324122307642116.3820773801445
Trimmed Mean ( 10 / 26 )13.30.80610663662106116.4990578116926
Trimmed Mean ( 11 / 26 )13.27586206896550.79762317193592116.6442783209815
Trimmed Mean ( 12 / 26 )13.26071428571430.79158183967634116.752170932997
Trimmed Mean ( 13 / 26 )13.24629629629630.78467463095906216.8812597905786
Trimmed Mean ( 14 / 26 )13.23269230769230.77583566172927817.0560506050955
Trimmed Mean ( 15 / 26 )13.2360.76932920688833117.2045983455314
Trimmed Mean ( 16 / 26 )13.22291666666670.764999186386117.2848767710885
Trimmed Mean ( 17 / 26 )13.21304347826090.76040676055903517.3762835413863
Trimmed Mean ( 18 / 26 )13.20.7548854273707117.4860972558127
Trimmed Mean ( 19 / 26 )13.18571428571430.74993279937863317.5825277900093
Trimmed Mean ( 20 / 26 )13.16750.74503818091802617.6735908806381
Trimmed Mean ( 21 / 26 )13.14736842105260.73821453166866717.8096852026662
Trimmed Mean ( 22 / 26 )13.12777777777780.73256031888936517.9204052407327
Trimmed Mean ( 23 / 26 )13.14117647058820.73374382021841517.9097610207831
Trimmed Mean ( 24 / 26 )13.16250.73543313439176117.8976162270497
Trimmed Mean ( 25 / 26 )13.190.73682060075784417.9012367276833
Trimmed Mean ( 26 / 26 )13.22857142857140.73651648872976617.9609983360808
Median13.75
Midrange19.75
Midmean - Weighted Average at Xnp13.0024390243902
Midmean - Weighted Average at X(n+1)p13.1675
Midmean - Empirical Distribution Function13.0024390243902
Midmean - Empirical Distribution Function - Averaging13.1675
Midmean - Empirical Distribution Function - Interpolation13.1675
Midmean - Closest Observation13.0024390243902
Midmean - True Basic - Statistics Graphics Toolkit13.1675
Midmean - MS Excel (old versions)13.1857142857143
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 14.275 & 1.04305190593806 & 13.6858002163967 \tabularnewline
Geometric Mean & 10.7546924177666 &  &  \tabularnewline
Harmonic Mean & 4.17001164811969 &  &  \tabularnewline
Quadratic Mean & 17.0212881416184 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 14.2925 & 1.03903676029316 & 13.7555287225521 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 14.2025 & 1.00300651682071 & 14.1599279384730 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 14.21 & 1.00192630922335 & 14.1826797731412 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 14.225 & 0.995849773887557 & 14.2842830043221 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 13.88125 & 0.9113578229693 & 15.2313939159192 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 13.89625 & 0.909232608256942 & 15.2834927760015 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 13.6075 & 0.854103599606488 & 15.9319080334861 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 13.5875 & 0.84429465543131 & 16.0933151863419 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 13.475 & 0.82558667287595 & 16.3217266493166 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 13.475 & 0.821763887059993 & 16.3976541342176 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 13.3925 & 0.796445376244832 & 16.8153402599239 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 13.3775 & 0.789750351116483 & 16.9388971857854 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 13.36125 & 0.787303308267443 & 16.9709054435489 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 13.20375 & 0.759256056085516 & 17.3903782448234 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 13.35375 & 0.733035875074044 & 18.2170483793186 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 13.31375 & 0.721853152581884 & 18.4438482430673 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 13.335 & 0.713165301199829 & 18.6983297947407 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 13.335 & 0.694838793798309 & 19.1915018548472 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 13.35875 & 0.678997058563566 & 19.6742383954663 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 13.35875 & 0.672346386742595 & 19.8688507343973 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 13.3325 & 0.648034455151338 & 20.5737517411577 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 13.0025 & 0.598151093798764 & 21.7378186461604 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 12.945 & 0.583770210123682 & 22.1748211462475 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 12.915 & 0.572591543728483 & 22.5553453267975 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 12.8525 & 0.565058457264894 & 22.7454342727851 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 13.08 & 0.536209150578911 & 24.3934665901885 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 14.1346153846154 & 1.00300551826693 & 14.0922608372467 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 13.9684210526316 & 0.96036946568425 & 14.5448408677584 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 13.8418918918919 & 0.933095088863007 & 14.8343851094088 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 13.7055555555556 & 0.901157508323523 & 15.2088346698157 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 13.5571428571429 & 0.865172875958494 & 15.6698657966171 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 13.4808823529412 & 0.849330308287985 & 15.8723669947855 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 13.3969696969697 & 0.830749288818024 & 16.1263691432474 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 13.359375 & 0.822014556019259 & 16.2519932307464 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 13.3225806451613 & 0.813241223076421 & 16.3820773801445 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 13.3 & 0.806106636621061 & 16.4990578116926 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 13.2758620689655 & 0.797623171935921 & 16.6442783209815 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 13.2607142857143 & 0.791581839676341 & 16.752170932997 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 13.2462962962963 & 0.784674630959062 & 16.8812597905786 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 13.2326923076923 & 0.775835661729278 & 17.0560506050955 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 13.236 & 0.769329206888331 & 17.2045983455314 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 13.2229166666667 & 0.7649991863861 & 17.2848767710885 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 13.2130434782609 & 0.760406760559035 & 17.3762835413863 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 13.2 & 0.75488542737071 & 17.4860972558127 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 13.1857142857143 & 0.749932799378633 & 17.5825277900093 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 13.1675 & 0.745038180918026 & 17.6735908806381 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 13.1473684210526 & 0.738214531668667 & 17.8096852026662 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 13.1277777777778 & 0.732560318889365 & 17.9204052407327 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 13.1411764705882 & 0.733743820218415 & 17.9097610207831 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 13.1625 & 0.735433134391761 & 17.8976162270497 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 13.19 & 0.736820600757844 & 17.9012367276833 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 13.2285714285714 & 0.736516488729766 & 17.9609983360808 \tabularnewline
Median & 13.75 &  &  \tabularnewline
Midrange & 19.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13.0024390243902 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13.1675 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13.0024390243902 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13.1675 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13.1675 &  &  \tabularnewline
Midmean - Closest Observation & 13.0024390243902 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13.1675 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13.1857142857143 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16349&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]14.275[/C][C]1.04305190593806[/C][C]13.6858002163967[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10.7546924177666[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.17001164811969[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17.0212881416184[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]14.2925[/C][C]1.03903676029316[/C][C]13.7555287225521[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]14.2025[/C][C]1.00300651682071[/C][C]14.1599279384730[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]14.21[/C][C]1.00192630922335[/C][C]14.1826797731412[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]14.225[/C][C]0.995849773887557[/C][C]14.2842830043221[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]13.88125[/C][C]0.9113578229693[/C][C]15.2313939159192[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]13.89625[/C][C]0.909232608256942[/C][C]15.2834927760015[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]13.6075[/C][C]0.854103599606488[/C][C]15.9319080334861[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]13.5875[/C][C]0.84429465543131[/C][C]16.0933151863419[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]13.475[/C][C]0.82558667287595[/C][C]16.3217266493166[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]13.475[/C][C]0.821763887059993[/C][C]16.3976541342176[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]13.3925[/C][C]0.796445376244832[/C][C]16.8153402599239[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]13.3775[/C][C]0.789750351116483[/C][C]16.9388971857854[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]13.36125[/C][C]0.787303308267443[/C][C]16.9709054435489[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]13.20375[/C][C]0.759256056085516[/C][C]17.3903782448234[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]13.35375[/C][C]0.733035875074044[/C][C]18.2170483793186[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]13.31375[/C][C]0.721853152581884[/C][C]18.4438482430673[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]13.335[/C][C]0.713165301199829[/C][C]18.6983297947407[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]13.335[/C][C]0.694838793798309[/C][C]19.1915018548472[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]13.35875[/C][C]0.678997058563566[/C][C]19.6742383954663[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]13.35875[/C][C]0.672346386742595[/C][C]19.8688507343973[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]13.3325[/C][C]0.648034455151338[/C][C]20.5737517411577[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]13.0025[/C][C]0.598151093798764[/C][C]21.7378186461604[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]12.945[/C][C]0.583770210123682[/C][C]22.1748211462475[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]12.915[/C][C]0.572591543728483[/C][C]22.5553453267975[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]12.8525[/C][C]0.565058457264894[/C][C]22.7454342727851[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]13.08[/C][C]0.536209150578911[/C][C]24.3934665901885[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]14.1346153846154[/C][C]1.00300551826693[/C][C]14.0922608372467[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]13.9684210526316[/C][C]0.96036946568425[/C][C]14.5448408677584[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]13.8418918918919[/C][C]0.933095088863007[/C][C]14.8343851094088[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]13.7055555555556[/C][C]0.901157508323523[/C][C]15.2088346698157[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]13.5571428571429[/C][C]0.865172875958494[/C][C]15.6698657966171[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]13.4808823529412[/C][C]0.849330308287985[/C][C]15.8723669947855[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]13.3969696969697[/C][C]0.830749288818024[/C][C]16.1263691432474[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]13.359375[/C][C]0.822014556019259[/C][C]16.2519932307464[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]13.3225806451613[/C][C]0.813241223076421[/C][C]16.3820773801445[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]13.3[/C][C]0.806106636621061[/C][C]16.4990578116926[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]13.2758620689655[/C][C]0.797623171935921[/C][C]16.6442783209815[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]13.2607142857143[/C][C]0.791581839676341[/C][C]16.752170932997[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]13.2462962962963[/C][C]0.784674630959062[/C][C]16.8812597905786[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]13.2326923076923[/C][C]0.775835661729278[/C][C]17.0560506050955[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]13.236[/C][C]0.769329206888331[/C][C]17.2045983455314[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]13.2229166666667[/C][C]0.7649991863861[/C][C]17.2848767710885[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]13.2130434782609[/C][C]0.760406760559035[/C][C]17.3762835413863[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]13.2[/C][C]0.75488542737071[/C][C]17.4860972558127[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]13.1857142857143[/C][C]0.749932799378633[/C][C]17.5825277900093[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]13.1675[/C][C]0.745038180918026[/C][C]17.6735908806381[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]13.1473684210526[/C][C]0.738214531668667[/C][C]17.8096852026662[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]13.1277777777778[/C][C]0.732560318889365[/C][C]17.9204052407327[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]13.1411764705882[/C][C]0.733743820218415[/C][C]17.9097610207831[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]13.1625[/C][C]0.735433134391761[/C][C]17.8976162270497[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]13.19[/C][C]0.736820600757844[/C][C]17.9012367276833[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]13.2285714285714[/C][C]0.736516488729766[/C][C]17.9609983360808[/C][/ROW]
[ROW][C]Median[/C][C]13.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13.0024390243902[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13.1675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13.0024390243902[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13.1675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13.1675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13.0024390243902[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13.1675[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13.1857142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=16349&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16349&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 Mean14.2751.0430519059380613.6858002163967
Geometric Mean10.7546924177666
Harmonic Mean4.17001164811969
Quadratic Mean17.0212881416184
Winsorized Mean ( 1 / 26 )14.29251.0390367602931613.7555287225521
Winsorized Mean ( 2 / 26 )14.20251.0030065168207114.1599279384730
Winsorized Mean ( 3 / 26 )14.211.0019263092233514.1826797731412
Winsorized Mean ( 4 / 26 )14.2250.99584977388755714.2842830043221
Winsorized Mean ( 5 / 26 )13.881250.911357822969315.2313939159192
Winsorized Mean ( 6 / 26 )13.896250.90923260825694215.2834927760015
Winsorized Mean ( 7 / 26 )13.60750.85410359960648815.9319080334861
Winsorized Mean ( 8 / 26 )13.58750.8442946554313116.0933151863419
Winsorized Mean ( 9 / 26 )13.4750.8255866728759516.3217266493166
Winsorized Mean ( 10 / 26 )13.4750.82176388705999316.3976541342176
Winsorized Mean ( 11 / 26 )13.39250.79644537624483216.8153402599239
Winsorized Mean ( 12 / 26 )13.37750.78975035111648316.9388971857854
Winsorized Mean ( 13 / 26 )13.361250.78730330826744316.9709054435489
Winsorized Mean ( 14 / 26 )13.203750.75925605608551617.3903782448234
Winsorized Mean ( 15 / 26 )13.353750.73303587507404418.2170483793186
Winsorized Mean ( 16 / 26 )13.313750.72185315258188418.4438482430673
Winsorized Mean ( 17 / 26 )13.3350.71316530119982918.6983297947407
Winsorized Mean ( 18 / 26 )13.3350.69483879379830919.1915018548472
Winsorized Mean ( 19 / 26 )13.358750.67899705856356619.6742383954663
Winsorized Mean ( 20 / 26 )13.358750.67234638674259519.8688507343973
Winsorized Mean ( 21 / 26 )13.33250.64803445515133820.5737517411577
Winsorized Mean ( 22 / 26 )13.00250.59815109379876421.7378186461604
Winsorized Mean ( 23 / 26 )12.9450.58377021012368222.1748211462475
Winsorized Mean ( 24 / 26 )12.9150.57259154372848322.5553453267975
Winsorized Mean ( 25 / 26 )12.85250.56505845726489422.7454342727851
Winsorized Mean ( 26 / 26 )13.080.53620915057891124.3934665901885
Trimmed Mean ( 1 / 26 )14.13461538461541.0030055182669314.0922608372467
Trimmed Mean ( 2 / 26 )13.96842105263160.9603694656842514.5448408677584
Trimmed Mean ( 3 / 26 )13.84189189189190.93309508886300714.8343851094088
Trimmed Mean ( 4 / 26 )13.70555555555560.90115750832352315.2088346698157
Trimmed Mean ( 5 / 26 )13.55714285714290.86517287595849415.6698657966171
Trimmed Mean ( 6 / 26 )13.48088235294120.84933030828798515.8723669947855
Trimmed Mean ( 7 / 26 )13.39696969696970.83074928881802416.1263691432474
Trimmed Mean ( 8 / 26 )13.3593750.82201455601925916.2519932307464
Trimmed Mean ( 9 / 26 )13.32258064516130.81324122307642116.3820773801445
Trimmed Mean ( 10 / 26 )13.30.80610663662106116.4990578116926
Trimmed Mean ( 11 / 26 )13.27586206896550.79762317193592116.6442783209815
Trimmed Mean ( 12 / 26 )13.26071428571430.79158183967634116.752170932997
Trimmed Mean ( 13 / 26 )13.24629629629630.78467463095906216.8812597905786
Trimmed Mean ( 14 / 26 )13.23269230769230.77583566172927817.0560506050955
Trimmed Mean ( 15 / 26 )13.2360.76932920688833117.2045983455314
Trimmed Mean ( 16 / 26 )13.22291666666670.764999186386117.2848767710885
Trimmed Mean ( 17 / 26 )13.21304347826090.76040676055903517.3762835413863
Trimmed Mean ( 18 / 26 )13.20.7548854273707117.4860972558127
Trimmed Mean ( 19 / 26 )13.18571428571430.74993279937863317.5825277900093
Trimmed Mean ( 20 / 26 )13.16750.74503818091802617.6735908806381
Trimmed Mean ( 21 / 26 )13.14736842105260.73821453166866717.8096852026662
Trimmed Mean ( 22 / 26 )13.12777777777780.73256031888936517.9204052407327
Trimmed Mean ( 23 / 26 )13.14117647058820.73374382021841517.9097610207831
Trimmed Mean ( 24 / 26 )13.16250.73543313439176117.8976162270497
Trimmed Mean ( 25 / 26 )13.190.73682060075784417.9012367276833
Trimmed Mean ( 26 / 26 )13.22857142857140.73651648872976617.9609983360808
Median13.75
Midrange19.75
Midmean - Weighted Average at Xnp13.0024390243902
Midmean - Weighted Average at X(n+1)p13.1675
Midmean - Empirical Distribution Function13.0024390243902
Midmean - Empirical Distribution Function - Averaging13.1675
Midmean - Empirical Distribution Function - Interpolation13.1675
Midmean - Closest Observation13.0024390243902
Midmean - True Basic - Statistics Graphics Toolkit13.1675
Midmean - MS Excel (old versions)13.1857142857143
Number of observations80



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')