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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 13 Dec 2011 15:41:51 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/13/t1323808938wrstyeq2vwfekvw.htm/, Retrieved Thu, 02 May 2024 13:58:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154706, Retrieved Thu, 02 May 2024 13:58:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
- R     [Central Tendency] [gemiddelde en med...] [2011-12-13 19:41:18] [22f8bc702946f784836540059d0d9516]
-    D    [Central Tendency] [gemiddelde en med...] [2011-12-13 19:46:47] [22f8bc702946f784836540059d0d9516]
-   PD      [Central Tendency] [central tendency ...] [2011-12-13 20:31:23] [22f8bc702946f784836540059d0d9516]
-    D          [Central Tendency] [gemiddelde en med...] [2011-12-13 20:41:51] [76a85a4cc6ea7903d92a0f5b9d2872d3] [Current]
- RM D            [Histogram] [gemiddelde en med...] [2011-12-13 20:50:34] [22f8bc702946f784836540059d0d9516]
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Dataseries X:
6
0
1
2
8
3
2
6
5
2
3
3
7
10
3
4
5
4
4
4
7
2
1
1
3
7
9
8
1
2
4
8
2
1
3
0
7
0
2
6
0
3
4
4
2
1
3
5
6
5
12
3
4
2
4
1
4
0
0
11
5
3
5
15
2
1
5
9
6
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154706&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154706&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154706&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.057142857142860.36678092382380111.0614881898598
Geometric Mean0
Harmonic Mean0
Quadratic Mean5.07374192710441
Winsorized Mean ( 1 / 23 )4.014285714285710.35038745613582111.4567049818406
Winsorized Mean ( 2 / 23 )3.985714285714290.34140912303731511.6743051569792
Winsorized Mean ( 3 / 23 )3.942857142857140.32930425074587511.9732956192535
Winsorized Mean ( 4 / 23 )3.885714285714290.31494378685573412.3378026425211
Winsorized Mean ( 5 / 23 )3.885714285714290.31494378685573412.3378026425211
Winsorized Mean ( 6 / 23 )3.885714285714290.2816270805187513.7973744519061
Winsorized Mean ( 7 / 23 )3.885714285714290.2816270805187513.7973744519061
Winsorized Mean ( 8 / 23 )3.885714285714290.2816270805187513.7973744519061
Winsorized Mean ( 9 / 23 )3.757142857142860.25613443859798814.6686360401532
Winsorized Mean ( 10 / 23 )3.757142857142860.25613443859798814.6686360401532
Winsorized Mean ( 11 / 23 )3.757142857142860.25613443859798814.6686360401532
Winsorized Mean ( 12 / 23 )3.757142857142860.25613443859798814.6686360401532
Winsorized Mean ( 13 / 23 )3.571428571428570.22436607598837615.9178634991753
Winsorized Mean ( 14 / 23 )3.771428571428570.19429911048688619.410426336888
Winsorized Mean ( 15 / 23 )3.771428571428570.19429911048688619.410426336888
Winsorized Mean ( 16 / 23 )3.771428571428570.19429911048688619.410426336888
Winsorized Mean ( 17 / 23 )3.771428571428570.19429911048688619.410426336888
Winsorized Mean ( 18 / 23 )3.514285714285710.15462886461925522.7272296342536
Winsorized Mean ( 19 / 23 )3.514285714285710.15462886461925522.7272296342536
Winsorized Mean ( 20 / 23 )3.514285714285710.15462886461925522.7272296342536
Winsorized Mean ( 21 / 23 )3.514285714285710.15462886461925522.7272296342536
Winsorized Mean ( 22 / 23 )3.514285714285710.15462886461925522.7272296342536
Winsorized Mean ( 23 / 23 )3.514285714285710.15462886461925522.7272296342536
Trimmed Mean ( 1 / 23 )3.955882352941180.3355141138628111.7905095180548
Trimmed Mean ( 2 / 23 )3.893939393939390.31742612001603212.2672305408979
Trimmed Mean ( 3 / 23 )3.843750.30146694092098112.7501542565741
Trimmed Mean ( 4 / 23 )3.806451612903230.28799229314029713.2171995694652
Trimmed Mean ( 5 / 23 )3.783333333333330.27728675999640413.6441182167602
Trimmed Mean ( 6 / 23 )3.758620689655170.26411782282933514.2308483743783
Trimmed Mean ( 7 / 23 )3.732142857142860.25797799089222114.4669041116073
Trimmed Mean ( 8 / 23 )3.70370370370370.2502683809323514.7989278146361
Trimmed Mean ( 9 / 23 )3.673076923076920.24053916600361515.2701823328918
Trimmed Mean ( 10 / 23 )3.660.2349294292648215.579146518397
Trimmed Mean ( 11 / 23 )3.645833333333330.22771136882924816.0107655233815
Trimmed Mean ( 12 / 23 )3.63043478260870.21837939695995416.6244381711267
Trimmed Mean ( 13 / 23 )3.613636363636360.20618324812790217.5263334749422
Trimmed Mean ( 14 / 23 )3.619047619047620.19857910172704218.2247154286265
Trimmed Mean ( 15 / 23 )3.60.19546132150665618.4179661339157
Trimmed Mean ( 16 / 23 )3.578947368421050.19094575930792318.7432671005255
Trimmed Mean ( 17 / 23 )3.555555555555560.18449607233073419.2717140838735
Trimmed Mean ( 18 / 23 )3.529411764705880.1752782057403920.1360559905172
Trimmed Mean ( 19 / 23 )3.531250.17381148830771220.3165511922224
Trimmed Mean ( 20 / 23 )3.533333333333330.17109070883990520.651813048712
Trimmed Mean ( 21 / 23 )3.535714285714290.16652488300283621.2323481149305
Trimmed Mean ( 22 / 23 )3.538461538461540.15913969896597822.2349392480503
Trimmed Mean ( 23 / 23 )3.541666666666670.1471857579489124.0625636340169
Median3.5
Midrange7.5
Midmean - Weighted Average at Xnp3.36842105263158
Midmean - Weighted Average at X(n+1)p3.67441860465116
Midmean - Empirical Distribution Function3.67441860465116
Midmean - Empirical Distribution Function - Averaging3.67441860465116
Midmean - Empirical Distribution Function - Interpolation3.36842105263158
Midmean - Closest Observation3.67441860465116
Midmean - True Basic - Statistics Graphics Toolkit3.67441860465116
Midmean - MS Excel (old versions)3.67441860465116
Number of observations70

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.05714285714286 & 0.366780923823801 & 11.0614881898598 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 5.07374192710441 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 4.01428571428571 & 0.350387456135821 & 11.4567049818406 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 3.98571428571429 & 0.341409123037315 & 11.6743051569792 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 3.94285714285714 & 0.329304250745875 & 11.9732956192535 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 3.88571428571429 & 0.314943786855734 & 12.3378026425211 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 3.88571428571429 & 0.314943786855734 & 12.3378026425211 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 3.88571428571429 & 0.28162708051875 & 13.7973744519061 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 3.88571428571429 & 0.28162708051875 & 13.7973744519061 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 3.88571428571429 & 0.28162708051875 & 13.7973744519061 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 3.75714285714286 & 0.256134438597988 & 14.6686360401532 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 3.75714285714286 & 0.256134438597988 & 14.6686360401532 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 3.75714285714286 & 0.256134438597988 & 14.6686360401532 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 3.75714285714286 & 0.256134438597988 & 14.6686360401532 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 3.57142857142857 & 0.224366075988376 & 15.9178634991753 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 3.77142857142857 & 0.194299110486886 & 19.410426336888 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 3.77142857142857 & 0.194299110486886 & 19.410426336888 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 3.77142857142857 & 0.194299110486886 & 19.410426336888 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 3.77142857142857 & 0.194299110486886 & 19.410426336888 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 3.51428571428571 & 0.154628864619255 & 22.7272296342536 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 3.51428571428571 & 0.154628864619255 & 22.7272296342536 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 3.51428571428571 & 0.154628864619255 & 22.7272296342536 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 3.51428571428571 & 0.154628864619255 & 22.7272296342536 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 3.51428571428571 & 0.154628864619255 & 22.7272296342536 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 3.51428571428571 & 0.154628864619255 & 22.7272296342536 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 3.95588235294118 & 0.33551411386281 & 11.7905095180548 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 3.89393939393939 & 0.317426120016032 & 12.2672305408979 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 3.84375 & 0.301466940920981 & 12.7501542565741 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 3.80645161290323 & 0.287992293140297 & 13.2171995694652 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 3.78333333333333 & 0.277286759996404 & 13.6441182167602 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 3.75862068965517 & 0.264117822829335 & 14.2308483743783 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 3.73214285714286 & 0.257977990892221 & 14.4669041116073 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 3.7037037037037 & 0.25026838093235 & 14.7989278146361 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 3.67307692307692 & 0.240539166003615 & 15.2701823328918 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 3.66 & 0.23492942926482 & 15.579146518397 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 3.64583333333333 & 0.227711368829248 & 16.0107655233815 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 3.6304347826087 & 0.218379396959954 & 16.6244381711267 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 3.61363636363636 & 0.206183248127902 & 17.5263334749422 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 3.61904761904762 & 0.198579101727042 & 18.2247154286265 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 3.6 & 0.195461321506656 & 18.4179661339157 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 3.57894736842105 & 0.190945759307923 & 18.7432671005255 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 3.55555555555556 & 0.184496072330734 & 19.2717140838735 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 3.52941176470588 & 0.17527820574039 & 20.1360559905172 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 3.53125 & 0.173811488307712 & 20.3165511922224 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 3.53333333333333 & 0.171090708839905 & 20.651813048712 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 3.53571428571429 & 0.166524883002836 & 21.2323481149305 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 3.53846153846154 & 0.159139698965978 & 22.2349392480503 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 3.54166666666667 & 0.14718575794891 & 24.0625636340169 \tabularnewline
Median & 3.5 &  &  \tabularnewline
Midrange & 7.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.36842105263158 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.67441860465116 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.67441860465116 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.67441860465116 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.36842105263158 &  &  \tabularnewline
Midmean - Closest Observation & 3.67441860465116 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.67441860465116 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.67441860465116 &  &  \tabularnewline
Number of observations & 70 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154706&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]4.05714285714286[/C][C]0.366780923823801[/C][C]11.0614881898598[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]5.07374192710441[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]4.01428571428571[/C][C]0.350387456135821[/C][C]11.4567049818406[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]3.98571428571429[/C][C]0.341409123037315[/C][C]11.6743051569792[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]3.94285714285714[/C][C]0.329304250745875[/C][C]11.9732956192535[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]3.88571428571429[/C][C]0.314943786855734[/C][C]12.3378026425211[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]3.88571428571429[/C][C]0.314943786855734[/C][C]12.3378026425211[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]3.88571428571429[/C][C]0.28162708051875[/C][C]13.7973744519061[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]3.88571428571429[/C][C]0.28162708051875[/C][C]13.7973744519061[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]3.88571428571429[/C][C]0.28162708051875[/C][C]13.7973744519061[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]3.75714285714286[/C][C]0.256134438597988[/C][C]14.6686360401532[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]3.75714285714286[/C][C]0.256134438597988[/C][C]14.6686360401532[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]3.75714285714286[/C][C]0.256134438597988[/C][C]14.6686360401532[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]3.75714285714286[/C][C]0.256134438597988[/C][C]14.6686360401532[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]3.57142857142857[/C][C]0.224366075988376[/C][C]15.9178634991753[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]3.77142857142857[/C][C]0.194299110486886[/C][C]19.410426336888[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]3.77142857142857[/C][C]0.194299110486886[/C][C]19.410426336888[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]3.77142857142857[/C][C]0.194299110486886[/C][C]19.410426336888[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]3.77142857142857[/C][C]0.194299110486886[/C][C]19.410426336888[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]3.51428571428571[/C][C]0.154628864619255[/C][C]22.7272296342536[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]3.51428571428571[/C][C]0.154628864619255[/C][C]22.7272296342536[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]3.51428571428571[/C][C]0.154628864619255[/C][C]22.7272296342536[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]3.51428571428571[/C][C]0.154628864619255[/C][C]22.7272296342536[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]3.51428571428571[/C][C]0.154628864619255[/C][C]22.7272296342536[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]3.51428571428571[/C][C]0.154628864619255[/C][C]22.7272296342536[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]3.95588235294118[/C][C]0.33551411386281[/C][C]11.7905095180548[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]3.89393939393939[/C][C]0.317426120016032[/C][C]12.2672305408979[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]3.84375[/C][C]0.301466940920981[/C][C]12.7501542565741[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]3.80645161290323[/C][C]0.287992293140297[/C][C]13.2171995694652[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]3.78333333333333[/C][C]0.277286759996404[/C][C]13.6441182167602[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]3.75862068965517[/C][C]0.264117822829335[/C][C]14.2308483743783[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]3.73214285714286[/C][C]0.257977990892221[/C][C]14.4669041116073[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]3.7037037037037[/C][C]0.25026838093235[/C][C]14.7989278146361[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]3.67307692307692[/C][C]0.240539166003615[/C][C]15.2701823328918[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]3.66[/C][C]0.23492942926482[/C][C]15.579146518397[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]3.64583333333333[/C][C]0.227711368829248[/C][C]16.0107655233815[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]3.6304347826087[/C][C]0.218379396959954[/C][C]16.6244381711267[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]3.61363636363636[/C][C]0.206183248127902[/C][C]17.5263334749422[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]3.61904761904762[/C][C]0.198579101727042[/C][C]18.2247154286265[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]3.6[/C][C]0.195461321506656[/C][C]18.4179661339157[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]3.57894736842105[/C][C]0.190945759307923[/C][C]18.7432671005255[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]3.55555555555556[/C][C]0.184496072330734[/C][C]19.2717140838735[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]3.52941176470588[/C][C]0.17527820574039[/C][C]20.1360559905172[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]3.53125[/C][C]0.173811488307712[/C][C]20.3165511922224[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]3.53333333333333[/C][C]0.171090708839905[/C][C]20.651813048712[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]3.53571428571429[/C][C]0.166524883002836[/C][C]21.2323481149305[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]3.53846153846154[/C][C]0.159139698965978[/C][C]22.2349392480503[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]3.54166666666667[/C][C]0.14718575794891[/C][C]24.0625636340169[/C][/ROW]
[ROW][C]Median[/C][C]3.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.36842105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.67441860465116[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.67441860465116[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.67441860465116[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.36842105263158[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.67441860465116[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.67441860465116[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.67441860465116[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]70[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154706&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154706&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 Mean4.057142857142860.36678092382380111.0614881898598
Geometric Mean0
Harmonic Mean0
Quadratic Mean5.07374192710441
Winsorized Mean ( 1 / 23 )4.014285714285710.35038745613582111.4567049818406
Winsorized Mean ( 2 / 23 )3.985714285714290.34140912303731511.6743051569792
Winsorized Mean ( 3 / 23 )3.942857142857140.32930425074587511.9732956192535
Winsorized Mean ( 4 / 23 )3.885714285714290.31494378685573412.3378026425211
Winsorized Mean ( 5 / 23 )3.885714285714290.31494378685573412.3378026425211
Winsorized Mean ( 6 / 23 )3.885714285714290.2816270805187513.7973744519061
Winsorized Mean ( 7 / 23 )3.885714285714290.2816270805187513.7973744519061
Winsorized Mean ( 8 / 23 )3.885714285714290.2816270805187513.7973744519061
Winsorized Mean ( 9 / 23 )3.757142857142860.25613443859798814.6686360401532
Winsorized Mean ( 10 / 23 )3.757142857142860.25613443859798814.6686360401532
Winsorized Mean ( 11 / 23 )3.757142857142860.25613443859798814.6686360401532
Winsorized Mean ( 12 / 23 )3.757142857142860.25613443859798814.6686360401532
Winsorized Mean ( 13 / 23 )3.571428571428570.22436607598837615.9178634991753
Winsorized Mean ( 14 / 23 )3.771428571428570.19429911048688619.410426336888
Winsorized Mean ( 15 / 23 )3.771428571428570.19429911048688619.410426336888
Winsorized Mean ( 16 / 23 )3.771428571428570.19429911048688619.410426336888
Winsorized Mean ( 17 / 23 )3.771428571428570.19429911048688619.410426336888
Winsorized Mean ( 18 / 23 )3.514285714285710.15462886461925522.7272296342536
Winsorized Mean ( 19 / 23 )3.514285714285710.15462886461925522.7272296342536
Winsorized Mean ( 20 / 23 )3.514285714285710.15462886461925522.7272296342536
Winsorized Mean ( 21 / 23 )3.514285714285710.15462886461925522.7272296342536
Winsorized Mean ( 22 / 23 )3.514285714285710.15462886461925522.7272296342536
Winsorized Mean ( 23 / 23 )3.514285714285710.15462886461925522.7272296342536
Trimmed Mean ( 1 / 23 )3.955882352941180.3355141138628111.7905095180548
Trimmed Mean ( 2 / 23 )3.893939393939390.31742612001603212.2672305408979
Trimmed Mean ( 3 / 23 )3.843750.30146694092098112.7501542565741
Trimmed Mean ( 4 / 23 )3.806451612903230.28799229314029713.2171995694652
Trimmed Mean ( 5 / 23 )3.783333333333330.27728675999640413.6441182167602
Trimmed Mean ( 6 / 23 )3.758620689655170.26411782282933514.2308483743783
Trimmed Mean ( 7 / 23 )3.732142857142860.25797799089222114.4669041116073
Trimmed Mean ( 8 / 23 )3.70370370370370.2502683809323514.7989278146361
Trimmed Mean ( 9 / 23 )3.673076923076920.24053916600361515.2701823328918
Trimmed Mean ( 10 / 23 )3.660.2349294292648215.579146518397
Trimmed Mean ( 11 / 23 )3.645833333333330.22771136882924816.0107655233815
Trimmed Mean ( 12 / 23 )3.63043478260870.21837939695995416.6244381711267
Trimmed Mean ( 13 / 23 )3.613636363636360.20618324812790217.5263334749422
Trimmed Mean ( 14 / 23 )3.619047619047620.19857910172704218.2247154286265
Trimmed Mean ( 15 / 23 )3.60.19546132150665618.4179661339157
Trimmed Mean ( 16 / 23 )3.578947368421050.19094575930792318.7432671005255
Trimmed Mean ( 17 / 23 )3.555555555555560.18449607233073419.2717140838735
Trimmed Mean ( 18 / 23 )3.529411764705880.1752782057403920.1360559905172
Trimmed Mean ( 19 / 23 )3.531250.17381148830771220.3165511922224
Trimmed Mean ( 20 / 23 )3.533333333333330.17109070883990520.651813048712
Trimmed Mean ( 21 / 23 )3.535714285714290.16652488300283621.2323481149305
Trimmed Mean ( 22 / 23 )3.538461538461540.15913969896597822.2349392480503
Trimmed Mean ( 23 / 23 )3.541666666666670.1471857579489124.0625636340169
Median3.5
Midrange7.5
Midmean - Weighted Average at Xnp3.36842105263158
Midmean - Weighted Average at X(n+1)p3.67441860465116
Midmean - Empirical Distribution Function3.67441860465116
Midmean - Empirical Distribution Function - Averaging3.67441860465116
Midmean - Empirical Distribution Function - Interpolation3.36842105263158
Midmean - Closest Observation3.67441860465116
Midmean - True Basic - Statistics Graphics Toolkit3.67441860465116
Midmean - MS Excel (old versions)3.67441860465116
Number of observations70



Parameters (Session):
par1 = 5 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
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')