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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 computationThu, 17 Jan 2008 02:37:58 -0700
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/Jan/17/t1200562973e6qvvbio5wkbs1r.htm/, Retrieved Wed, 15 May 2024 03:00:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=8018, Retrieved Wed, 15 May 2024 03:00:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact306
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2008-01-17 09:37:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
10
4
2
2
0
0
10
12
0
0
8
6
1
4
10
2
12
6
4
5
1
7
2
4
0
4
2
1
4
2
2
4
3
7
4
7
2
7
8
0
7
1
5
1
1
1
30
4
2
4
7
3
4
1
2
4
4




Summary of compuational 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 compuational 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=8018&T=0

[TABLE]
[ROW][C]Summary of compuational 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=8018&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=8018&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 compuational 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 Mean4.38596491228070.6155637970174717.12511836065014
Geometric Mean0
Harmonic Mean0
Quadratic Mean6.3605141577452
Winsorized Mean ( 1 / 19 )4.070175438596490.4356164424284739.34348441006058
Winsorized Mean ( 2 / 19 )4.070175438596490.4356164424284739.34348441006058
Winsorized Mean ( 3 / 19 )3.964912280701750.4043659849689869.80525669340326
Winsorized Mean ( 4 / 19 )3.964912280701750.4043659849689869.80525669340326
Winsorized Mean ( 5 / 19 )3.964912280701750.4043659849689869.80525669340326
Winsorized Mean ( 6 / 19 )3.859649122807020.33530612625297311.5108219642104
Winsorized Mean ( 7 / 19 )3.859649122807020.33530612625297311.5108219642104
Winsorized Mean ( 8 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 9 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 10 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 11 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 12 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 13 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 14 / 19 )3.719298245614040.2235428812946516.6379632582066
Winsorized Mean ( 15 / 19 )3.719298245614040.2235428812946516.6379632582066
Winsorized Mean ( 16 / 19 )3.438596491228070.17525052576020619.6210338103811
Winsorized Mean ( 17 / 19 )3.438596491228070.17525052576020619.6210338103811
Winsorized Mean ( 18 / 19 )3.122807017543860.13023541302632823.9781711055239
Winsorized Mean ( 19 / 19 )3.122807017543860.13023541302632823.9781711055239
Trimmed Mean ( 1 / 19 )40.4208377087481319.50485167286654
Trimmed Mean ( 2 / 19 )3.924528301886790.4021432571572599.75903047493371
Trimmed Mean ( 3 / 19 )3.843137254901960.37820271462366910.1615803015219
Trimmed Mean ( 4 / 19 )3.795918367346940.36419185513155310.4228535423336
Trimmed Mean ( 5 / 19 )3.744680851063830.34607363558280110.8204742171638
Trimmed Mean ( 6 / 19 )3.688888888888890.32227446459112611.4464200369366
Trimmed Mean ( 7 / 19 )3.651162790697670.31549802590890611.5726961529448
Trimmed Mean ( 8 / 19 )3.609756097560980.30619228929707711.7891802757276
Trimmed Mean ( 9 / 19 )3.589743589743590.30230323391157911.8746450155196
Trimmed Mean ( 10 / 19 )3.567567567567570.29647716525953812.0331950841627
Trimmed Mean ( 11 / 19 )3.542857142857140.28797425521853112.3026870584963
Trimmed Mean ( 12 / 19 )3.515151515151520.27565765755545812.7518732703601
Trimmed Mean ( 13 / 19 )3.483870967741940.25766097480923713.5211433175756
Trimmed Mean ( 14 / 19 )3.448275862068970.23058186676785114.9546705922919
Trimmed Mean ( 15 / 19 )3.407407407407410.22174688002609715.3662022527956
Trimmed Mean ( 16 / 19 )3.360.20720360357226716.2159341926122
Trimmed Mean ( 17 / 19 )3.347826086956520.20477207663223116.3490361675102
Trimmed Mean ( 18 / 19 )3.333333333333330.19920476822239916.7332005306815
Trimmed Mean ( 19 / 19 )3.368421052631580.20534561246876516.4036670281618
Median4
Midrange15
Midmean - Weighted Average at Xnp3.44827586206897
Midmean - Weighted Average at X(n+1)p3.44827586206897
Midmean - Empirical Distribution Function3.44827586206897
Midmean - Empirical Distribution Function - Averaging3.44827586206897
Midmean - Empirical Distribution Function - Interpolation3.44827586206897
Midmean - Closest Observation2.91891891891892
Midmean - True Basic - Statistics Graphics Toolkit3.44827586206897
Midmean - MS Excel (old versions)3.44827586206897
Number of observations57

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.3859649122807 & 0.615563797017471 & 7.12511836065014 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 6.3605141577452 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 4.07017543859649 & 0.435616442428473 & 9.34348441006058 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 4.07017543859649 & 0.435616442428473 & 9.34348441006058 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 3.96491228070175 & 0.404365984968986 & 9.80525669340326 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 3.96491228070175 & 0.404365984968986 & 9.80525669340326 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 3.96491228070175 & 0.404365984968986 & 9.80525669340326 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 3.85964912280702 & 0.335306126252973 & 11.5108219642104 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 3.85964912280702 & 0.335306126252973 & 11.5108219642104 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 3.71929824561404 & 0.306318574200653 & 12.1419285634887 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 3.71929824561404 & 0.306318574200653 & 12.1419285634887 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 3.71929824561404 & 0.306318574200653 & 12.1419285634887 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 3.71929824561404 & 0.306318574200653 & 12.1419285634887 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 3.71929824561404 & 0.306318574200653 & 12.1419285634887 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 3.71929824561404 & 0.306318574200653 & 12.1419285634887 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 3.71929824561404 & 0.22354288129465 & 16.6379632582066 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 3.71929824561404 & 0.22354288129465 & 16.6379632582066 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 3.43859649122807 & 0.175250525760206 & 19.6210338103811 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 3.43859649122807 & 0.175250525760206 & 19.6210338103811 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 3.12280701754386 & 0.130235413026328 & 23.9781711055239 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 3.12280701754386 & 0.130235413026328 & 23.9781711055239 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 4 & 0.420837708748131 & 9.50485167286654 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 3.92452830188679 & 0.402143257157259 & 9.75903047493371 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 3.84313725490196 & 0.378202714623669 & 10.1615803015219 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 3.79591836734694 & 0.364191855131553 & 10.4228535423336 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 3.74468085106383 & 0.346073635582801 & 10.8204742171638 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 3.68888888888889 & 0.322274464591126 & 11.4464200369366 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 3.65116279069767 & 0.315498025908906 & 11.5726961529448 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 3.60975609756098 & 0.306192289297077 & 11.7891802757276 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 3.58974358974359 & 0.302303233911579 & 11.8746450155196 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 3.56756756756757 & 0.296477165259538 & 12.0331950841627 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 3.54285714285714 & 0.287974255218531 & 12.3026870584963 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 3.51515151515152 & 0.275657657555458 & 12.7518732703601 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 3.48387096774194 & 0.257660974809237 & 13.5211433175756 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 3.44827586206897 & 0.230581866767851 & 14.9546705922919 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 3.40740740740741 & 0.221746880026097 & 15.3662022527956 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 3.36 & 0.207203603572267 & 16.2159341926122 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 3.34782608695652 & 0.204772076632231 & 16.3490361675102 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 3.33333333333333 & 0.199204768222399 & 16.7332005306815 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 3.36842105263158 & 0.205345612468765 & 16.4036670281618 \tabularnewline
Median & 4 &  &  \tabularnewline
Midrange & 15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.44827586206897 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.44827586206897 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.44827586206897 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.44827586206897 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.44827586206897 &  &  \tabularnewline
Midmean - Closest Observation & 2.91891891891892 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.44827586206897 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.44827586206897 &  &  \tabularnewline
Number of observations & 57 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=8018&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]4.3859649122807[/C][C]0.615563797017471[/C][C]7.12511836065014[/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]6.3605141577452[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]4.07017543859649[/C][C]0.435616442428473[/C][C]9.34348441006058[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]4.07017543859649[/C][C]0.435616442428473[/C][C]9.34348441006058[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]3.96491228070175[/C][C]0.404365984968986[/C][C]9.80525669340326[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]3.96491228070175[/C][C]0.404365984968986[/C][C]9.80525669340326[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]3.96491228070175[/C][C]0.404365984968986[/C][C]9.80525669340326[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]3.85964912280702[/C][C]0.335306126252973[/C][C]11.5108219642104[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]3.85964912280702[/C][C]0.335306126252973[/C][C]11.5108219642104[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]3.71929824561404[/C][C]0.306318574200653[/C][C]12.1419285634887[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]3.71929824561404[/C][C]0.306318574200653[/C][C]12.1419285634887[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]3.71929824561404[/C][C]0.306318574200653[/C][C]12.1419285634887[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]3.71929824561404[/C][C]0.306318574200653[/C][C]12.1419285634887[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]3.71929824561404[/C][C]0.306318574200653[/C][C]12.1419285634887[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]3.71929824561404[/C][C]0.306318574200653[/C][C]12.1419285634887[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]3.71929824561404[/C][C]0.22354288129465[/C][C]16.6379632582066[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]3.71929824561404[/C][C]0.22354288129465[/C][C]16.6379632582066[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]3.43859649122807[/C][C]0.175250525760206[/C][C]19.6210338103811[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]3.43859649122807[/C][C]0.175250525760206[/C][C]19.6210338103811[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]3.12280701754386[/C][C]0.130235413026328[/C][C]23.9781711055239[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]3.12280701754386[/C][C]0.130235413026328[/C][C]23.9781711055239[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]4[/C][C]0.420837708748131[/C][C]9.50485167286654[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]3.92452830188679[/C][C]0.402143257157259[/C][C]9.75903047493371[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]3.84313725490196[/C][C]0.378202714623669[/C][C]10.1615803015219[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]3.79591836734694[/C][C]0.364191855131553[/C][C]10.4228535423336[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]3.74468085106383[/C][C]0.346073635582801[/C][C]10.8204742171638[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]3.68888888888889[/C][C]0.322274464591126[/C][C]11.4464200369366[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]3.65116279069767[/C][C]0.315498025908906[/C][C]11.5726961529448[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]3.60975609756098[/C][C]0.306192289297077[/C][C]11.7891802757276[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]3.58974358974359[/C][C]0.302303233911579[/C][C]11.8746450155196[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]3.56756756756757[/C][C]0.296477165259538[/C][C]12.0331950841627[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]3.54285714285714[/C][C]0.287974255218531[/C][C]12.3026870584963[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]3.51515151515152[/C][C]0.275657657555458[/C][C]12.7518732703601[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]3.48387096774194[/C][C]0.257660974809237[/C][C]13.5211433175756[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]3.44827586206897[/C][C]0.230581866767851[/C][C]14.9546705922919[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]3.40740740740741[/C][C]0.221746880026097[/C][C]15.3662022527956[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]3.36[/C][C]0.207203603572267[/C][C]16.2159341926122[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]3.34782608695652[/C][C]0.204772076632231[/C][C]16.3490361675102[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]3.33333333333333[/C][C]0.199204768222399[/C][C]16.7332005306815[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]3.36842105263158[/C][C]0.205345612468765[/C][C]16.4036670281618[/C][/ROW]
[ROW][C]Median[/C][C]4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.44827586206897[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.44827586206897[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.44827586206897[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.44827586206897[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.44827586206897[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.91891891891892[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.44827586206897[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.44827586206897[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]57[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=8018&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=8018&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 Mean4.38596491228070.6155637970174717.12511836065014
Geometric Mean0
Harmonic Mean0
Quadratic Mean6.3605141577452
Winsorized Mean ( 1 / 19 )4.070175438596490.4356164424284739.34348441006058
Winsorized Mean ( 2 / 19 )4.070175438596490.4356164424284739.34348441006058
Winsorized Mean ( 3 / 19 )3.964912280701750.4043659849689869.80525669340326
Winsorized Mean ( 4 / 19 )3.964912280701750.4043659849689869.80525669340326
Winsorized Mean ( 5 / 19 )3.964912280701750.4043659849689869.80525669340326
Winsorized Mean ( 6 / 19 )3.859649122807020.33530612625297311.5108219642104
Winsorized Mean ( 7 / 19 )3.859649122807020.33530612625297311.5108219642104
Winsorized Mean ( 8 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 9 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 10 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 11 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 12 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 13 / 19 )3.719298245614040.30631857420065312.1419285634887
Winsorized Mean ( 14 / 19 )3.719298245614040.2235428812946516.6379632582066
Winsorized Mean ( 15 / 19 )3.719298245614040.2235428812946516.6379632582066
Winsorized Mean ( 16 / 19 )3.438596491228070.17525052576020619.6210338103811
Winsorized Mean ( 17 / 19 )3.438596491228070.17525052576020619.6210338103811
Winsorized Mean ( 18 / 19 )3.122807017543860.13023541302632823.9781711055239
Winsorized Mean ( 19 / 19 )3.122807017543860.13023541302632823.9781711055239
Trimmed Mean ( 1 / 19 )40.4208377087481319.50485167286654
Trimmed Mean ( 2 / 19 )3.924528301886790.4021432571572599.75903047493371
Trimmed Mean ( 3 / 19 )3.843137254901960.37820271462366910.1615803015219
Trimmed Mean ( 4 / 19 )3.795918367346940.36419185513155310.4228535423336
Trimmed Mean ( 5 / 19 )3.744680851063830.34607363558280110.8204742171638
Trimmed Mean ( 6 / 19 )3.688888888888890.32227446459112611.4464200369366
Trimmed Mean ( 7 / 19 )3.651162790697670.31549802590890611.5726961529448
Trimmed Mean ( 8 / 19 )3.609756097560980.30619228929707711.7891802757276
Trimmed Mean ( 9 / 19 )3.589743589743590.30230323391157911.8746450155196
Trimmed Mean ( 10 / 19 )3.567567567567570.29647716525953812.0331950841627
Trimmed Mean ( 11 / 19 )3.542857142857140.28797425521853112.3026870584963
Trimmed Mean ( 12 / 19 )3.515151515151520.27565765755545812.7518732703601
Trimmed Mean ( 13 / 19 )3.483870967741940.25766097480923713.5211433175756
Trimmed Mean ( 14 / 19 )3.448275862068970.23058186676785114.9546705922919
Trimmed Mean ( 15 / 19 )3.407407407407410.22174688002609715.3662022527956
Trimmed Mean ( 16 / 19 )3.360.20720360357226716.2159341926122
Trimmed Mean ( 17 / 19 )3.347826086956520.20477207663223116.3490361675102
Trimmed Mean ( 18 / 19 )3.333333333333330.19920476822239916.7332005306815
Trimmed Mean ( 19 / 19 )3.368421052631580.20534561246876516.4036670281618
Median4
Midrange15
Midmean - Weighted Average at Xnp3.44827586206897
Midmean - Weighted Average at X(n+1)p3.44827586206897
Midmean - Empirical Distribution Function3.44827586206897
Midmean - Empirical Distribution Function - Averaging3.44827586206897
Midmean - Empirical Distribution Function - Interpolation3.44827586206897
Midmean - Closest Observation2.91891891891892
Midmean - True Basic - Statistics Graphics Toolkit3.44827586206897
Midmean - MS Excel (old versions)3.44827586206897
Number of observations57



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')