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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 computationWed, 21 Oct 2009 15:29:45 -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/2009/Oct/21/t1256160618lq4zugreuvs6811.htm/, Retrieved Thu, 02 May 2024 08:14:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49622, Retrieved Thu, 02 May 2024 08:14:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Tendancy] [2009-10-21 21:29:45] [abbb6febea381ea822009ab8520873eb] [Current]
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Dataseries X:
-84
-84
-90
-84
-57
-32
-80
-121
-143
-132
-110
-84
-72
-54
-75
-17
-26
-60
-52
-60
-28
-26
-20
-22
24
7
-88
-9
13
-12
10
26
11
-8
-16
-16
-8
0
-12
0
3
3
28
-9
11
0
11
-54
0
66
75
-80
-24
0
88
38
-54
-34
-55
-66




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49622&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49622&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49622&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 time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-29.06666666666676.28736813911519-4.62302604580065
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean56.3666568105649
Winsorized Mean ( 1 / 20 )-29.16.16806519490412-4.71784896567592
Winsorized Mean ( 2 / 20 )-29.03333333333335.9851023461727-4.85093347683508
Winsorized Mean ( 3 / 20 )-29.88333333333335.50921629802785-5.42424397895409
Winsorized Mean ( 4 / 20 )-29.21666666666675.07481271629421-5.75719111226663
Winsorized Mean ( 5 / 20 )-29.21666666666675.00982603229124-5.83187249983298
Winsorized Mean ( 6 / 20 )-29.01666666666674.89491213235003-5.9279239099918
Winsorized Mean ( 7 / 20 )-30.34.67601766922858-6.4798728626273
Winsorized Mean ( 8 / 20 )-30.56666666666674.63482071805504-6.59500518490253
Winsorized Mean ( 9 / 20 )-30.56666666666674.63482071805504-6.59500518490253
Winsorized Mean ( 10 / 20 )-29.94.50684977731167-6.63434582411028
Winsorized Mean ( 11 / 20 )-30.08333333333334.47884491683706-6.71676155167659
Winsorized Mean ( 12 / 20 )-29.68333333333334.20300482145693-7.06240763317609
Winsorized Mean ( 13 / 20 )-29.93.95980510848389-7.55087666712161
Winsorized Mean ( 14 / 20 )-28.53.71365627621258-7.67437745451932
Winsorized Mean ( 15 / 20 )-27.753.35630151908401-8.26802950873538
Winsorized Mean ( 16 / 20 )-27.753.35630151908401-8.26802950873538
Winsorized Mean ( 17 / 20 )-26.93.21970451674393-8.35480394555083
Winsorized Mean ( 18 / 20 )-26.33.12546493716476-8.41474805468713
Winsorized Mean ( 19 / 20 )-25.98333333333333.07638092337204-8.4460715303269
Winsorized Mean ( 20 / 20 )-28.652.71226811084095-10.5631150126663
Trimmed Mean ( 1 / 20 )-29.12068965517245.85296123552562-4.97537716095215
Trimmed Mean ( 2 / 20 )-29.14285714285715.46027142250467-5.3372543025506
Trimmed Mean ( 3 / 20 )-29.20370370370375.0965095158377-5.7301381686724
Trimmed Mean ( 4 / 20 )-28.94230769230774.88521436096648-5.92447036174311
Trimmed Mean ( 5 / 20 )-28.864.79455558579793-6.01932743995855
Trimmed Mean ( 6 / 20 )-28.77083333333334.69893601048308-6.12283999380862
Trimmed Mean ( 7 / 20 )-28.71739130434784.60923909839385-6.23039740211237
Trimmed Mean ( 8 / 20 )-28.40909090909094.55043595962418-6.24315805368179
Trimmed Mean ( 9 / 20 )-28.02380952380954.47777945207384-6.25841666025569
Trimmed Mean ( 10 / 20 )-27.64.37530951286116-6.30812515523078
Trimmed Mean ( 11 / 20 )-27.23684210526324.26895142223642-6.3802183279458
Trimmed Mean ( 12 / 20 )-26.80555555555564.12557248445776-6.49741476038536
Trimmed Mean ( 13 / 20 )-26.38235294117654.00245350464328-6.5915451386431
Trimmed Mean ( 14 / 20 )-25.8753.89135466502762-6.64935536011244
Trimmed Mean ( 15 / 20 )-25.53.80161792538055-6.70767039206009
Trimmed Mean ( 16 / 20 )-25.17857142857143.76739477842152-6.68328457978085
Trimmed Mean ( 17 / 20 )-24.80769230769233.69615984951085-6.71174768347081
Trimmed Mean ( 18 / 20 )-24.53.61809061662984-6.77152747014974
Trimmed Mean ( 19 / 20 )-24.22727272727273.51060965720902-6.90115822974569
Trimmed Mean ( 20 / 20 )-23.953.33204141630923-7.18778580685485
Median-21
Midrange-27.5
Midmean - Weighted Average at Xnp-26.8064516129032
Midmean - Weighted Average at X(n+1)p-25.5
Midmean - Empirical Distribution Function-26.8064516129032
Midmean - Empirical Distribution Function - Averaging-25.5
Midmean - Empirical Distribution Function - Interpolation-25.5
Midmean - Closest Observation-26.8064516129032
Midmean - True Basic - Statistics Graphics Toolkit-25.5
Midmean - MS Excel (old versions)-25
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -29.0666666666667 & 6.28736813911519 & -4.62302604580065 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 56.3666568105649 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & -29.1 & 6.16806519490412 & -4.71784896567592 \tabularnewline
Winsorized Mean ( 2 / 20 ) & -29.0333333333333 & 5.9851023461727 & -4.85093347683508 \tabularnewline
Winsorized Mean ( 3 / 20 ) & -29.8833333333333 & 5.50921629802785 & -5.42424397895409 \tabularnewline
Winsorized Mean ( 4 / 20 ) & -29.2166666666667 & 5.07481271629421 & -5.75719111226663 \tabularnewline
Winsorized Mean ( 5 / 20 ) & -29.2166666666667 & 5.00982603229124 & -5.83187249983298 \tabularnewline
Winsorized Mean ( 6 / 20 ) & -29.0166666666667 & 4.89491213235003 & -5.9279239099918 \tabularnewline
Winsorized Mean ( 7 / 20 ) & -30.3 & 4.67601766922858 & -6.4798728626273 \tabularnewline
Winsorized Mean ( 8 / 20 ) & -30.5666666666667 & 4.63482071805504 & -6.59500518490253 \tabularnewline
Winsorized Mean ( 9 / 20 ) & -30.5666666666667 & 4.63482071805504 & -6.59500518490253 \tabularnewline
Winsorized Mean ( 10 / 20 ) & -29.9 & 4.50684977731167 & -6.63434582411028 \tabularnewline
Winsorized Mean ( 11 / 20 ) & -30.0833333333333 & 4.47884491683706 & -6.71676155167659 \tabularnewline
Winsorized Mean ( 12 / 20 ) & -29.6833333333333 & 4.20300482145693 & -7.06240763317609 \tabularnewline
Winsorized Mean ( 13 / 20 ) & -29.9 & 3.95980510848389 & -7.55087666712161 \tabularnewline
Winsorized Mean ( 14 / 20 ) & -28.5 & 3.71365627621258 & -7.67437745451932 \tabularnewline
Winsorized Mean ( 15 / 20 ) & -27.75 & 3.35630151908401 & -8.26802950873538 \tabularnewline
Winsorized Mean ( 16 / 20 ) & -27.75 & 3.35630151908401 & -8.26802950873538 \tabularnewline
Winsorized Mean ( 17 / 20 ) & -26.9 & 3.21970451674393 & -8.35480394555083 \tabularnewline
Winsorized Mean ( 18 / 20 ) & -26.3 & 3.12546493716476 & -8.41474805468713 \tabularnewline
Winsorized Mean ( 19 / 20 ) & -25.9833333333333 & 3.07638092337204 & -8.4460715303269 \tabularnewline
Winsorized Mean ( 20 / 20 ) & -28.65 & 2.71226811084095 & -10.5631150126663 \tabularnewline
Trimmed Mean ( 1 / 20 ) & -29.1206896551724 & 5.85296123552562 & -4.97537716095215 \tabularnewline
Trimmed Mean ( 2 / 20 ) & -29.1428571428571 & 5.46027142250467 & -5.3372543025506 \tabularnewline
Trimmed Mean ( 3 / 20 ) & -29.2037037037037 & 5.0965095158377 & -5.7301381686724 \tabularnewline
Trimmed Mean ( 4 / 20 ) & -28.9423076923077 & 4.88521436096648 & -5.92447036174311 \tabularnewline
Trimmed Mean ( 5 / 20 ) & -28.86 & 4.79455558579793 & -6.01932743995855 \tabularnewline
Trimmed Mean ( 6 / 20 ) & -28.7708333333333 & 4.69893601048308 & -6.12283999380862 \tabularnewline
Trimmed Mean ( 7 / 20 ) & -28.7173913043478 & 4.60923909839385 & -6.23039740211237 \tabularnewline
Trimmed Mean ( 8 / 20 ) & -28.4090909090909 & 4.55043595962418 & -6.24315805368179 \tabularnewline
Trimmed Mean ( 9 / 20 ) & -28.0238095238095 & 4.47777945207384 & -6.25841666025569 \tabularnewline
Trimmed Mean ( 10 / 20 ) & -27.6 & 4.37530951286116 & -6.30812515523078 \tabularnewline
Trimmed Mean ( 11 / 20 ) & -27.2368421052632 & 4.26895142223642 & -6.3802183279458 \tabularnewline
Trimmed Mean ( 12 / 20 ) & -26.8055555555556 & 4.12557248445776 & -6.49741476038536 \tabularnewline
Trimmed Mean ( 13 / 20 ) & -26.3823529411765 & 4.00245350464328 & -6.5915451386431 \tabularnewline
Trimmed Mean ( 14 / 20 ) & -25.875 & 3.89135466502762 & -6.64935536011244 \tabularnewline
Trimmed Mean ( 15 / 20 ) & -25.5 & 3.80161792538055 & -6.70767039206009 \tabularnewline
Trimmed Mean ( 16 / 20 ) & -25.1785714285714 & 3.76739477842152 & -6.68328457978085 \tabularnewline
Trimmed Mean ( 17 / 20 ) & -24.8076923076923 & 3.69615984951085 & -6.71174768347081 \tabularnewline
Trimmed Mean ( 18 / 20 ) & -24.5 & 3.61809061662984 & -6.77152747014974 \tabularnewline
Trimmed Mean ( 19 / 20 ) & -24.2272727272727 & 3.51060965720902 & -6.90115822974569 \tabularnewline
Trimmed Mean ( 20 / 20 ) & -23.95 & 3.33204141630923 & -7.18778580685485 \tabularnewline
Median & -21 &  &  \tabularnewline
Midrange & -27.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & -26.8064516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & -25.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function & -26.8064516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & -25.5 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & -25.5 &  &  \tabularnewline
Midmean - Closest Observation & -26.8064516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & -25.5 &  &  \tabularnewline
Midmean - MS Excel (old versions) & -25 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49622&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]-29.0666666666667[/C][C]6.28736813911519[/C][C]-4.62302604580065[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/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]56.3666568105649[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]-29.1[/C][C]6.16806519490412[/C][C]-4.71784896567592[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]-29.0333333333333[/C][C]5.9851023461727[/C][C]-4.85093347683508[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]-29.8833333333333[/C][C]5.50921629802785[/C][C]-5.42424397895409[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]-29.2166666666667[/C][C]5.07481271629421[/C][C]-5.75719111226663[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]-29.2166666666667[/C][C]5.00982603229124[/C][C]-5.83187249983298[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]-29.0166666666667[/C][C]4.89491213235003[/C][C]-5.9279239099918[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]-30.3[/C][C]4.67601766922858[/C][C]-6.4798728626273[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]-30.5666666666667[/C][C]4.63482071805504[/C][C]-6.59500518490253[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]-30.5666666666667[/C][C]4.63482071805504[/C][C]-6.59500518490253[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]-29.9[/C][C]4.50684977731167[/C][C]-6.63434582411028[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]-30.0833333333333[/C][C]4.47884491683706[/C][C]-6.71676155167659[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]-29.6833333333333[/C][C]4.20300482145693[/C][C]-7.06240763317609[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]-29.9[/C][C]3.95980510848389[/C][C]-7.55087666712161[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]-28.5[/C][C]3.71365627621258[/C][C]-7.67437745451932[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]-27.75[/C][C]3.35630151908401[/C][C]-8.26802950873538[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]-27.75[/C][C]3.35630151908401[/C][C]-8.26802950873538[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]-26.9[/C][C]3.21970451674393[/C][C]-8.35480394555083[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]-26.3[/C][C]3.12546493716476[/C][C]-8.41474805468713[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]-25.9833333333333[/C][C]3.07638092337204[/C][C]-8.4460715303269[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]-28.65[/C][C]2.71226811084095[/C][C]-10.5631150126663[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]-29.1206896551724[/C][C]5.85296123552562[/C][C]-4.97537716095215[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]-29.1428571428571[/C][C]5.46027142250467[/C][C]-5.3372543025506[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]-29.2037037037037[/C][C]5.0965095158377[/C][C]-5.7301381686724[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]-28.9423076923077[/C][C]4.88521436096648[/C][C]-5.92447036174311[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]-28.86[/C][C]4.79455558579793[/C][C]-6.01932743995855[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]-28.7708333333333[/C][C]4.69893601048308[/C][C]-6.12283999380862[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]-28.7173913043478[/C][C]4.60923909839385[/C][C]-6.23039740211237[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]-28.4090909090909[/C][C]4.55043595962418[/C][C]-6.24315805368179[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]-28.0238095238095[/C][C]4.47777945207384[/C][C]-6.25841666025569[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]-27.6[/C][C]4.37530951286116[/C][C]-6.30812515523078[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]-27.2368421052632[/C][C]4.26895142223642[/C][C]-6.3802183279458[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]-26.8055555555556[/C][C]4.12557248445776[/C][C]-6.49741476038536[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]-26.3823529411765[/C][C]4.00245350464328[/C][C]-6.5915451386431[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]-25.875[/C][C]3.89135466502762[/C][C]-6.64935536011244[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]-25.5[/C][C]3.80161792538055[/C][C]-6.70767039206009[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]-25.1785714285714[/C][C]3.76739477842152[/C][C]-6.68328457978085[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]-24.8076923076923[/C][C]3.69615984951085[/C][C]-6.71174768347081[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]-24.5[/C][C]3.61809061662984[/C][C]-6.77152747014974[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]-24.2272727272727[/C][C]3.51060965720902[/C][C]-6.90115822974569[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]-23.95[/C][C]3.33204141630923[/C][C]-7.18778580685485[/C][/ROW]
[ROW][C]Median[/C][C]-21[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-27.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]-26.8064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]-25.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]-26.8064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]-25.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]-25.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]-26.8064516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]-25.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]-25[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49622&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49622&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 Mean-29.06666666666676.28736813911519-4.62302604580065
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean56.3666568105649
Winsorized Mean ( 1 / 20 )-29.16.16806519490412-4.71784896567592
Winsorized Mean ( 2 / 20 )-29.03333333333335.9851023461727-4.85093347683508
Winsorized Mean ( 3 / 20 )-29.88333333333335.50921629802785-5.42424397895409
Winsorized Mean ( 4 / 20 )-29.21666666666675.07481271629421-5.75719111226663
Winsorized Mean ( 5 / 20 )-29.21666666666675.00982603229124-5.83187249983298
Winsorized Mean ( 6 / 20 )-29.01666666666674.89491213235003-5.9279239099918
Winsorized Mean ( 7 / 20 )-30.34.67601766922858-6.4798728626273
Winsorized Mean ( 8 / 20 )-30.56666666666674.63482071805504-6.59500518490253
Winsorized Mean ( 9 / 20 )-30.56666666666674.63482071805504-6.59500518490253
Winsorized Mean ( 10 / 20 )-29.94.50684977731167-6.63434582411028
Winsorized Mean ( 11 / 20 )-30.08333333333334.47884491683706-6.71676155167659
Winsorized Mean ( 12 / 20 )-29.68333333333334.20300482145693-7.06240763317609
Winsorized Mean ( 13 / 20 )-29.93.95980510848389-7.55087666712161
Winsorized Mean ( 14 / 20 )-28.53.71365627621258-7.67437745451932
Winsorized Mean ( 15 / 20 )-27.753.35630151908401-8.26802950873538
Winsorized Mean ( 16 / 20 )-27.753.35630151908401-8.26802950873538
Winsorized Mean ( 17 / 20 )-26.93.21970451674393-8.35480394555083
Winsorized Mean ( 18 / 20 )-26.33.12546493716476-8.41474805468713
Winsorized Mean ( 19 / 20 )-25.98333333333333.07638092337204-8.4460715303269
Winsorized Mean ( 20 / 20 )-28.652.71226811084095-10.5631150126663
Trimmed Mean ( 1 / 20 )-29.12068965517245.85296123552562-4.97537716095215
Trimmed Mean ( 2 / 20 )-29.14285714285715.46027142250467-5.3372543025506
Trimmed Mean ( 3 / 20 )-29.20370370370375.0965095158377-5.7301381686724
Trimmed Mean ( 4 / 20 )-28.94230769230774.88521436096648-5.92447036174311
Trimmed Mean ( 5 / 20 )-28.864.79455558579793-6.01932743995855
Trimmed Mean ( 6 / 20 )-28.77083333333334.69893601048308-6.12283999380862
Trimmed Mean ( 7 / 20 )-28.71739130434784.60923909839385-6.23039740211237
Trimmed Mean ( 8 / 20 )-28.40909090909094.55043595962418-6.24315805368179
Trimmed Mean ( 9 / 20 )-28.02380952380954.47777945207384-6.25841666025569
Trimmed Mean ( 10 / 20 )-27.64.37530951286116-6.30812515523078
Trimmed Mean ( 11 / 20 )-27.23684210526324.26895142223642-6.3802183279458
Trimmed Mean ( 12 / 20 )-26.80555555555564.12557248445776-6.49741476038536
Trimmed Mean ( 13 / 20 )-26.38235294117654.00245350464328-6.5915451386431
Trimmed Mean ( 14 / 20 )-25.8753.89135466502762-6.64935536011244
Trimmed Mean ( 15 / 20 )-25.53.80161792538055-6.70767039206009
Trimmed Mean ( 16 / 20 )-25.17857142857143.76739477842152-6.68328457978085
Trimmed Mean ( 17 / 20 )-24.80769230769233.69615984951085-6.71174768347081
Trimmed Mean ( 18 / 20 )-24.53.61809061662984-6.77152747014974
Trimmed Mean ( 19 / 20 )-24.22727272727273.51060965720902-6.90115822974569
Trimmed Mean ( 20 / 20 )-23.953.33204141630923-7.18778580685485
Median-21
Midrange-27.5
Midmean - Weighted Average at Xnp-26.8064516129032
Midmean - Weighted Average at X(n+1)p-25.5
Midmean - Empirical Distribution Function-26.8064516129032
Midmean - Empirical Distribution Function - Averaging-25.5
Midmean - Empirical Distribution Function - Interpolation-25.5
Midmean - Closest Observation-26.8064516129032
Midmean - True Basic - Statistics Graphics Toolkit-25.5
Midmean - MS Excel (old versions)-25
Number of observations60



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')