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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 17:12:15 -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/2012/Mar/07/t1331158834w6urcq81tnyy38p.htm/, Retrieved Mon, 29 Apr 2024 06:17:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163729, Retrieved Mon, 29 Apr 2024 06:17:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Goudkoers centrum...] [2012-03-07 22:12:15] [49d363860b48c50a69486db091fa88e4] [Current]
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Dataseries X:
15,579
16,348
15,928
16,171
15,937
15,713
15,594
15,683
16,438
17,032
17,696
17,745
19,394
20,148
20,108
18,584
18,441
18,391
19,178
18,079
18,483
19,644
19,195
19,650
20,830
23,595
22,937
21,814
21,928
21,777
21,383
21,467
22,052
22,680
24,320
24,977
25,204
25,739
26,434
27,525
30,695
32,436
30,160
30,236
31,293
31,077
32,226
33,865
32,810
32,242
32,700
32,819
33,947
34,148
35,261
39,506
41,591
39,148
41,216
40,225




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163729&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163729&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163729&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean24.79036666666670.98935504585605125.0570983293632
Geometric Mean23.7009122699725
Harmonic Mean22.714803902131
Quadratic Mean25.9289965186983
Winsorized Mean ( 1 / 20 )24.78436666666670.98753484297155925.097207296594
Winsorized Mean ( 2 / 20 )24.75430.97798012362388525.31165961561
Winsorized Mean ( 3 / 20 )24.719850.96827131674907325.5298794587821
Winsorized Mean ( 4 / 20 )24.71031666666670.9598989855316425.7426219207648
Winsorized Mean ( 5 / 20 )24.387150.88443418499329127.5737306560409
Winsorized Mean ( 6 / 20 )24.299250.85822882144427428.3132532872852
Winsorized Mean ( 7 / 20 )24.296450.85039974097429828.5706225311919
Winsorized Mean ( 8 / 20 )24.29751666666670.84640606798167328.706690069704
Winsorized Mean ( 9 / 20 )24.22971666666670.80335519407569630.1606522810178
Winsorized Mean ( 10 / 20 )24.33888333333330.78675595290427930.9357472841321
Winsorized Mean ( 11 / 20 )24.32770.7818017591211831.1174792281699
Winsorized Mean ( 12 / 20 )24.34170.76284610087213531.9090573736577
Winsorized Mean ( 13 / 20 )24.36726666666670.74601234137512332.663355973107
Winsorized Mean ( 14 / 20 )24.37520.74376352052468732.7727823795452
Winsorized Mean ( 15 / 20 )24.152450.70132194281353534.4384633155868
Winsorized Mean ( 16 / 20 )24.12178333333330.68773185637025635.0744016143798
Winsorized Mean ( 17 / 20 )24.181850.64668185876426337.3937349134995
Winsorized Mean ( 18 / 20 )24.049250.62265962653973238.6234291978226
Winsorized Mean ( 19 / 20 )24.08820.61033280298168539.4673199315535
Winsorized Mean ( 20 / 20 )23.29320.45533714509823951.1559407150376
Trimmed Mean ( 1 / 20 )24.65951724137930.96786404748967625.4782862379671
Trimmed Mean ( 2 / 20 )24.525750.94312765151142426.0046982618905
Trimmed Mean ( 3 / 20 )24.39877777777780.9184226024202526.5659596284777
Trimmed Mean ( 4 / 20 )24.27528846153850.89190116325746227.2174647388939
Trimmed Mean ( 5 / 20 )24.144780.86139586400356528.029830428696
Trimmed Mean ( 6 / 20 )24.08418750.84917375239228628.3619075980036
Trimmed Mean ( 7 / 20 )24.03743478260870.84063275837106528.5944540505264
Trimmed Mean ( 8 / 20 )23.98697727272730.83062242542827628.8783164749728
Trimmed Mean ( 9 / 20 )23.93152380952380.81744298798390829.2760769390745
Trimmed Mean ( 10 / 20 )23.8818250.81018096734974529.4771488870221
Trimmed Mean ( 11 / 20 )23.80965789473680.8026444311752329.6640168048943
Trimmed Mean ( 12 / 20 )23.73116666666670.79170235257915329.9748593513167
Trimmed Mean ( 13 / 20 )23.64138235294120.77950776439360830.3286040663523
Trimmed Mean ( 14 / 20 )23.53668750.76456002190261930.7846170682958
Trimmed Mean ( 15 / 20 )23.41690.74121285873494131.5926791124032
Trimmed Mean ( 16 / 20 )23.31182142857140.71942940546928832.4032090589416
Trimmed Mean ( 17 / 20 )23.1950.68868252370852233.6802506256382
Trimmed Mean ( 18 / 20 )23.0498750.65302056338580235.2973187865483
Trimmed Mean ( 19 / 20 )22.89845454545450.60371813227279137.9290488745961
Trimmed Mean ( 20 / 20 )22.71060.51979421231665843.6915214942115
Median21.99
Midrange28.585
Midmean - Weighted Average at Xnp23.2563870967742
Midmean - Weighted Average at X(n+1)p23.4169
Midmean - Empirical Distribution Function23.2563870967742
Midmean - Empirical Distribution Function - Averaging23.4169
Midmean - Empirical Distribution Function - Interpolation23.4169
Midmean - Closest Observation23.2563870967742
Midmean - True Basic - Statistics Graphics Toolkit23.4169
Midmean - MS Excel (old versions)23.5366875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 24.7903666666667 & 0.989355045856051 & 25.0570983293632 \tabularnewline
Geometric Mean & 23.7009122699725 &  &  \tabularnewline
Harmonic Mean & 22.714803902131 &  &  \tabularnewline
Quadratic Mean & 25.9289965186983 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 24.7843666666667 & 0.987534842971559 & 25.097207296594 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 24.7543 & 0.977980123623885 & 25.31165961561 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 24.71985 & 0.968271316749073 & 25.5298794587821 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 24.7103166666667 & 0.95989898553164 & 25.7426219207648 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 24.38715 & 0.884434184993291 & 27.5737306560409 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 24.29925 & 0.858228821444274 & 28.3132532872852 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 24.29645 & 0.850399740974298 & 28.5706225311919 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 24.2975166666667 & 0.846406067981673 & 28.706690069704 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 24.2297166666667 & 0.803355194075696 & 30.1606522810178 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 24.3388833333333 & 0.786755952904279 & 30.9357472841321 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 24.3277 & 0.78180175912118 & 31.1174792281699 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 24.3417 & 0.762846100872135 & 31.9090573736577 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 24.3672666666667 & 0.746012341375123 & 32.663355973107 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 24.3752 & 0.743763520524687 & 32.7727823795452 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 24.15245 & 0.701321942813535 & 34.4384633155868 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 24.1217833333333 & 0.687731856370256 & 35.0744016143798 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 24.18185 & 0.646681858764263 & 37.3937349134995 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 24.04925 & 0.622659626539732 & 38.6234291978226 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 24.0882 & 0.610332802981685 & 39.4673199315535 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 23.2932 & 0.455337145098239 & 51.1559407150376 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 24.6595172413793 & 0.967864047489676 & 25.4782862379671 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 24.52575 & 0.943127651511424 & 26.0046982618905 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 24.3987777777778 & 0.91842260242025 & 26.5659596284777 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 24.2752884615385 & 0.891901163257462 & 27.2174647388939 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 24.14478 & 0.861395864003565 & 28.029830428696 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 24.0841875 & 0.849173752392286 & 28.3619075980036 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 24.0374347826087 & 0.840632758371065 & 28.5944540505264 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 23.9869772727273 & 0.830622425428276 & 28.8783164749728 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 23.9315238095238 & 0.817442987983908 & 29.2760769390745 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 23.881825 & 0.810180967349745 & 29.4771488870221 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 23.8096578947368 & 0.80264443117523 & 29.6640168048943 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 23.7311666666667 & 0.791702352579153 & 29.9748593513167 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 23.6413823529412 & 0.779507764393608 & 30.3286040663523 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 23.5366875 & 0.764560021902619 & 30.7846170682958 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 23.4169 & 0.741212858734941 & 31.5926791124032 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 23.3118214285714 & 0.719429405469288 & 32.4032090589416 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 23.195 & 0.688682523708522 & 33.6802506256382 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 23.049875 & 0.653020563385802 & 35.2973187865483 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 22.8984545454545 & 0.603718132272791 & 37.9290488745961 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 22.7106 & 0.519794212316658 & 43.6915214942115 \tabularnewline
Median & 21.99 &  &  \tabularnewline
Midrange & 28.585 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 23.2563870967742 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 23.4169 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 23.2563870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 23.4169 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 23.4169 &  &  \tabularnewline
Midmean - Closest Observation & 23.2563870967742 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 23.4169 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 23.5366875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163729&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]24.7903666666667[/C][C]0.989355045856051[/C][C]25.0570983293632[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]23.7009122699725[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]22.714803902131[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]25.9289965186983[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]24.7843666666667[/C][C]0.987534842971559[/C][C]25.097207296594[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]24.7543[/C][C]0.977980123623885[/C][C]25.31165961561[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]24.71985[/C][C]0.968271316749073[/C][C]25.5298794587821[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]24.7103166666667[/C][C]0.95989898553164[/C][C]25.7426219207648[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]24.38715[/C][C]0.884434184993291[/C][C]27.5737306560409[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]24.29925[/C][C]0.858228821444274[/C][C]28.3132532872852[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]24.29645[/C][C]0.850399740974298[/C][C]28.5706225311919[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]24.2975166666667[/C][C]0.846406067981673[/C][C]28.706690069704[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]24.2297166666667[/C][C]0.803355194075696[/C][C]30.1606522810178[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]24.3388833333333[/C][C]0.786755952904279[/C][C]30.9357472841321[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]24.3277[/C][C]0.78180175912118[/C][C]31.1174792281699[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]24.3417[/C][C]0.762846100872135[/C][C]31.9090573736577[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]24.3672666666667[/C][C]0.746012341375123[/C][C]32.663355973107[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]24.3752[/C][C]0.743763520524687[/C][C]32.7727823795452[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]24.15245[/C][C]0.701321942813535[/C][C]34.4384633155868[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]24.1217833333333[/C][C]0.687731856370256[/C][C]35.0744016143798[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]24.18185[/C][C]0.646681858764263[/C][C]37.3937349134995[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]24.04925[/C][C]0.622659626539732[/C][C]38.6234291978226[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]24.0882[/C][C]0.610332802981685[/C][C]39.4673199315535[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]23.2932[/C][C]0.455337145098239[/C][C]51.1559407150376[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]24.6595172413793[/C][C]0.967864047489676[/C][C]25.4782862379671[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]24.52575[/C][C]0.943127651511424[/C][C]26.0046982618905[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]24.3987777777778[/C][C]0.91842260242025[/C][C]26.5659596284777[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]24.2752884615385[/C][C]0.891901163257462[/C][C]27.2174647388939[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]24.14478[/C][C]0.861395864003565[/C][C]28.029830428696[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]24.0841875[/C][C]0.849173752392286[/C][C]28.3619075980036[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]24.0374347826087[/C][C]0.840632758371065[/C][C]28.5944540505264[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]23.9869772727273[/C][C]0.830622425428276[/C][C]28.8783164749728[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]23.9315238095238[/C][C]0.817442987983908[/C][C]29.2760769390745[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]23.881825[/C][C]0.810180967349745[/C][C]29.4771488870221[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]23.8096578947368[/C][C]0.80264443117523[/C][C]29.6640168048943[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]23.7311666666667[/C][C]0.791702352579153[/C][C]29.9748593513167[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]23.6413823529412[/C][C]0.779507764393608[/C][C]30.3286040663523[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]23.5366875[/C][C]0.764560021902619[/C][C]30.7846170682958[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]23.4169[/C][C]0.741212858734941[/C][C]31.5926791124032[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]23.3118214285714[/C][C]0.719429405469288[/C][C]32.4032090589416[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]23.195[/C][C]0.688682523708522[/C][C]33.6802506256382[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]23.049875[/C][C]0.653020563385802[/C][C]35.2973187865483[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]22.8984545454545[/C][C]0.603718132272791[/C][C]37.9290488745961[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]22.7106[/C][C]0.519794212316658[/C][C]43.6915214942115[/C][/ROW]
[ROW][C]Median[/C][C]21.99[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]28.585[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]23.2563870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]23.4169[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]23.2563870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]23.4169[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]23.4169[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]23.2563870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]23.4169[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]23.5366875[/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=163729&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163729&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 Mean24.79036666666670.98935504585605125.0570983293632
Geometric Mean23.7009122699725
Harmonic Mean22.714803902131
Quadratic Mean25.9289965186983
Winsorized Mean ( 1 / 20 )24.78436666666670.98753484297155925.097207296594
Winsorized Mean ( 2 / 20 )24.75430.97798012362388525.31165961561
Winsorized Mean ( 3 / 20 )24.719850.96827131674907325.5298794587821
Winsorized Mean ( 4 / 20 )24.71031666666670.9598989855316425.7426219207648
Winsorized Mean ( 5 / 20 )24.387150.88443418499329127.5737306560409
Winsorized Mean ( 6 / 20 )24.299250.85822882144427428.3132532872852
Winsorized Mean ( 7 / 20 )24.296450.85039974097429828.5706225311919
Winsorized Mean ( 8 / 20 )24.29751666666670.84640606798167328.706690069704
Winsorized Mean ( 9 / 20 )24.22971666666670.80335519407569630.1606522810178
Winsorized Mean ( 10 / 20 )24.33888333333330.78675595290427930.9357472841321
Winsorized Mean ( 11 / 20 )24.32770.7818017591211831.1174792281699
Winsorized Mean ( 12 / 20 )24.34170.76284610087213531.9090573736577
Winsorized Mean ( 13 / 20 )24.36726666666670.74601234137512332.663355973107
Winsorized Mean ( 14 / 20 )24.37520.74376352052468732.7727823795452
Winsorized Mean ( 15 / 20 )24.152450.70132194281353534.4384633155868
Winsorized Mean ( 16 / 20 )24.12178333333330.68773185637025635.0744016143798
Winsorized Mean ( 17 / 20 )24.181850.64668185876426337.3937349134995
Winsorized Mean ( 18 / 20 )24.049250.62265962653973238.6234291978226
Winsorized Mean ( 19 / 20 )24.08820.61033280298168539.4673199315535
Winsorized Mean ( 20 / 20 )23.29320.45533714509823951.1559407150376
Trimmed Mean ( 1 / 20 )24.65951724137930.96786404748967625.4782862379671
Trimmed Mean ( 2 / 20 )24.525750.94312765151142426.0046982618905
Trimmed Mean ( 3 / 20 )24.39877777777780.9184226024202526.5659596284777
Trimmed Mean ( 4 / 20 )24.27528846153850.89190116325746227.2174647388939
Trimmed Mean ( 5 / 20 )24.144780.86139586400356528.029830428696
Trimmed Mean ( 6 / 20 )24.08418750.84917375239228628.3619075980036
Trimmed Mean ( 7 / 20 )24.03743478260870.84063275837106528.5944540505264
Trimmed Mean ( 8 / 20 )23.98697727272730.83062242542827628.8783164749728
Trimmed Mean ( 9 / 20 )23.93152380952380.81744298798390829.2760769390745
Trimmed Mean ( 10 / 20 )23.8818250.81018096734974529.4771488870221
Trimmed Mean ( 11 / 20 )23.80965789473680.8026444311752329.6640168048943
Trimmed Mean ( 12 / 20 )23.73116666666670.79170235257915329.9748593513167
Trimmed Mean ( 13 / 20 )23.64138235294120.77950776439360830.3286040663523
Trimmed Mean ( 14 / 20 )23.53668750.76456002190261930.7846170682958
Trimmed Mean ( 15 / 20 )23.41690.74121285873494131.5926791124032
Trimmed Mean ( 16 / 20 )23.31182142857140.71942940546928832.4032090589416
Trimmed Mean ( 17 / 20 )23.1950.68868252370852233.6802506256382
Trimmed Mean ( 18 / 20 )23.0498750.65302056338580235.2973187865483
Trimmed Mean ( 19 / 20 )22.89845454545450.60371813227279137.9290488745961
Trimmed Mean ( 20 / 20 )22.71060.51979421231665843.6915214942115
Median21.99
Midrange28.585
Midmean - Weighted Average at Xnp23.2563870967742
Midmean - Weighted Average at X(n+1)p23.4169
Midmean - Empirical Distribution Function23.2563870967742
Midmean - Empirical Distribution Function - Averaging23.4169
Midmean - Empirical Distribution Function - Interpolation23.4169
Midmean - Closest Observation23.2563870967742
Midmean - True Basic - Statistics Graphics Toolkit23.4169
Midmean - MS Excel (old versions)23.5366875
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')