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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 computationSun, 04 Nov 2007 04:29:40 -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/2007/Nov/04/zvljlv7y20ev5kc1194175824.htm/, Retrieved Sun, 05 May 2024 11:25:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=393, Retrieved Sun, 05 May 2024 11:25:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsScheidingen
Estimated Impact173
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper WS2 Q3] [2007-11-04 11:29:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2529
2196
3202
2718
2728
2354
2697
2651
2067
2641
2539
2294
2712
2314
3092
2677
2813
2668
2939
2617
2231
2481
2421
2408
2560
2100
3315
2801
2403
3024
2507
2980
2211
2471
2594
2452
2232
2373
3127
2802
2641
2787
2619
2806
2193
2323
2529
2412
2262
2154
3230
2295
2715
2733
2317
2730
1913
2390
2484
1960




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=393&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=393&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=393&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean2557.2333333333340.254194901355463.5271265417167
Geometric Mean2538.73307144390
Harmonic Mean2520.3928715651
Quadratic Mean2575.85829061564
Winsorized Mean ( 1 / 20 )2556.639.617694215025464.5317717412839
Winsorized Mean ( 2 / 20 )2559.2333333333338.508685399843366.4586003588621
Winsorized Mean ( 3 / 20 )2557.1333333333337.138855851196768.8533148026674
Winsorized Mean ( 4 / 20 )2558.435.820197566070471.4233916572076
Winsorized Mean ( 5 / 20 )2555.9833333333333.832158770071375.54892818706
Winsorized Mean ( 6 / 20 )2551.8833333333332.773913869419977.8632464679296
Winsorized Mean ( 7 / 20 )2548.8531.419944231017181.1220408686731
Winsorized Mean ( 8 / 20 )2534.7166666666727.710683367485491.4707383088503
Winsorized Mean ( 9 / 20 )2533.8166666666727.505382027698592.1207589160207
Winsorized Mean ( 10 / 20 )2538.1526.486014057950895.8298215219016
Winsorized Mean ( 11 / 20 )2543.8333333333325.447766006605299.9629331970854
Winsorized Mean ( 12 / 20 )2541.2333333333324.9407135063766101.890963652007
Winsorized Mean ( 13 / 20 )2533.6522.3889200931589113.165350961888
Winsorized Mean ( 14 / 20 )2533.6522.1673759497414114.296342776176
Winsorized Mean ( 15 / 20 )2534.6521.8449314733063116.029203529306
Winsorized Mean ( 16 / 20 )2540.2520.1165899015101126.276372508310
Winsorized Mean ( 17 / 20 )2544.7833333333319.1571421925823132.837315072949
Winsorized Mean ( 18 / 20 )2548.9833333333318.2570857951805139.616111899207
Winsorized Mean ( 19 / 20 )2548.3516.9409213558230150.425702739247
Winsorized Mean ( 20 / 20 )2543.3515.7215499480287161.774761929176
Trimmed Mean ( 1 / 20 )2555.2758620689737.891922859224567.4358984515589
Trimmed Mean ( 2 / 20 )2553.8571428571435.752707903723671.4311528439825
Trimmed Mean ( 3 / 20 )2550.8703703703733.850434032730875.357094916534
Trimmed Mean ( 4 / 20 )2548.4615384615432.166123068482479.2281224888621
Trimmed Mean ( 5 / 20 )2545.4830.589036851627283.2154347437257
Trimmed Mean ( 6 / 20 )2542.8541666666729.31611140530986.7391357438412
Trimmed Mean ( 7 / 20 )2540.8913043478328.038124980568290.622725524934
Trimmed Mean ( 8 / 20 )2539.3409090909126.809541688775294.71780377932
Trimmed Mean ( 9 / 20 )2540.1666666666726.28670028154696.6331505841353
Trimmed Mean ( 10 / 20 )2541.22525.623093737726399.1771339562488
Trimmed Mean ( 11 / 20 )2541.7105263157924.9925709557803101.698642000972
Trimmed Mean ( 12 / 20 )2541.3888888888924.3915246071897104.191473465328
Trimmed Mean ( 13 / 20 )2541.4117647058823.6695957734126107.370306997831
Trimmed Mean ( 14 / 20 )2542.5312523.3343935021009108.960674284124
Trimmed Mean ( 15 / 20 )2543.822.8458301233067111.346358887825
Trimmed Mean ( 16 / 20 )2545.1071428571422.1631360886712114.835153864262
Trimmed Mean ( 17 / 20 )2545.8076923076921.6590374976693117.540204294934
Trimmed Mean ( 18 / 20 )2545.9583333333321.1291301739616120.495179516232
Trimmed Mean ( 19 / 20 )2545.520.5201569152587124.048759008620
Trimmed Mean ( 20 / 20 )2545.0519.9522423222106127.557091523838
Median2534
Midrange2614
Midmean - Weighted Average at Xnp2536.48387096774
Midmean - Weighted Average at X(n+1)p2543.8
Midmean - Empirical Distribution Function2536.48387096774
Midmean - Empirical Distribution Function - Averaging2543.8
Midmean - Empirical Distribution Function - Interpolation2543.8
Midmean - Closest Observation2536.48387096774
Midmean - True Basic - Statistics Graphics Toolkit2543.8
Midmean - MS Excel (old versions)2542.53125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2557.23333333333 & 40.2541949013554 & 63.5271265417167 \tabularnewline
Geometric Mean & 2538.73307144390 &  &  \tabularnewline
Harmonic Mean & 2520.3928715651 &  &  \tabularnewline
Quadratic Mean & 2575.85829061564 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2556.6 & 39.6176942150254 & 64.5317717412839 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2559.23333333333 & 38.5086853998433 & 66.4586003588621 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2557.13333333333 & 37.1388558511967 & 68.8533148026674 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2558.4 & 35.8201975660704 & 71.4233916572076 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2555.98333333333 & 33.8321587700713 & 75.54892818706 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2551.88333333333 & 32.7739138694199 & 77.8632464679296 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2548.85 & 31.4199442310171 & 81.1220408686731 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2534.71666666667 & 27.7106833674854 & 91.4707383088503 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2533.81666666667 & 27.5053820276985 & 92.1207589160207 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2538.15 & 26.4860140579508 & 95.8298215219016 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2543.83333333333 & 25.4477660066052 & 99.9629331970854 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2541.23333333333 & 24.9407135063766 & 101.890963652007 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2533.65 & 22.3889200931589 & 113.165350961888 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2533.65 & 22.1673759497414 & 114.296342776176 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2534.65 & 21.8449314733063 & 116.029203529306 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2540.25 & 20.1165899015101 & 126.276372508310 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2544.78333333333 & 19.1571421925823 & 132.837315072949 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2548.98333333333 & 18.2570857951805 & 139.616111899207 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2548.35 & 16.9409213558230 & 150.425702739247 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2543.35 & 15.7215499480287 & 161.774761929176 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2555.27586206897 & 37.8919228592245 & 67.4358984515589 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2553.85714285714 & 35.7527079037236 & 71.4311528439825 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2550.87037037037 & 33.8504340327308 & 75.357094916534 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2548.46153846154 & 32.1661230684824 & 79.2281224888621 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2545.48 & 30.5890368516272 & 83.2154347437257 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2542.85416666667 & 29.316111405309 & 86.7391357438412 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2540.89130434783 & 28.0381249805682 & 90.622725524934 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2539.34090909091 & 26.8095416887752 & 94.71780377932 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2540.16666666667 & 26.286700281546 & 96.6331505841353 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2541.225 & 25.6230937377263 & 99.1771339562488 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2541.71052631579 & 24.9925709557803 & 101.698642000972 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2541.38888888889 & 24.3915246071897 & 104.191473465328 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2541.41176470588 & 23.6695957734126 & 107.370306997831 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2542.53125 & 23.3343935021009 & 108.960674284124 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2543.8 & 22.8458301233067 & 111.346358887825 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2545.10714285714 & 22.1631360886712 & 114.835153864262 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2545.80769230769 & 21.6590374976693 & 117.540204294934 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2545.95833333333 & 21.1291301739616 & 120.495179516232 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2545.5 & 20.5201569152587 & 124.048759008620 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2545.05 & 19.9522423222106 & 127.557091523838 \tabularnewline
Median & 2534 &  &  \tabularnewline
Midrange & 2614 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2536.48387096774 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2543.8 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2536.48387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2543.8 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2543.8 &  &  \tabularnewline
Midmean - Closest Observation & 2536.48387096774 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2543.8 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2542.53125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=393&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]2557.23333333333[/C][C]40.2541949013554[/C][C]63.5271265417167[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2538.73307144390[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2520.3928715651[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2575.85829061564[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2556.6[/C][C]39.6176942150254[/C][C]64.5317717412839[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2559.23333333333[/C][C]38.5086853998433[/C][C]66.4586003588621[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2557.13333333333[/C][C]37.1388558511967[/C][C]68.8533148026674[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2558.4[/C][C]35.8201975660704[/C][C]71.4233916572076[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2555.98333333333[/C][C]33.8321587700713[/C][C]75.54892818706[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2551.88333333333[/C][C]32.7739138694199[/C][C]77.8632464679296[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2548.85[/C][C]31.4199442310171[/C][C]81.1220408686731[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2534.71666666667[/C][C]27.7106833674854[/C][C]91.4707383088503[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2533.81666666667[/C][C]27.5053820276985[/C][C]92.1207589160207[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2538.15[/C][C]26.4860140579508[/C][C]95.8298215219016[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2543.83333333333[/C][C]25.4477660066052[/C][C]99.9629331970854[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2541.23333333333[/C][C]24.9407135063766[/C][C]101.890963652007[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2533.65[/C][C]22.3889200931589[/C][C]113.165350961888[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2533.65[/C][C]22.1673759497414[/C][C]114.296342776176[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2534.65[/C][C]21.8449314733063[/C][C]116.029203529306[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2540.25[/C][C]20.1165899015101[/C][C]126.276372508310[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2544.78333333333[/C][C]19.1571421925823[/C][C]132.837315072949[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2548.98333333333[/C][C]18.2570857951805[/C][C]139.616111899207[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2548.35[/C][C]16.9409213558230[/C][C]150.425702739247[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2543.35[/C][C]15.7215499480287[/C][C]161.774761929176[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2555.27586206897[/C][C]37.8919228592245[/C][C]67.4358984515589[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2553.85714285714[/C][C]35.7527079037236[/C][C]71.4311528439825[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2550.87037037037[/C][C]33.8504340327308[/C][C]75.357094916534[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2548.46153846154[/C][C]32.1661230684824[/C][C]79.2281224888621[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2545.48[/C][C]30.5890368516272[/C][C]83.2154347437257[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2542.85416666667[/C][C]29.316111405309[/C][C]86.7391357438412[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2540.89130434783[/C][C]28.0381249805682[/C][C]90.622725524934[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2539.34090909091[/C][C]26.8095416887752[/C][C]94.71780377932[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2540.16666666667[/C][C]26.286700281546[/C][C]96.6331505841353[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2541.225[/C][C]25.6230937377263[/C][C]99.1771339562488[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2541.71052631579[/C][C]24.9925709557803[/C][C]101.698642000972[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2541.38888888889[/C][C]24.3915246071897[/C][C]104.191473465328[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2541.41176470588[/C][C]23.6695957734126[/C][C]107.370306997831[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2542.53125[/C][C]23.3343935021009[/C][C]108.960674284124[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2543.8[/C][C]22.8458301233067[/C][C]111.346358887825[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2545.10714285714[/C][C]22.1631360886712[/C][C]114.835153864262[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2545.80769230769[/C][C]21.6590374976693[/C][C]117.540204294934[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2545.95833333333[/C][C]21.1291301739616[/C][C]120.495179516232[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2545.5[/C][C]20.5201569152587[/C][C]124.048759008620[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2545.05[/C][C]19.9522423222106[/C][C]127.557091523838[/C][/ROW]
[ROW][C]Median[/C][C]2534[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2614[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2536.48387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2543.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2536.48387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2543.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2543.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2536.48387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2543.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2542.53125[/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=393&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=393&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 Mean2557.2333333333340.254194901355463.5271265417167
Geometric Mean2538.73307144390
Harmonic Mean2520.3928715651
Quadratic Mean2575.85829061564
Winsorized Mean ( 1 / 20 )2556.639.617694215025464.5317717412839
Winsorized Mean ( 2 / 20 )2559.2333333333338.508685399843366.4586003588621
Winsorized Mean ( 3 / 20 )2557.1333333333337.138855851196768.8533148026674
Winsorized Mean ( 4 / 20 )2558.435.820197566070471.4233916572076
Winsorized Mean ( 5 / 20 )2555.9833333333333.832158770071375.54892818706
Winsorized Mean ( 6 / 20 )2551.8833333333332.773913869419977.8632464679296
Winsorized Mean ( 7 / 20 )2548.8531.419944231017181.1220408686731
Winsorized Mean ( 8 / 20 )2534.7166666666727.710683367485491.4707383088503
Winsorized Mean ( 9 / 20 )2533.8166666666727.505382027698592.1207589160207
Winsorized Mean ( 10 / 20 )2538.1526.486014057950895.8298215219016
Winsorized Mean ( 11 / 20 )2543.8333333333325.447766006605299.9629331970854
Winsorized Mean ( 12 / 20 )2541.2333333333324.9407135063766101.890963652007
Winsorized Mean ( 13 / 20 )2533.6522.3889200931589113.165350961888
Winsorized Mean ( 14 / 20 )2533.6522.1673759497414114.296342776176
Winsorized Mean ( 15 / 20 )2534.6521.8449314733063116.029203529306
Winsorized Mean ( 16 / 20 )2540.2520.1165899015101126.276372508310
Winsorized Mean ( 17 / 20 )2544.7833333333319.1571421925823132.837315072949
Winsorized Mean ( 18 / 20 )2548.9833333333318.2570857951805139.616111899207
Winsorized Mean ( 19 / 20 )2548.3516.9409213558230150.425702739247
Winsorized Mean ( 20 / 20 )2543.3515.7215499480287161.774761929176
Trimmed Mean ( 1 / 20 )2555.2758620689737.891922859224567.4358984515589
Trimmed Mean ( 2 / 20 )2553.8571428571435.752707903723671.4311528439825
Trimmed Mean ( 3 / 20 )2550.8703703703733.850434032730875.357094916534
Trimmed Mean ( 4 / 20 )2548.4615384615432.166123068482479.2281224888621
Trimmed Mean ( 5 / 20 )2545.4830.589036851627283.2154347437257
Trimmed Mean ( 6 / 20 )2542.8541666666729.31611140530986.7391357438412
Trimmed Mean ( 7 / 20 )2540.8913043478328.038124980568290.622725524934
Trimmed Mean ( 8 / 20 )2539.3409090909126.809541688775294.71780377932
Trimmed Mean ( 9 / 20 )2540.1666666666726.28670028154696.6331505841353
Trimmed Mean ( 10 / 20 )2541.22525.623093737726399.1771339562488
Trimmed Mean ( 11 / 20 )2541.7105263157924.9925709557803101.698642000972
Trimmed Mean ( 12 / 20 )2541.3888888888924.3915246071897104.191473465328
Trimmed Mean ( 13 / 20 )2541.4117647058823.6695957734126107.370306997831
Trimmed Mean ( 14 / 20 )2542.5312523.3343935021009108.960674284124
Trimmed Mean ( 15 / 20 )2543.822.8458301233067111.346358887825
Trimmed Mean ( 16 / 20 )2545.1071428571422.1631360886712114.835153864262
Trimmed Mean ( 17 / 20 )2545.8076923076921.6590374976693117.540204294934
Trimmed Mean ( 18 / 20 )2545.9583333333321.1291301739616120.495179516232
Trimmed Mean ( 19 / 20 )2545.520.5201569152587124.048759008620
Trimmed Mean ( 20 / 20 )2545.0519.9522423222106127.557091523838
Median2534
Midrange2614
Midmean - Weighted Average at Xnp2536.48387096774
Midmean - Weighted Average at X(n+1)p2543.8
Midmean - Empirical Distribution Function2536.48387096774
Midmean - Empirical Distribution Function - Averaging2543.8
Midmean - Empirical Distribution Function - Interpolation2543.8
Midmean - Closest Observation2536.48387096774
Midmean - True Basic - Statistics Graphics Toolkit2543.8
Midmean - MS Excel (old versions)2542.53125
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')