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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 computationThu, 16 Oct 2008 08:28:19 -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/2008/Oct/16/t1224167342vfsylqnwfezgecg.htm/, Retrieved Sun, 19 May 2024 13:03:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=16348, Retrieved Sun, 19 May 2024 13:03:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordskatrien bourdiaudhy reeks 2
Estimated Impact205
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [werkzoekenden <25...] [2008-10-13 19:30:09] [7173087adebe3e3a714c80ea2417b3eb]
- RMP     [Central Tendency] [central tendency] [2008-10-16 14:28:19] [95d95b0e883740fcbc85e18ec42dcafb] [Current]
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Dataseries X:
122860
117702
113537
108366
111078
150739
159129
157928
147768
137507
136919
136151
133001
125554
119647
114158
116193
152803
161761
160942
149470
139208
134588
130322
126611
122401
117352
112135
112879
148729
157230
157221
146681
136524
132111
125326
122716
116615
113719
110737
112093
143565
149946
149147
134339
122683
115614
116566
111272
104609
101802
94542
93051
124129
130374
123946
114971
105531
104919
104782




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16348&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]2 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=16348&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16348&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean127569.9833333332329.0799020446454.772695097898
Geometric Mean126327.932586707
Harmonic Mean125102.648644306
Quadratic Mean128818.293832372
Winsorized Mean ( 1 / 20 )127581.1833333332319.5969669273055.0014442820798
Winsorized Mean ( 2 / 20 )127762.752252.1613686182956.7289501455142
Winsorized Mean ( 3 / 20 )127843.052211.9359732952557.7969035014809
Winsorized Mean ( 4 / 20 )127808.052199.2463912680858.114475261822
Winsorized Mean ( 5 / 20 )127818.7166666672197.0548828474658.177298011331
Winsorized Mean ( 6 / 20 )127438.1166666672090.5665719075360.9586503386907
Winsorized Mean ( 7 / 20 )127528.0666666671985.4426047226464.231555403981
Winsorized Mean ( 8 / 20 )127738.4666666671914.8935167496066.7078694190234
Winsorized Mean ( 9 / 20 )127718.2166666671893.2652555137167.4592301816747
Winsorized Mean ( 10 / 20 )127696.7166666671878.0080303871767.9958310084228
Winsorized Mean ( 11 / 20 )127770.61841.1772353517269.3961436991111
Winsorized Mean ( 12 / 20 )127586.81803.1872207273370.7562689738545
Winsorized Mean ( 13 / 20 )127512.4833333331735.5715282454773.4700248639356
Winsorized Mean ( 14 / 20 )126938.951580.5539334038380.3129506163885
Winsorized Mean ( 15 / 20 )125895.21387.6952924708590.7225099653096
Winsorized Mean ( 16 / 20 )125558.6666666671297.9624187508896.735209627641
Winsorized Mean ( 17 / 20 )125622.4166666671238.13268008647101.46119126578
Winsorized Mean ( 18 / 20 )125696.8166666671191.95096813890105.454687337457
Winsorized Mean ( 19 / 20 )125762.051147.69430476467109.578003025629
Winsorized Mean ( 20 / 20 )125365.3833333331051.33890451280119.243550100934
Trimmed Mean ( 1 / 20 )127575.6379310342257.1083524633956.521716288808
Trimmed Mean ( 2 / 20 )127569.6964285712180.0456981567458.5169827111575
Trimmed Mean ( 3 / 20 )127462.4444444442129.4104307146959.8580915195688
Trimmed Mean ( 4 / 20 )127316.0576923082084.7319333903961.0707092135602
Trimmed Mean ( 5 / 20 )127168.462032.6075974150562.5641959430464
Trimmed Mean ( 6 / 20 )127005.8958333331966.3275001836264.5904081702938
Trimmed Mean ( 7 / 20 )126911.9347826091915.5642002343666.253031230737
Trimmed Mean ( 8 / 20 )126791.9090909091879.4699839387267.4615238202405
Trimmed Mean ( 9 / 20 )126622.8809523811849.167632442168.475609636946
Trimmed Mean ( 10 / 20 )126440.3251812.2226767105669.7708546664405
Trimmed Mean ( 11 / 20 )126241.9473684211764.2145714110871.5570256669223
Trimmed Mean ( 12 / 20 )126010.3333333331706.2717000190073.8512707747133
Trimmed Mean ( 13 / 20 )125778.51635.3299673307376.9132239442188
Trimmed Mean ( 14 / 20 )125528.406251553.8895318316080.7833527921621
Trimmed Mean ( 15 / 20 )125326.91487.4669569207484.2552497834602
Trimmed Mean ( 16 / 20 )125245.7142857141453.5636666329486.1645878751465
Trimmed Mean ( 17 / 20 )125200.5769230771427.1990192445387.7246797642493
Trimmed Mean ( 18 / 20 )125138.5416666671400.0032556628489.3844647578475
Trimmed Mean ( 19 / 20 )125053.9545454551365.4852355382891.5820627647852
Trimmed Mean ( 20 / 20 )124942.151317.4048737754794.8395990383243
Median124037.5
Midrange127406
Midmean - Weighted Average at Xnp124946.580645161
Midmean - Weighted Average at X(n+1)p125326.9
Midmean - Empirical Distribution Function124946.580645161
Midmean - Empirical Distribution Function - Averaging125326.9
Midmean - Empirical Distribution Function - Interpolation125326.9
Midmean - Closest Observation124946.580645161
Midmean - True Basic - Statistics Graphics Toolkit125326.9
Midmean - MS Excel (old versions)125528.40625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 127569.983333333 & 2329.07990204464 & 54.772695097898 \tabularnewline
Geometric Mean & 126327.932586707 &  &  \tabularnewline
Harmonic Mean & 125102.648644306 &  &  \tabularnewline
Quadratic Mean & 128818.293832372 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 127581.183333333 & 2319.59696692730 & 55.0014442820798 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 127762.75 & 2252.16136861829 & 56.7289501455142 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 127843.05 & 2211.93597329525 & 57.7969035014809 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 127808.05 & 2199.24639126808 & 58.114475261822 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 127818.716666667 & 2197.05488284746 & 58.177298011331 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 127438.116666667 & 2090.56657190753 & 60.9586503386907 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 127528.066666667 & 1985.44260472264 & 64.231555403981 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 127738.466666667 & 1914.89351674960 & 66.7078694190234 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 127718.216666667 & 1893.26525551371 & 67.4592301816747 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 127696.716666667 & 1878.00803038717 & 67.9958310084228 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 127770.6 & 1841.17723535172 & 69.3961436991111 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 127586.8 & 1803.18722072733 & 70.7562689738545 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 127512.483333333 & 1735.57152824547 & 73.4700248639356 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 126938.95 & 1580.55393340383 & 80.3129506163885 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 125895.2 & 1387.69529247085 & 90.7225099653096 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 125558.666666667 & 1297.96241875088 & 96.735209627641 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 125622.416666667 & 1238.13268008647 & 101.46119126578 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 125696.816666667 & 1191.95096813890 & 105.454687337457 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 125762.05 & 1147.69430476467 & 109.578003025629 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 125365.383333333 & 1051.33890451280 & 119.243550100934 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 127575.637931034 & 2257.10835246339 & 56.521716288808 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 127569.696428571 & 2180.04569815674 & 58.5169827111575 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 127462.444444444 & 2129.41043071469 & 59.8580915195688 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 127316.057692308 & 2084.73193339039 & 61.0707092135602 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 127168.46 & 2032.60759741505 & 62.5641959430464 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 127005.895833333 & 1966.32750018362 & 64.5904081702938 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 126911.934782609 & 1915.56420023436 & 66.253031230737 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 126791.909090909 & 1879.46998393872 & 67.4615238202405 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 126622.880952381 & 1849.1676324421 & 68.475609636946 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 126440.325 & 1812.22267671056 & 69.7708546664405 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 126241.947368421 & 1764.21457141108 & 71.5570256669223 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 126010.333333333 & 1706.27170001900 & 73.8512707747133 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 125778.5 & 1635.32996733073 & 76.9132239442188 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 125528.40625 & 1553.88953183160 & 80.7833527921621 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 125326.9 & 1487.46695692074 & 84.2552497834602 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 125245.714285714 & 1453.56366663294 & 86.1645878751465 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 125200.576923077 & 1427.19901924453 & 87.7246797642493 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 125138.541666667 & 1400.00325566284 & 89.3844647578475 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 125053.954545455 & 1365.48523553828 & 91.5820627647852 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 124942.15 & 1317.40487377547 & 94.8395990383243 \tabularnewline
Median & 124037.5 &  &  \tabularnewline
Midrange & 127406 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 124946.580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 125326.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 124946.580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 125326.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 125326.9 &  &  \tabularnewline
Midmean - Closest Observation & 124946.580645161 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 125326.9 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 125528.40625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=16348&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]127569.983333333[/C][C]2329.07990204464[/C][C]54.772695097898[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]126327.932586707[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]125102.648644306[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]128818.293832372[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]127581.183333333[/C][C]2319.59696692730[/C][C]55.0014442820798[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]127762.75[/C][C]2252.16136861829[/C][C]56.7289501455142[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]127843.05[/C][C]2211.93597329525[/C][C]57.7969035014809[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]127808.05[/C][C]2199.24639126808[/C][C]58.114475261822[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]127818.716666667[/C][C]2197.05488284746[/C][C]58.177298011331[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]127438.116666667[/C][C]2090.56657190753[/C][C]60.9586503386907[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]127528.066666667[/C][C]1985.44260472264[/C][C]64.231555403981[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]127738.466666667[/C][C]1914.89351674960[/C][C]66.7078694190234[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]127718.216666667[/C][C]1893.26525551371[/C][C]67.4592301816747[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]127696.716666667[/C][C]1878.00803038717[/C][C]67.9958310084228[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]127770.6[/C][C]1841.17723535172[/C][C]69.3961436991111[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]127586.8[/C][C]1803.18722072733[/C][C]70.7562689738545[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]127512.483333333[/C][C]1735.57152824547[/C][C]73.4700248639356[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]126938.95[/C][C]1580.55393340383[/C][C]80.3129506163885[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]125895.2[/C][C]1387.69529247085[/C][C]90.7225099653096[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]125558.666666667[/C][C]1297.96241875088[/C][C]96.735209627641[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]125622.416666667[/C][C]1238.13268008647[/C][C]101.46119126578[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]125696.816666667[/C][C]1191.95096813890[/C][C]105.454687337457[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]125762.05[/C][C]1147.69430476467[/C][C]109.578003025629[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]125365.383333333[/C][C]1051.33890451280[/C][C]119.243550100934[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]127575.637931034[/C][C]2257.10835246339[/C][C]56.521716288808[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]127569.696428571[/C][C]2180.04569815674[/C][C]58.5169827111575[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]127462.444444444[/C][C]2129.41043071469[/C][C]59.8580915195688[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]127316.057692308[/C][C]2084.73193339039[/C][C]61.0707092135602[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]127168.46[/C][C]2032.60759741505[/C][C]62.5641959430464[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]127005.895833333[/C][C]1966.32750018362[/C][C]64.5904081702938[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]126911.934782609[/C][C]1915.56420023436[/C][C]66.253031230737[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]126791.909090909[/C][C]1879.46998393872[/C][C]67.4615238202405[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]126622.880952381[/C][C]1849.1676324421[/C][C]68.475609636946[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]126440.325[/C][C]1812.22267671056[/C][C]69.7708546664405[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]126241.947368421[/C][C]1764.21457141108[/C][C]71.5570256669223[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]126010.333333333[/C][C]1706.27170001900[/C][C]73.8512707747133[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]125778.5[/C][C]1635.32996733073[/C][C]76.9132239442188[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]125528.40625[/C][C]1553.88953183160[/C][C]80.7833527921621[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]125326.9[/C][C]1487.46695692074[/C][C]84.2552497834602[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]125245.714285714[/C][C]1453.56366663294[/C][C]86.1645878751465[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]125200.576923077[/C][C]1427.19901924453[/C][C]87.7246797642493[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]125138.541666667[/C][C]1400.00325566284[/C][C]89.3844647578475[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]125053.954545455[/C][C]1365.48523553828[/C][C]91.5820627647852[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]124942.15[/C][C]1317.40487377547[/C][C]94.8395990383243[/C][/ROW]
[ROW][C]Median[/C][C]124037.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]127406[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]124946.580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]125326.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]124946.580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]125326.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]125326.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]124946.580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]125326.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]125528.40625[/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=16348&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=16348&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 Mean127569.9833333332329.0799020446454.772695097898
Geometric Mean126327.932586707
Harmonic Mean125102.648644306
Quadratic Mean128818.293832372
Winsorized Mean ( 1 / 20 )127581.1833333332319.5969669273055.0014442820798
Winsorized Mean ( 2 / 20 )127762.752252.1613686182956.7289501455142
Winsorized Mean ( 3 / 20 )127843.052211.9359732952557.7969035014809
Winsorized Mean ( 4 / 20 )127808.052199.2463912680858.114475261822
Winsorized Mean ( 5 / 20 )127818.7166666672197.0548828474658.177298011331
Winsorized Mean ( 6 / 20 )127438.1166666672090.5665719075360.9586503386907
Winsorized Mean ( 7 / 20 )127528.0666666671985.4426047226464.231555403981
Winsorized Mean ( 8 / 20 )127738.4666666671914.8935167496066.7078694190234
Winsorized Mean ( 9 / 20 )127718.2166666671893.2652555137167.4592301816747
Winsorized Mean ( 10 / 20 )127696.7166666671878.0080303871767.9958310084228
Winsorized Mean ( 11 / 20 )127770.61841.1772353517269.3961436991111
Winsorized Mean ( 12 / 20 )127586.81803.1872207273370.7562689738545
Winsorized Mean ( 13 / 20 )127512.4833333331735.5715282454773.4700248639356
Winsorized Mean ( 14 / 20 )126938.951580.5539334038380.3129506163885
Winsorized Mean ( 15 / 20 )125895.21387.6952924708590.7225099653096
Winsorized Mean ( 16 / 20 )125558.6666666671297.9624187508896.735209627641
Winsorized Mean ( 17 / 20 )125622.4166666671238.13268008647101.46119126578
Winsorized Mean ( 18 / 20 )125696.8166666671191.95096813890105.454687337457
Winsorized Mean ( 19 / 20 )125762.051147.69430476467109.578003025629
Winsorized Mean ( 20 / 20 )125365.3833333331051.33890451280119.243550100934
Trimmed Mean ( 1 / 20 )127575.6379310342257.1083524633956.521716288808
Trimmed Mean ( 2 / 20 )127569.6964285712180.0456981567458.5169827111575
Trimmed Mean ( 3 / 20 )127462.4444444442129.4104307146959.8580915195688
Trimmed Mean ( 4 / 20 )127316.0576923082084.7319333903961.0707092135602
Trimmed Mean ( 5 / 20 )127168.462032.6075974150562.5641959430464
Trimmed Mean ( 6 / 20 )127005.8958333331966.3275001836264.5904081702938
Trimmed Mean ( 7 / 20 )126911.9347826091915.5642002343666.253031230737
Trimmed Mean ( 8 / 20 )126791.9090909091879.4699839387267.4615238202405
Trimmed Mean ( 9 / 20 )126622.8809523811849.167632442168.475609636946
Trimmed Mean ( 10 / 20 )126440.3251812.2226767105669.7708546664405
Trimmed Mean ( 11 / 20 )126241.9473684211764.2145714110871.5570256669223
Trimmed Mean ( 12 / 20 )126010.3333333331706.2717000190073.8512707747133
Trimmed Mean ( 13 / 20 )125778.51635.3299673307376.9132239442188
Trimmed Mean ( 14 / 20 )125528.406251553.8895318316080.7833527921621
Trimmed Mean ( 15 / 20 )125326.91487.4669569207484.2552497834602
Trimmed Mean ( 16 / 20 )125245.7142857141453.5636666329486.1645878751465
Trimmed Mean ( 17 / 20 )125200.5769230771427.1990192445387.7246797642493
Trimmed Mean ( 18 / 20 )125138.5416666671400.0032556628489.3844647578475
Trimmed Mean ( 19 / 20 )125053.9545454551365.4852355382891.5820627647852
Trimmed Mean ( 20 / 20 )124942.151317.4048737754794.8395990383243
Median124037.5
Midrange127406
Midmean - Weighted Average at Xnp124946.580645161
Midmean - Weighted Average at X(n+1)p125326.9
Midmean - Empirical Distribution Function124946.580645161
Midmean - Empirical Distribution Function - Averaging125326.9
Midmean - Empirical Distribution Function - Interpolation125326.9
Midmean - Closest Observation124946.580645161
Midmean - True Basic - Statistics Graphics Toolkit125326.9
Midmean - MS Excel (old versions)125528.40625
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')