Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 09 Mar 2017 19:52:50 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/09/t1489089222q0o3i0gcv11f86m.htm/, Retrieved Wed, 15 May 2024 12:30:53 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 12:30:53 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
8 899
8 899
9 093
9 093
9 093
9 116
9 116
9 116
10 073
10 073
10 073
9 223
9 223
9 223
9 151
9 151
9 151
6 727
6 727
6 727
7 232
7 232
7 232
6 370
6 370
6 370
6 862
6 862
6 862
7 029
7 029
7 029
7 031
7 031
7 031
7 223
7 223
7 223
8 065
8 065
8 065
7 657
7 657
7 657
7 328
7 328
7 328
7 115
7 115
7 115
7 926
7 926
7 926
8 681
8 681
8 681
8 670
8 670
8 670
8 028
8 028




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7960.16393442623131.16023275336560.6903767043064
Geometric Mean7896.41388591516
Harmonic Mean7834.07769262871
Quadratic Mean8024.7361490765
Winsorized Mean ( 1 / 20 )7960.16393442623131.16023275336560.6903767043064
Winsorized Mean ( 2 / 20 )7960.16393442623131.16023275336560.6903767043064
Winsorized Mean ( 3 / 20 )7935.91803278689118.38553830756867.0345225121096
Winsorized Mean ( 4 / 20 )7935.91803278689118.38553830756867.0345225121096
Winsorized Mean ( 5 / 20 )7935.91803278689118.38553830756867.0345225121096
Winsorized Mean ( 6 / 20 )7942.11475409836114.95190512082669.0907623127287
Winsorized Mean ( 7 / 20 )7942.11475409836114.95190512082669.0907623127287
Winsorized Mean ( 8 / 20 )7942.11475409836114.95190512082669.0907623127287
Winsorized Mean ( 9 / 20 )7961.59016393443110.38121815232872.1281237623893
Winsorized Mean ( 10 / 20 )7961.59016393443110.38121815232872.1281237623893
Winsorized Mean ( 11 / 20 )7961.59016393443110.38121815232872.1281237623893
Winsorized Mean ( 12 / 20 )7957.45901639344109.54057704090272.6439391808402
Winsorized Mean ( 13 / 20 )7957.45901639344109.54057704090272.6439391808402
Winsorized Mean ( 14 / 20 )7957.45901639344109.54057704090272.6439391808402
Winsorized Mean ( 15 / 20 )7930.4098360655798.623128714887280.4112578804091
Winsorized Mean ( 16 / 20 )7930.4098360655798.623128714887280.4112578804091
Winsorized Mean ( 17 / 20 )7869.6557377049289.01806743990588.4051514937418
Winsorized Mean ( 18 / 20 )7901.5245901639384.634426351230493.3606444896647
Winsorized Mean ( 19 / 20 )7901.5245901639384.634426351230493.3606444896647
Winsorized Mean ( 20 / 20 )7897.9180327868984.081645512362993.9315350533384
Trimmed Mean ( 1 / 20 )7951.30508474576127.88537353206262.1752501098361
Trimmed Mean ( 2 / 20 )7941.82456140351123.84610043613664.1265613809043
Trimmed Mean ( 3 / 20 )7931.65454545455118.83300173691666.7462273065726
Trimmed Mean ( 4 / 20 )7930.01886792453118.68489121996166.8157402885228
Trimmed Mean ( 5 / 20 )7928.25490196078118.32505525246967.0040245072724
Trimmed Mean ( 6 / 20 )7926.34693877551117.69926493038767.3440649222707
Trimmed Mean ( 7 / 20 )7922.93617021277117.6971741198467.3162820557238
Trimmed Mean ( 8 / 20 )7919.22222222222117.45411263397867.4239670678954
Trimmed Mean ( 9 / 20 )7915.16279069767116.89818160189767.7098880601341
Trimmed Mean ( 10 / 20 )7907.48780487805116.99909902692167.5858863071978
Trimmed Mean ( 11 / 20 )7899.02564102564116.79069648014767.6340314690082
Trimmed Mean ( 12 / 20 )7889.64864864865116.16156564741267.9196135544204
Trimmed Mean ( 13 / 20 )7879.8115.17114630486468.4181781011516
Trimmed Mean ( 14 / 20 )7868.75757575758113.43587187080269.3674535751768
Trimmed Mean ( 15 / 20 )7856.29032258064110.63289282746371.0122470975508
Trimmed Mean ( 16 / 20 )7845.89655172414109.53874795035371.626677304
Trimmed Mean ( 17 / 20 )7833.96296296296107.38999515016272.948722569629
Trimmed Mean ( 18 / 20 )7828.84106.93344783867573.2122657431841
Trimmed Mean ( 19 / 20 )7818.13043478261106.73931719552573.2450856928508
Trimmed Mean ( 20 / 20 )7805.38095238095105.36628800772174.0785416281246
Median7926
Midrange8221.5
Midmean - Weighted Average at Xnp7856.29032258064
Midmean - Weighted Average at X(n+1)p7856.29032258064
Midmean - Empirical Distribution Function7856.29032258064
Midmean - Empirical Distribution Function - Averaging7856.29032258064
Midmean - Empirical Distribution Function - Interpolation7856.29032258064
Midmean - Closest Observation7783.47058823529
Midmean - True Basic - Statistics Graphics Toolkit7856.29032258064
Midmean - MS Excel (old versions)7856.29032258064
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7960.16393442623 & 131.160232753365 & 60.6903767043064 \tabularnewline
Geometric Mean & 7896.41388591516 &  &  \tabularnewline
Harmonic Mean & 7834.07769262871 &  &  \tabularnewline
Quadratic Mean & 8024.7361490765 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7960.16393442623 & 131.160232753365 & 60.6903767043064 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7960.16393442623 & 131.160232753365 & 60.6903767043064 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7935.91803278689 & 118.385538307568 & 67.0345225121096 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7935.91803278689 & 118.385538307568 & 67.0345225121096 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7935.91803278689 & 118.385538307568 & 67.0345225121096 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7942.11475409836 & 114.951905120826 & 69.0907623127287 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7942.11475409836 & 114.951905120826 & 69.0907623127287 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7942.11475409836 & 114.951905120826 & 69.0907623127287 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7961.59016393443 & 110.381218152328 & 72.1281237623893 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7961.59016393443 & 110.381218152328 & 72.1281237623893 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7961.59016393443 & 110.381218152328 & 72.1281237623893 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7957.45901639344 & 109.540577040902 & 72.6439391808402 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7957.45901639344 & 109.540577040902 & 72.6439391808402 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7957.45901639344 & 109.540577040902 & 72.6439391808402 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7930.40983606557 & 98.6231287148872 & 80.4112578804091 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7930.40983606557 & 98.6231287148872 & 80.4112578804091 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7869.65573770492 & 89.018067439905 & 88.4051514937418 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7901.52459016393 & 84.6344263512304 & 93.3606444896647 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7901.52459016393 & 84.6344263512304 & 93.3606444896647 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7897.91803278689 & 84.0816455123629 & 93.9315350533384 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7951.30508474576 & 127.885373532062 & 62.1752501098361 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7941.82456140351 & 123.846100436136 & 64.1265613809043 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7931.65454545455 & 118.833001736916 & 66.7462273065726 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7930.01886792453 & 118.684891219961 & 66.8157402885228 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7928.25490196078 & 118.325055252469 & 67.0040245072724 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7926.34693877551 & 117.699264930387 & 67.3440649222707 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7922.93617021277 & 117.69717411984 & 67.3162820557238 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7919.22222222222 & 117.454112633978 & 67.4239670678954 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7915.16279069767 & 116.898181601897 & 67.7098880601341 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7907.48780487805 & 116.999099026921 & 67.5858863071978 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7899.02564102564 & 116.790696480147 & 67.6340314690082 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7889.64864864865 & 116.161565647412 & 67.9196135544204 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7879.8 & 115.171146304864 & 68.4181781011516 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7868.75757575758 & 113.435871870802 & 69.3674535751768 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7856.29032258064 & 110.632892827463 & 71.0122470975508 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7845.89655172414 & 109.538747950353 & 71.626677304 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7833.96296296296 & 107.389995150162 & 72.948722569629 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7828.84 & 106.933447838675 & 73.2122657431841 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7818.13043478261 & 106.739317195525 & 73.2450856928508 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7805.38095238095 & 105.366288007721 & 74.0785416281246 \tabularnewline
Median & 7926 &  &  \tabularnewline
Midrange & 8221.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7856.29032258064 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7856.29032258064 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7856.29032258064 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7856.29032258064 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7856.29032258064 &  &  \tabularnewline
Midmean - Closest Observation & 7783.47058823529 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7856.29032258064 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7856.29032258064 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]7960.16393442623[/C][C]131.160232753365[/C][C]60.6903767043064[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7896.41388591516[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7834.07769262871[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8024.7361490765[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7960.16393442623[/C][C]131.160232753365[/C][C]60.6903767043064[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7960.16393442623[/C][C]131.160232753365[/C][C]60.6903767043064[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7935.91803278689[/C][C]118.385538307568[/C][C]67.0345225121096[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7935.91803278689[/C][C]118.385538307568[/C][C]67.0345225121096[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7935.91803278689[/C][C]118.385538307568[/C][C]67.0345225121096[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7942.11475409836[/C][C]114.951905120826[/C][C]69.0907623127287[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7942.11475409836[/C][C]114.951905120826[/C][C]69.0907623127287[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7942.11475409836[/C][C]114.951905120826[/C][C]69.0907623127287[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7961.59016393443[/C][C]110.381218152328[/C][C]72.1281237623893[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7961.59016393443[/C][C]110.381218152328[/C][C]72.1281237623893[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7961.59016393443[/C][C]110.381218152328[/C][C]72.1281237623893[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7957.45901639344[/C][C]109.540577040902[/C][C]72.6439391808402[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7957.45901639344[/C][C]109.540577040902[/C][C]72.6439391808402[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7957.45901639344[/C][C]109.540577040902[/C][C]72.6439391808402[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7930.40983606557[/C][C]98.6231287148872[/C][C]80.4112578804091[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7930.40983606557[/C][C]98.6231287148872[/C][C]80.4112578804091[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7869.65573770492[/C][C]89.018067439905[/C][C]88.4051514937418[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7901.52459016393[/C][C]84.6344263512304[/C][C]93.3606444896647[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7901.52459016393[/C][C]84.6344263512304[/C][C]93.3606444896647[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7897.91803278689[/C][C]84.0816455123629[/C][C]93.9315350533384[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7951.30508474576[/C][C]127.885373532062[/C][C]62.1752501098361[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7941.82456140351[/C][C]123.846100436136[/C][C]64.1265613809043[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7931.65454545455[/C][C]118.833001736916[/C][C]66.7462273065726[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7930.01886792453[/C][C]118.684891219961[/C][C]66.8157402885228[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7928.25490196078[/C][C]118.325055252469[/C][C]67.0040245072724[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7926.34693877551[/C][C]117.699264930387[/C][C]67.3440649222707[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7922.93617021277[/C][C]117.69717411984[/C][C]67.3162820557238[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7919.22222222222[/C][C]117.454112633978[/C][C]67.4239670678954[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7915.16279069767[/C][C]116.898181601897[/C][C]67.7098880601341[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7907.48780487805[/C][C]116.999099026921[/C][C]67.5858863071978[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7899.02564102564[/C][C]116.790696480147[/C][C]67.6340314690082[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7889.64864864865[/C][C]116.161565647412[/C][C]67.9196135544204[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7879.8[/C][C]115.171146304864[/C][C]68.4181781011516[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7868.75757575758[/C][C]113.435871870802[/C][C]69.3674535751768[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7856.29032258064[/C][C]110.632892827463[/C][C]71.0122470975508[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7845.89655172414[/C][C]109.538747950353[/C][C]71.626677304[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7833.96296296296[/C][C]107.389995150162[/C][C]72.948722569629[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7828.84[/C][C]106.933447838675[/C][C]73.2122657431841[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7818.13043478261[/C][C]106.739317195525[/C][C]73.2450856928508[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7805.38095238095[/C][C]105.366288007721[/C][C]74.0785416281246[/C][/ROW]
[ROW][C]Median[/C][C]7926[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8221.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7856.29032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7856.29032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7856.29032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7856.29032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7856.29032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7783.47058823529[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7856.29032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7856.29032258064[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean7960.16393442623131.16023275336560.6903767043064
Geometric Mean7896.41388591516
Harmonic Mean7834.07769262871
Quadratic Mean8024.7361490765
Winsorized Mean ( 1 / 20 )7960.16393442623131.16023275336560.6903767043064
Winsorized Mean ( 2 / 20 )7960.16393442623131.16023275336560.6903767043064
Winsorized Mean ( 3 / 20 )7935.91803278689118.38553830756867.0345225121096
Winsorized Mean ( 4 / 20 )7935.91803278689118.38553830756867.0345225121096
Winsorized Mean ( 5 / 20 )7935.91803278689118.38553830756867.0345225121096
Winsorized Mean ( 6 / 20 )7942.11475409836114.95190512082669.0907623127287
Winsorized Mean ( 7 / 20 )7942.11475409836114.95190512082669.0907623127287
Winsorized Mean ( 8 / 20 )7942.11475409836114.95190512082669.0907623127287
Winsorized Mean ( 9 / 20 )7961.59016393443110.38121815232872.1281237623893
Winsorized Mean ( 10 / 20 )7961.59016393443110.38121815232872.1281237623893
Winsorized Mean ( 11 / 20 )7961.59016393443110.38121815232872.1281237623893
Winsorized Mean ( 12 / 20 )7957.45901639344109.54057704090272.6439391808402
Winsorized Mean ( 13 / 20 )7957.45901639344109.54057704090272.6439391808402
Winsorized Mean ( 14 / 20 )7957.45901639344109.54057704090272.6439391808402
Winsorized Mean ( 15 / 20 )7930.4098360655798.623128714887280.4112578804091
Winsorized Mean ( 16 / 20 )7930.4098360655798.623128714887280.4112578804091
Winsorized Mean ( 17 / 20 )7869.6557377049289.01806743990588.4051514937418
Winsorized Mean ( 18 / 20 )7901.5245901639384.634426351230493.3606444896647
Winsorized Mean ( 19 / 20 )7901.5245901639384.634426351230493.3606444896647
Winsorized Mean ( 20 / 20 )7897.9180327868984.081645512362993.9315350533384
Trimmed Mean ( 1 / 20 )7951.30508474576127.88537353206262.1752501098361
Trimmed Mean ( 2 / 20 )7941.82456140351123.84610043613664.1265613809043
Trimmed Mean ( 3 / 20 )7931.65454545455118.83300173691666.7462273065726
Trimmed Mean ( 4 / 20 )7930.01886792453118.68489121996166.8157402885228
Trimmed Mean ( 5 / 20 )7928.25490196078118.32505525246967.0040245072724
Trimmed Mean ( 6 / 20 )7926.34693877551117.69926493038767.3440649222707
Trimmed Mean ( 7 / 20 )7922.93617021277117.6971741198467.3162820557238
Trimmed Mean ( 8 / 20 )7919.22222222222117.45411263397867.4239670678954
Trimmed Mean ( 9 / 20 )7915.16279069767116.89818160189767.7098880601341
Trimmed Mean ( 10 / 20 )7907.48780487805116.99909902692167.5858863071978
Trimmed Mean ( 11 / 20 )7899.02564102564116.79069648014767.6340314690082
Trimmed Mean ( 12 / 20 )7889.64864864865116.16156564741267.9196135544204
Trimmed Mean ( 13 / 20 )7879.8115.17114630486468.4181781011516
Trimmed Mean ( 14 / 20 )7868.75757575758113.43587187080269.3674535751768
Trimmed Mean ( 15 / 20 )7856.29032258064110.63289282746371.0122470975508
Trimmed Mean ( 16 / 20 )7845.89655172414109.53874795035371.626677304
Trimmed Mean ( 17 / 20 )7833.96296296296107.38999515016272.948722569629
Trimmed Mean ( 18 / 20 )7828.84106.93344783867573.2122657431841
Trimmed Mean ( 19 / 20 )7818.13043478261106.73931719552573.2450856928508
Trimmed Mean ( 20 / 20 )7805.38095238095105.36628800772174.0785416281246
Median7926
Midrange8221.5
Midmean - Weighted Average at Xnp7856.29032258064
Midmean - Weighted Average at X(n+1)p7856.29032258064
Midmean - Empirical Distribution Function7856.29032258064
Midmean - Empirical Distribution Function - Averaging7856.29032258064
Midmean - Empirical Distribution Function - Interpolation7856.29032258064
Midmean - Closest Observation7783.47058823529
Midmean - True Basic - Statistics Graphics Toolkit7856.29032258064
Midmean - MS Excel (old versions)7856.29032258064
Number of observations61



Parameters (Session):
par1 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;
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')