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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2007 10:53:25 -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/Oct/22/ofqelpdukcojtpw1193075325.htm/, Retrieved Mon, 06 May 2024 08:39:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1548, Retrieved Mon, 06 May 2024 08:39:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWerkloosheid, <25, central tendency
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency <25] [2007-10-22 17:53:25] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
18,9
19,1
18,2
17,9
21,4
20,9
20,2
19,4
18,6
19
23,9
24,9
24,8
23,5
22,2
22,1
20,2
19,8
18,9
17,9
17,2
17,5
24,3
25,3
25,2
23,3
22,1
21,5
21
20,5
19,9
20,3
19,6
19,7
22,7
23,7
23,7
23,1
21,9
21,3
20,5
20,2
19,4
19,1
18,7
18,9
22,5
23,3
23,1
21,3
19,8
18,9
19,3
18,6
17,7
20
18,9
18,7
20,8
21,7
20,8




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1548&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1548&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1548&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean20.78360655737700.27316381849906276.0847709318738
Geometric Mean20.6782495583907
Harmonic Mean20.5754321650376
Quadratic Mean20.8910365907502
Winsorized Mean ( 1 / 20 )20.78688524590160.27168242680997276.5117033515055
Winsorized Mean ( 2 / 20 )20.78360655737700.26779998579672577.6086917836992
Winsorized Mean ( 3 / 20 )20.78852459016390.26471036198322278.533097210156
Winsorized Mean ( 4 / 20 )20.75573770491800.25679321899789480.8266580633045
Winsorized Mean ( 5 / 20 )20.74754098360660.24508955157590484.6528987066225
Winsorized Mean ( 6 / 20 )20.76721311475410.23448258713444988.566120702372
Winsorized Mean ( 7 / 20 )20.76721311475410.23448258713444988.5661207023721
Winsorized Mean ( 8 / 20 )20.75409836065570.22710549497905691.3852760919313
Winsorized Mean ( 9 / 20 )20.72459016393440.22126876738291193.6625191573922
Winsorized Mean ( 10 / 20 )20.75737704918030.21642221203026695.9114910362225
Winsorized Mean ( 11 / 20 )20.72131147540980.20947651059806498.9194989750863
Winsorized Mean ( 12 / 20 )20.72131147540980.20947651059806498.9194989750863
Winsorized Mean ( 13 / 20 )20.63606557377050.19382591460957106.467009921446
Winsorized Mean ( 14 / 20 )20.59016393442620.185818304198060110.808049956584
Winsorized Mean ( 15 / 20 )20.54098360655740.169753550856257121.004736000786
Winsorized Mean ( 16 / 20 )20.54098360655740.161573158397819127.131163432371
Winsorized Mean ( 17 / 20 )20.54098360655740.161573158397819127.131163432371
Winsorized Mean ( 18 / 20 )20.54098360655740.143518949248296143.123843326223
Winsorized Mean ( 19 / 20 )20.50983606557380.129346928712638158.564538560782
Winsorized Mean ( 20 / 20 )20.44426229508200.119482595622264171.106613382547
Trimmed Mean ( 1 / 20 )20.76779661016950.26474562052722778.4443443060984
Trimmed Mean ( 2 / 20 )20.74736842105260.25619034256543880.984194069506
Trimmed Mean ( 3 / 20 )20.72727272727270.24819149966933183.513225694224
Trimmed Mean ( 4 / 20 )20.70377358490570.23969262888879386.3763465772295
Trimmed Mean ( 5 / 20 )20.68823529411760.23223799589186789.0820436796671
Trimmed Mean ( 6 / 20 )20.67346938775510.22683071376208591.1405208090064
Trimmed Mean ( 7 / 20 )20.65319148936170.22302377185097692.6053367224104
Trimmed Mean ( 8 / 20 )20.63111111111110.21790606404990194.6789214015933
Trimmed Mean ( 9 / 20 )20.60930232558140.21312976393128296.6983772957508
Trimmed Mean ( 10 / 20 )20.59024390243900.20826826269140898.8640498382016
Trimmed Mean ( 11 / 20 )20.56410256410260.202730589775855101.435617519975
Trimmed Mean ( 12 / 20 )20.54054054054050.196991618069098104.271139766645
Trimmed Mean ( 13 / 20 )20.51428571428570.188810645314065108.650048201268
Trimmed Mean ( 14 / 20 )20.49696969696970.182131989294397112.539097477481
Trimmed Mean ( 15 / 20 )20.48387096774190.174940651945416117.090400315492
Trimmed Mean ( 16 / 20 )20.47586206896550.169442375255895120.842628876292
Trimmed Mean ( 17 / 20 )20.46666666666670.163560804449406125.131853781005
Trimmed Mean ( 18 / 20 )20.4560.154064921380566132.775195136538
Trimmed Mean ( 19 / 20 )20.44347826086960.14620713107146139.825452500519
Trimmed Mean ( 20 / 20 )20.43333333333330.13927248614434146.714788390842
Median20.3
Midrange21.25
Midmean - Weighted Average at Xnp20.4266666666667
Midmean - Weighted Average at X(n+1)p20.4838709677419
Midmean - Empirical Distribution Function20.4838709677419
Midmean - Empirical Distribution Function - Averaging20.4838709677419
Midmean - Empirical Distribution Function - Interpolation20.4838709677419
Midmean - Closest Observation20.2638888888889
Midmean - True Basic - Statistics Graphics Toolkit20.4838709677419
Midmean - MS Excel (old versions)20.4838709677419
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 20.7836065573770 & 0.273163818499062 & 76.0847709318738 \tabularnewline
Geometric Mean & 20.6782495583907 &  &  \tabularnewline
Harmonic Mean & 20.5754321650376 &  &  \tabularnewline
Quadratic Mean & 20.8910365907502 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 20.7868852459016 & 0.271682426809972 & 76.5117033515055 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 20.7836065573770 & 0.267799985796725 & 77.6086917836992 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 20.7885245901639 & 0.264710361983222 & 78.533097210156 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 20.7557377049180 & 0.256793218997894 & 80.8266580633045 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 20.7475409836066 & 0.245089551575904 & 84.6528987066225 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 20.7672131147541 & 0.234482587134449 & 88.566120702372 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 20.7672131147541 & 0.234482587134449 & 88.5661207023721 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 20.7540983606557 & 0.227105494979056 & 91.3852760919313 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 20.7245901639344 & 0.221268767382911 & 93.6625191573922 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 20.7573770491803 & 0.216422212030266 & 95.9114910362225 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 20.7213114754098 & 0.209476510598064 & 98.9194989750863 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 20.7213114754098 & 0.209476510598064 & 98.9194989750863 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 20.6360655737705 & 0.19382591460957 & 106.467009921446 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 20.5901639344262 & 0.185818304198060 & 110.808049956584 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 20.5409836065574 & 0.169753550856257 & 121.004736000786 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 20.5409836065574 & 0.161573158397819 & 127.131163432371 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 20.5409836065574 & 0.161573158397819 & 127.131163432371 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 20.5409836065574 & 0.143518949248296 & 143.123843326223 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 20.5098360655738 & 0.129346928712638 & 158.564538560782 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 20.4442622950820 & 0.119482595622264 & 171.106613382547 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 20.7677966101695 & 0.264745620527227 & 78.4443443060984 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 20.7473684210526 & 0.256190342565438 & 80.984194069506 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 20.7272727272727 & 0.248191499669331 & 83.513225694224 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 20.7037735849057 & 0.239692628888793 & 86.3763465772295 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 20.6882352941176 & 0.232237995891867 & 89.0820436796671 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 20.6734693877551 & 0.226830713762085 & 91.1405208090064 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 20.6531914893617 & 0.223023771850976 & 92.6053367224104 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 20.6311111111111 & 0.217906064049901 & 94.6789214015933 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 20.6093023255814 & 0.213129763931282 & 96.6983772957508 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 20.5902439024390 & 0.208268262691408 & 98.8640498382016 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 20.5641025641026 & 0.202730589775855 & 101.435617519975 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 20.5405405405405 & 0.196991618069098 & 104.271139766645 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 20.5142857142857 & 0.188810645314065 & 108.650048201268 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 20.4969696969697 & 0.182131989294397 & 112.539097477481 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 20.4838709677419 & 0.174940651945416 & 117.090400315492 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 20.4758620689655 & 0.169442375255895 & 120.842628876292 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 20.4666666666667 & 0.163560804449406 & 125.131853781005 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 20.456 & 0.154064921380566 & 132.775195136538 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 20.4434782608696 & 0.14620713107146 & 139.825452500519 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 20.4333333333333 & 0.13927248614434 & 146.714788390842 \tabularnewline
Median & 20.3 &  &  \tabularnewline
Midrange & 21.25 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20.4266666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 20.4838709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20.4838709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 20.4838709677419 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 20.4838709677419 &  &  \tabularnewline
Midmean - Closest Observation & 20.2638888888889 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 20.4838709677419 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 20.4838709677419 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1548&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]20.7836065573770[/C][C]0.273163818499062[/C][C]76.0847709318738[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]20.6782495583907[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]20.5754321650376[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]20.8910365907502[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]20.7868852459016[/C][C]0.271682426809972[/C][C]76.5117033515055[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]20.7836065573770[/C][C]0.267799985796725[/C][C]77.6086917836992[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]20.7885245901639[/C][C]0.264710361983222[/C][C]78.533097210156[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]20.7557377049180[/C][C]0.256793218997894[/C][C]80.8266580633045[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]20.7475409836066[/C][C]0.245089551575904[/C][C]84.6528987066225[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]20.7672131147541[/C][C]0.234482587134449[/C][C]88.566120702372[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]20.7672131147541[/C][C]0.234482587134449[/C][C]88.5661207023721[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]20.7540983606557[/C][C]0.227105494979056[/C][C]91.3852760919313[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]20.7245901639344[/C][C]0.221268767382911[/C][C]93.6625191573922[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]20.7573770491803[/C][C]0.216422212030266[/C][C]95.9114910362225[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]20.7213114754098[/C][C]0.209476510598064[/C][C]98.9194989750863[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]20.7213114754098[/C][C]0.209476510598064[/C][C]98.9194989750863[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]20.6360655737705[/C][C]0.19382591460957[/C][C]106.467009921446[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]20.5901639344262[/C][C]0.185818304198060[/C][C]110.808049956584[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]20.5409836065574[/C][C]0.169753550856257[/C][C]121.004736000786[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]20.5409836065574[/C][C]0.161573158397819[/C][C]127.131163432371[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]20.5409836065574[/C][C]0.161573158397819[/C][C]127.131163432371[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]20.5409836065574[/C][C]0.143518949248296[/C][C]143.123843326223[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]20.5098360655738[/C][C]0.129346928712638[/C][C]158.564538560782[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]20.4442622950820[/C][C]0.119482595622264[/C][C]171.106613382547[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]20.7677966101695[/C][C]0.264745620527227[/C][C]78.4443443060984[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]20.7473684210526[/C][C]0.256190342565438[/C][C]80.984194069506[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]20.7272727272727[/C][C]0.248191499669331[/C][C]83.513225694224[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]20.7037735849057[/C][C]0.239692628888793[/C][C]86.3763465772295[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]20.6882352941176[/C][C]0.232237995891867[/C][C]89.0820436796671[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]20.6734693877551[/C][C]0.226830713762085[/C][C]91.1405208090064[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]20.6531914893617[/C][C]0.223023771850976[/C][C]92.6053367224104[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]20.6311111111111[/C][C]0.217906064049901[/C][C]94.6789214015933[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]20.6093023255814[/C][C]0.213129763931282[/C][C]96.6983772957508[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]20.5902439024390[/C][C]0.208268262691408[/C][C]98.8640498382016[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]20.5641025641026[/C][C]0.202730589775855[/C][C]101.435617519975[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]20.5405405405405[/C][C]0.196991618069098[/C][C]104.271139766645[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]20.5142857142857[/C][C]0.188810645314065[/C][C]108.650048201268[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]20.4969696969697[/C][C]0.182131989294397[/C][C]112.539097477481[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]20.4838709677419[/C][C]0.174940651945416[/C][C]117.090400315492[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]20.4758620689655[/C][C]0.169442375255895[/C][C]120.842628876292[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]20.4666666666667[/C][C]0.163560804449406[/C][C]125.131853781005[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]20.456[/C][C]0.154064921380566[/C][C]132.775195136538[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]20.4434782608696[/C][C]0.14620713107146[/C][C]139.825452500519[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]20.4333333333333[/C][C]0.13927248614434[/C][C]146.714788390842[/C][/ROW]
[ROW][C]Median[/C][C]20.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21.25[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20.4266666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]20.4838709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20.4838709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]20.4838709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]20.4838709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20.2638888888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]20.4838709677419[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]20.4838709677419[/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=1548&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1548&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 Mean20.78360655737700.27316381849906276.0847709318738
Geometric Mean20.6782495583907
Harmonic Mean20.5754321650376
Quadratic Mean20.8910365907502
Winsorized Mean ( 1 / 20 )20.78688524590160.27168242680997276.5117033515055
Winsorized Mean ( 2 / 20 )20.78360655737700.26779998579672577.6086917836992
Winsorized Mean ( 3 / 20 )20.78852459016390.26471036198322278.533097210156
Winsorized Mean ( 4 / 20 )20.75573770491800.25679321899789480.8266580633045
Winsorized Mean ( 5 / 20 )20.74754098360660.24508955157590484.6528987066225
Winsorized Mean ( 6 / 20 )20.76721311475410.23448258713444988.566120702372
Winsorized Mean ( 7 / 20 )20.76721311475410.23448258713444988.5661207023721
Winsorized Mean ( 8 / 20 )20.75409836065570.22710549497905691.3852760919313
Winsorized Mean ( 9 / 20 )20.72459016393440.22126876738291193.6625191573922
Winsorized Mean ( 10 / 20 )20.75737704918030.21642221203026695.9114910362225
Winsorized Mean ( 11 / 20 )20.72131147540980.20947651059806498.9194989750863
Winsorized Mean ( 12 / 20 )20.72131147540980.20947651059806498.9194989750863
Winsorized Mean ( 13 / 20 )20.63606557377050.19382591460957106.467009921446
Winsorized Mean ( 14 / 20 )20.59016393442620.185818304198060110.808049956584
Winsorized Mean ( 15 / 20 )20.54098360655740.169753550856257121.004736000786
Winsorized Mean ( 16 / 20 )20.54098360655740.161573158397819127.131163432371
Winsorized Mean ( 17 / 20 )20.54098360655740.161573158397819127.131163432371
Winsorized Mean ( 18 / 20 )20.54098360655740.143518949248296143.123843326223
Winsorized Mean ( 19 / 20 )20.50983606557380.129346928712638158.564538560782
Winsorized Mean ( 20 / 20 )20.44426229508200.119482595622264171.106613382547
Trimmed Mean ( 1 / 20 )20.76779661016950.26474562052722778.4443443060984
Trimmed Mean ( 2 / 20 )20.74736842105260.25619034256543880.984194069506
Trimmed Mean ( 3 / 20 )20.72727272727270.24819149966933183.513225694224
Trimmed Mean ( 4 / 20 )20.70377358490570.23969262888879386.3763465772295
Trimmed Mean ( 5 / 20 )20.68823529411760.23223799589186789.0820436796671
Trimmed Mean ( 6 / 20 )20.67346938775510.22683071376208591.1405208090064
Trimmed Mean ( 7 / 20 )20.65319148936170.22302377185097692.6053367224104
Trimmed Mean ( 8 / 20 )20.63111111111110.21790606404990194.6789214015933
Trimmed Mean ( 9 / 20 )20.60930232558140.21312976393128296.6983772957508
Trimmed Mean ( 10 / 20 )20.59024390243900.20826826269140898.8640498382016
Trimmed Mean ( 11 / 20 )20.56410256410260.202730589775855101.435617519975
Trimmed Mean ( 12 / 20 )20.54054054054050.196991618069098104.271139766645
Trimmed Mean ( 13 / 20 )20.51428571428570.188810645314065108.650048201268
Trimmed Mean ( 14 / 20 )20.49696969696970.182131989294397112.539097477481
Trimmed Mean ( 15 / 20 )20.48387096774190.174940651945416117.090400315492
Trimmed Mean ( 16 / 20 )20.47586206896550.169442375255895120.842628876292
Trimmed Mean ( 17 / 20 )20.46666666666670.163560804449406125.131853781005
Trimmed Mean ( 18 / 20 )20.4560.154064921380566132.775195136538
Trimmed Mean ( 19 / 20 )20.44347826086960.14620713107146139.825452500519
Trimmed Mean ( 20 / 20 )20.43333333333330.13927248614434146.714788390842
Median20.3
Midrange21.25
Midmean - Weighted Average at Xnp20.4266666666667
Midmean - Weighted Average at X(n+1)p20.4838709677419
Midmean - Empirical Distribution Function20.4838709677419
Midmean - Empirical Distribution Function - Averaging20.4838709677419
Midmean - Empirical Distribution Function - Interpolation20.4838709677419
Midmean - Closest Observation20.2638888888889
Midmean - True Basic - Statistics Graphics Toolkit20.4838709677419
Midmean - MS Excel (old versions)20.4838709677419
Number of observations61



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')