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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 computationWed, 30 Dec 2009 03:48:48 -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/2009/Dec/30/t1262170236wlsdbbj9mbl7h6b.htm/, Retrieved Sun, 28 Apr 2024 23:47:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=71243, Retrieved Sun, 28 Apr 2024 23:47:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [beschrijving] [2009-12-11 09:21:01] [517ac0676608e46c618c738721d88e41]
- RMPD    [Central Tendency] [] [2009-12-30 10:48:48] [5d37783481a916b2505b66314b556267] [Current]
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Dataseries X:
17192.4
15386.1
14287.1
17526.6
14497
14398.3
16629.6
16670.7
16614.8
16869.2
15663.9
16359.9
18447.7
16889
16505
18320.9
15052.1
15699.8
18135.3
16768.7
18883
19021
18101.9
17776.1
21489.9
17065.3
18690
18953.1
16398.9
16895.6
18553
19270
19422.1
17579.4
18637.3
18076.7
20438.6
18075.2
19563
19899.2
19227.5
17789.6
19220.8
21968.9
21131.5
19484.6
22168.7
20866.8
22176.2
23533.8
21479.6
24347.7
22751.6
20328.3
23650.4
23335.7
19614.9
18042.3
17282.5
16847.2
18159.5




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=71243&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=71243&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71243&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 Mean18591.9918032787307.47208237297160.4672517250726
Geometric Mean18443.2322068031
Harmonic Mean18298.1128278306
Quadratic Mean18743.9191232652
Winsorized Mean ( 1 / 20 )18582.3836065574303.67587734599561.1915038130784
Winsorized Mean ( 2 / 20 )18581.7967213115301.88512239841261.5525421514090
Winsorized Mean ( 3 / 20 )18599.3540983607293.40906334198863.3905234095712
Winsorized Mean ( 4 / 20 )18582.9540983607279.1818373162766.5621885613892
Winsorized Mean ( 5 / 20 )18558.5606557377263.64784794930370.3914740821489
Winsorized Mean ( 6 / 20 )18561.3540983607262.83566833590870.6196164922295
Winsorized Mean ( 7 / 20 )18614.1754098361244.87445701332876.0151778869403
Winsorized Mean ( 8 / 20 )18556.4704918033230.2254220026780.6013094921728
Winsorized Mean ( 9 / 20 )18570.6049180328227.49491287684481.6308579527936
Winsorized Mean ( 10 / 20 )18531.5393442623212.88424892105487.0498378258812
Winsorized Mean ( 11 / 20 )18486.4754098361202.95270758786391.0876017844348
Winsorized Mean ( 12 / 20 )18410.3245901639185.78421109183399.0952055719293
Winsorized Mean ( 13 / 20 )18407.7032786885178.304913106937103.237218526046
Winsorized Mean ( 14 / 20 )18327.2377049180158.503973147767115.626361541311
Winsorized Mean ( 15 / 20 )18262.7377049180146.483214487459124.674610458399
Winsorized Mean ( 16 / 20 )18254.3180327869143.578642233130127.138115731357
Winsorized Mean ( 17 / 20 )18234.3081967213140.000266418464130.244810693564
Winsorized Mean ( 18 / 20 )18265.9409836066129.387290707379141.172605777151
Winsorized Mean ( 19 / 20 )18258.1540983607116.335069292959156.944541395186
Winsorized Mean ( 20 / 20 )18273.7606557377109.838924423279166.368714476093
Trimmed Mean ( 1 / 20 )18567.4016949153293.27006763156763.311615279611
Trimmed Mean ( 2 / 20 )18551.3684210526280.46470488092966.1451088076433
Trimmed Mean ( 3 / 20 )18534.4945454545265.7851407051469.7348786929235
Trimmed Mean ( 4 / 20 )18509.6113207547251.69563496575773.5396596101992
Trimmed Mean ( 5 / 20 )18487.6803921569239.95031250394777.0479529667323
Trimmed Mean ( 6 / 20 )18470.0326530612230.7421252440580.046210173049
Trimmed Mean ( 7 / 20 )18450.2787234043219.16959815657984.1826552523175
Trimmed Mean ( 8 / 20 )18418.54209.68547476464187.8388930882013
Trimmed Mean ( 9 / 20 )18394.0813953488201.76232838853891.167075351782
Trimmed Mean ( 10 / 20 )18364.9191.90118744787095.6997725977535
Trimmed Mean ( 11 / 20 )18338.8358974359183.038030033169100.191396804875
Trimmed Mean ( 12 / 20 )18316.7081081081173.985954326718105.276935595113
Trimmed Mean ( 13 / 20 )18303.1114285714166.785937519150109.740135774156
Trimmed Mean ( 14 / 20 )18288.2393939394158.830292325538115.143271010645
Trimmed Mean ( 15 / 20 )18282.7580645161153.689595059498118.958983901534
Trimmed Mean ( 16 / 20 )18285.5655172414149.688017533140122.157844152042
Trimmed Mean ( 17 / 20 )18289.9777777778144.270047744372126.775987557620
Trimmed Mean ( 18 / 20 )18297.968136.859493851663133.698930816101
Trimmed Mean ( 19 / 20 )18302.6869565217129.262558017820141.593105050564
Trimmed Mean ( 20 / 20 )18309.4952380952122.331052102032149.671689431919
Median18159.5
Midrange19317.4
Midmean - Weighted Average at Xnp18238.3533333333
Midmean - Weighted Average at X(n+1)p18282.7580645161
Midmean - Empirical Distribution Function18282.7580645161
Midmean - Empirical Distribution Function - Averaging18282.7580645161
Midmean - Empirical Distribution Function - Interpolation18282.7580645161
Midmean - Closest Observation18237.896875
Midmean - True Basic - Statistics Graphics Toolkit18282.7580645161
Midmean - MS Excel (old versions)18282.7580645161
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18591.9918032787 & 307.472082372971 & 60.4672517250726 \tabularnewline
Geometric Mean & 18443.2322068031 &  &  \tabularnewline
Harmonic Mean & 18298.1128278306 &  &  \tabularnewline
Quadratic Mean & 18743.9191232652 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 18582.3836065574 & 303.675877345995 & 61.1915038130784 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 18581.7967213115 & 301.885122398412 & 61.5525421514090 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 18599.3540983607 & 293.409063341988 & 63.3905234095712 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 18582.9540983607 & 279.18183731627 & 66.5621885613892 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 18558.5606557377 & 263.647847949303 & 70.3914740821489 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 18561.3540983607 & 262.835668335908 & 70.6196164922295 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 18614.1754098361 & 244.874457013328 & 76.0151778869403 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 18556.4704918033 & 230.22542200267 & 80.6013094921728 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 18570.6049180328 & 227.494912876844 & 81.6308579527936 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 18531.5393442623 & 212.884248921054 & 87.0498378258812 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 18486.4754098361 & 202.952707587863 & 91.0876017844348 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 18410.3245901639 & 185.784211091833 & 99.0952055719293 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 18407.7032786885 & 178.304913106937 & 103.237218526046 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 18327.2377049180 & 158.503973147767 & 115.626361541311 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 18262.7377049180 & 146.483214487459 & 124.674610458399 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 18254.3180327869 & 143.578642233130 & 127.138115731357 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 18234.3081967213 & 140.000266418464 & 130.244810693564 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 18265.9409836066 & 129.387290707379 & 141.172605777151 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 18258.1540983607 & 116.335069292959 & 156.944541395186 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 18273.7606557377 & 109.838924423279 & 166.368714476093 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 18567.4016949153 & 293.270067631567 & 63.311615279611 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18551.3684210526 & 280.464704880929 & 66.1451088076433 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 18534.4945454545 & 265.78514070514 & 69.7348786929235 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 18509.6113207547 & 251.695634965757 & 73.5396596101992 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 18487.6803921569 & 239.950312503947 & 77.0479529667323 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 18470.0326530612 & 230.74212524405 & 80.046210173049 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 18450.2787234043 & 219.169598156579 & 84.1826552523175 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 18418.54 & 209.685474764641 & 87.8388930882013 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 18394.0813953488 & 201.762328388538 & 91.167075351782 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 18364.9 & 191.901187447870 & 95.6997725977535 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 18338.8358974359 & 183.038030033169 & 100.191396804875 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 18316.7081081081 & 173.985954326718 & 105.276935595113 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 18303.1114285714 & 166.785937519150 & 109.740135774156 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 18288.2393939394 & 158.830292325538 & 115.143271010645 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 18282.7580645161 & 153.689595059498 & 118.958983901534 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 18285.5655172414 & 149.688017533140 & 122.157844152042 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 18289.9777777778 & 144.270047744372 & 126.775987557620 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 18297.968 & 136.859493851663 & 133.698930816101 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 18302.6869565217 & 129.262558017820 & 141.593105050564 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 18309.4952380952 & 122.331052102032 & 149.671689431919 \tabularnewline
Median & 18159.5 &  &  \tabularnewline
Midrange & 19317.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18238.3533333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18282.7580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18282.7580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18282.7580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18282.7580645161 &  &  \tabularnewline
Midmean - Closest Observation & 18237.896875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18282.7580645161 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18282.7580645161 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=71243&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]18591.9918032787[/C][C]307.472082372971[/C][C]60.4672517250726[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18443.2322068031[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18298.1128278306[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18743.9191232652[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]18582.3836065574[/C][C]303.675877345995[/C][C]61.1915038130784[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]18581.7967213115[/C][C]301.885122398412[/C][C]61.5525421514090[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]18599.3540983607[/C][C]293.409063341988[/C][C]63.3905234095712[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]18582.9540983607[/C][C]279.18183731627[/C][C]66.5621885613892[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]18558.5606557377[/C][C]263.647847949303[/C][C]70.3914740821489[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]18561.3540983607[/C][C]262.835668335908[/C][C]70.6196164922295[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]18614.1754098361[/C][C]244.874457013328[/C][C]76.0151778869403[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]18556.4704918033[/C][C]230.22542200267[/C][C]80.6013094921728[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]18570.6049180328[/C][C]227.494912876844[/C][C]81.6308579527936[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]18531.5393442623[/C][C]212.884248921054[/C][C]87.0498378258812[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]18486.4754098361[/C][C]202.952707587863[/C][C]91.0876017844348[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]18410.3245901639[/C][C]185.784211091833[/C][C]99.0952055719293[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]18407.7032786885[/C][C]178.304913106937[/C][C]103.237218526046[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]18327.2377049180[/C][C]158.503973147767[/C][C]115.626361541311[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]18262.7377049180[/C][C]146.483214487459[/C][C]124.674610458399[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]18254.3180327869[/C][C]143.578642233130[/C][C]127.138115731357[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]18234.3081967213[/C][C]140.000266418464[/C][C]130.244810693564[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]18265.9409836066[/C][C]129.387290707379[/C][C]141.172605777151[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]18258.1540983607[/C][C]116.335069292959[/C][C]156.944541395186[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]18273.7606557377[/C][C]109.838924423279[/C][C]166.368714476093[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]18567.4016949153[/C][C]293.270067631567[/C][C]63.311615279611[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18551.3684210526[/C][C]280.464704880929[/C][C]66.1451088076433[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]18534.4945454545[/C][C]265.78514070514[/C][C]69.7348786929235[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]18509.6113207547[/C][C]251.695634965757[/C][C]73.5396596101992[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]18487.6803921569[/C][C]239.950312503947[/C][C]77.0479529667323[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]18470.0326530612[/C][C]230.74212524405[/C][C]80.046210173049[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]18450.2787234043[/C][C]219.169598156579[/C][C]84.1826552523175[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]18418.54[/C][C]209.685474764641[/C][C]87.8388930882013[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]18394.0813953488[/C][C]201.762328388538[/C][C]91.167075351782[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]18364.9[/C][C]191.901187447870[/C][C]95.6997725977535[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]18338.8358974359[/C][C]183.038030033169[/C][C]100.191396804875[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]18316.7081081081[/C][C]173.985954326718[/C][C]105.276935595113[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]18303.1114285714[/C][C]166.785937519150[/C][C]109.740135774156[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]18288.2393939394[/C][C]158.830292325538[/C][C]115.143271010645[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]18282.7580645161[/C][C]153.689595059498[/C][C]118.958983901534[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]18285.5655172414[/C][C]149.688017533140[/C][C]122.157844152042[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]18289.9777777778[/C][C]144.270047744372[/C][C]126.775987557620[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]18297.968[/C][C]136.859493851663[/C][C]133.698930816101[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]18302.6869565217[/C][C]129.262558017820[/C][C]141.593105050564[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]18309.4952380952[/C][C]122.331052102032[/C][C]149.671689431919[/C][/ROW]
[ROW][C]Median[/C][C]18159.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]19317.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18238.3533333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18282.7580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18282.7580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18282.7580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18282.7580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18237.896875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18282.7580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18282.7580645161[/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=71243&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=71243&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 Mean18591.9918032787307.47208237297160.4672517250726
Geometric Mean18443.2322068031
Harmonic Mean18298.1128278306
Quadratic Mean18743.9191232652
Winsorized Mean ( 1 / 20 )18582.3836065574303.67587734599561.1915038130784
Winsorized Mean ( 2 / 20 )18581.7967213115301.88512239841261.5525421514090
Winsorized Mean ( 3 / 20 )18599.3540983607293.40906334198863.3905234095712
Winsorized Mean ( 4 / 20 )18582.9540983607279.1818373162766.5621885613892
Winsorized Mean ( 5 / 20 )18558.5606557377263.64784794930370.3914740821489
Winsorized Mean ( 6 / 20 )18561.3540983607262.83566833590870.6196164922295
Winsorized Mean ( 7 / 20 )18614.1754098361244.87445701332876.0151778869403
Winsorized Mean ( 8 / 20 )18556.4704918033230.2254220026780.6013094921728
Winsorized Mean ( 9 / 20 )18570.6049180328227.49491287684481.6308579527936
Winsorized Mean ( 10 / 20 )18531.5393442623212.88424892105487.0498378258812
Winsorized Mean ( 11 / 20 )18486.4754098361202.95270758786391.0876017844348
Winsorized Mean ( 12 / 20 )18410.3245901639185.78421109183399.0952055719293
Winsorized Mean ( 13 / 20 )18407.7032786885178.304913106937103.237218526046
Winsorized Mean ( 14 / 20 )18327.2377049180158.503973147767115.626361541311
Winsorized Mean ( 15 / 20 )18262.7377049180146.483214487459124.674610458399
Winsorized Mean ( 16 / 20 )18254.3180327869143.578642233130127.138115731357
Winsorized Mean ( 17 / 20 )18234.3081967213140.000266418464130.244810693564
Winsorized Mean ( 18 / 20 )18265.9409836066129.387290707379141.172605777151
Winsorized Mean ( 19 / 20 )18258.1540983607116.335069292959156.944541395186
Winsorized Mean ( 20 / 20 )18273.7606557377109.838924423279166.368714476093
Trimmed Mean ( 1 / 20 )18567.4016949153293.27006763156763.311615279611
Trimmed Mean ( 2 / 20 )18551.3684210526280.46470488092966.1451088076433
Trimmed Mean ( 3 / 20 )18534.4945454545265.7851407051469.7348786929235
Trimmed Mean ( 4 / 20 )18509.6113207547251.69563496575773.5396596101992
Trimmed Mean ( 5 / 20 )18487.6803921569239.95031250394777.0479529667323
Trimmed Mean ( 6 / 20 )18470.0326530612230.7421252440580.046210173049
Trimmed Mean ( 7 / 20 )18450.2787234043219.16959815657984.1826552523175
Trimmed Mean ( 8 / 20 )18418.54209.68547476464187.8388930882013
Trimmed Mean ( 9 / 20 )18394.0813953488201.76232838853891.167075351782
Trimmed Mean ( 10 / 20 )18364.9191.90118744787095.6997725977535
Trimmed Mean ( 11 / 20 )18338.8358974359183.038030033169100.191396804875
Trimmed Mean ( 12 / 20 )18316.7081081081173.985954326718105.276935595113
Trimmed Mean ( 13 / 20 )18303.1114285714166.785937519150109.740135774156
Trimmed Mean ( 14 / 20 )18288.2393939394158.830292325538115.143271010645
Trimmed Mean ( 15 / 20 )18282.7580645161153.689595059498118.958983901534
Trimmed Mean ( 16 / 20 )18285.5655172414149.688017533140122.157844152042
Trimmed Mean ( 17 / 20 )18289.9777777778144.270047744372126.775987557620
Trimmed Mean ( 18 / 20 )18297.968136.859493851663133.698930816101
Trimmed Mean ( 19 / 20 )18302.6869565217129.262558017820141.593105050564
Trimmed Mean ( 20 / 20 )18309.4952380952122.331052102032149.671689431919
Median18159.5
Midrange19317.4
Midmean - Weighted Average at Xnp18238.3533333333
Midmean - Weighted Average at X(n+1)p18282.7580645161
Midmean - Empirical Distribution Function18282.7580645161
Midmean - Empirical Distribution Function - Averaging18282.7580645161
Midmean - Empirical Distribution Function - Interpolation18282.7580645161
Midmean - Closest Observation18237.896875
Midmean - True Basic - Statistics Graphics Toolkit18282.7580645161
Midmean - MS Excel (old versions)18282.7580645161
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')