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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 computationFri, 11 Dec 2009 04:40:13 -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/11/t12605317011hgyo8z3336honv.htm/, Retrieved Sun, 28 Apr 2024 22:22:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66021, Retrieved Sun, 28 Apr 2024 22:22:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Central Tendency] [2009-12-10 18:31:24] [830e13ac5e5ac1e5b21c6af0c149b21d]
-    D    [Central Tendency] [Central Tendency] [2009-12-11 11:40:13] [9f6463b67b1eb7bae5c03a796abf0348] [Current]
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Dataseries X:
12610
10862
52929
56902
81776
87876
82103
72846
60632
33521
15342
7758
8668
13082
38157
58263
81153
88476
72329
75845
61108
37665
12755
2793
12935
19533
33404
52074
70735
69702
61656
82993
53990
32283
15686
2713
12842
19244
48488
54464
84192
84458
85793
75163
68212
49233
24302
5402
15058
33559
70358
85934
94452
129305
113882
107256
94274
57842
26611
14521




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66021&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]6 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=66021&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66021&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 time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean51466.66666666674172.4880710676112.3347666404467
Geometric Mean37671.7953065482
Harmonic Mean21812.4682622998
Quadratic Mean60629.9226724451
Winsorized Mean ( 1 / 20 )51210.954098.2059868892112.4959433868946
Winsorized Mean ( 2 / 20 )51077.054026.3734122709412.6856217171352
Winsorized Mean ( 3 / 20 )50554.653866.4100524513.0753462033768
Winsorized Mean ( 4 / 20 )50603.453852.8416142841713.1340592388721
Winsorized Mean ( 5 / 20 )50303.11666666673731.2163554278413.4816938700138
Winsorized Mean ( 6 / 20 )50417.91666666673690.01301027313.6633438761064
Winsorized Mean ( 7 / 20 )50208.26666666673648.7782566259613.7602954017530
Winsorized Mean ( 8 / 20 )50201.06666666673643.6450086523513.7777051681646
Winsorized Mean ( 9 / 20 )50014.76666666673608.4407265525813.8604927880995
Winsorized Mean ( 10 / 20 )49994.93333333333597.0184208957913.8989928555558
Winsorized Mean ( 11 / 20 )50038.93333333333516.3167883250914.2304963817461
Winsorized Mean ( 12 / 20 )49968.33333333333469.8574952964314.4006874636979
Winsorized Mean ( 13 / 20 )49959.01666666673448.2752436848714.4881174315075
Winsorized Mean ( 14 / 20 )49893.91666666673411.9729907240414.6231862920108
Winsorized Mean ( 15 / 20 )49456.41666666673061.6592419346916.1534686777927
Winsorized Mean ( 16 / 20 )49351.61666666673022.3233176167616.3290328268329
Winsorized Mean ( 17 / 20 )50046.352705.7437842282518.4963374180954
Winsorized Mean ( 18 / 20 )50583.952572.9817150321619.6596616697557
Winsorized Mean ( 19 / 20 )51875.31666666672224.0934771706523.3242519701371
Winsorized Mean ( 20 / 20 )52123.31666666672150.5679588135624.2370004877328
Trimmed Mean ( 1 / 20 )50965.20689655174010.7189181022612.7072497318428
Trimmed Mean ( 2 / 20 )50701.91071428573902.0851578868112.9935428528022
Trimmed Mean ( 3 / 20 )50493.53814.5385023419413.2371189775643
Trimmed Mean ( 4 / 20 )50469.98076923083779.6297192780013.3531548108559
Trimmed Mean ( 5 / 20 )50429.943737.2441828127013.4938841384578
Trimmed Mean ( 6 / 20 )50461.64583333333719.1975304928513.5678853891491
Trimmed Mean ( 7 / 20 )50471.1521739133702.2892476680513.6324173498068
Trimmed Mean ( 8 / 20 )50522.36363636363685.089409027613.7099424270672
Trimmed Mean ( 9 / 20 )50579.73809523813656.9802305417513.8310121757878
Trimmed Mean ( 10 / 20 )50673.93621.8670806289413.9910987542923
Trimmed Mean ( 11 / 20 )50781.10526315793570.7546775133714.2213929125261
Trimmed Mean ( 12 / 20 )50893.55555555563515.7299213777114.4759571109523
Trimmed Mean ( 13 / 20 )51029.61764705883444.9068253984514.8130617846701
Trimmed Mean ( 14 / 20 )51184.031253344.3944873270615.3044239978125
Trimmed Mean ( 15 / 20 )51368.33333333333204.9219264732916.0279515419770
Trimmed Mean ( 16 / 20 )51641.46428571433108.0748105106116.6152578152488
Trimmed Mean ( 17 / 20 )51971.73076923082965.4433963744117.5257874868804
Trimmed Mean ( 18 / 20 )52254.8752859.2375835357318.2758072644602
Trimmed Mean ( 19 / 20 )52508.04545454552732.9729942587219.2127933809999
Trimmed Mean ( 20 / 20 )52607.952670.1416121276819.7023070840351
Median54227
Midrange66009
Midmean - Weighted Average at Xnp50217.2903225806
Midmean - Weighted Average at X(n+1)p51368.3333333333
Midmean - Empirical Distribution Function50217.2903225806
Midmean - Empirical Distribution Function - Averaging51368.3333333333
Midmean - Empirical Distribution Function - Interpolation51368.3333333333
Midmean - Closest Observation50217.2903225806
Midmean - True Basic - Statistics Graphics Toolkit51368.3333333333
Midmean - MS Excel (old versions)51184.03125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 51466.6666666667 & 4172.48807106761 & 12.3347666404467 \tabularnewline
Geometric Mean & 37671.7953065482 &  &  \tabularnewline
Harmonic Mean & 21812.4682622998 &  &  \tabularnewline
Quadratic Mean & 60629.9226724451 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 51210.95 & 4098.20598688921 & 12.4959433868946 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 51077.05 & 4026.37341227094 & 12.6856217171352 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 50554.65 & 3866.41005245 & 13.0753462033768 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 50603.45 & 3852.84161428417 & 13.1340592388721 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 50303.1166666667 & 3731.21635542784 & 13.4816938700138 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 50417.9166666667 & 3690.013010273 & 13.6633438761064 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 50208.2666666667 & 3648.77825662596 & 13.7602954017530 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 50201.0666666667 & 3643.64500865235 & 13.7777051681646 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 50014.7666666667 & 3608.44072655258 & 13.8604927880995 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 49994.9333333333 & 3597.01842089579 & 13.8989928555558 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 50038.9333333333 & 3516.31678832509 & 14.2304963817461 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 49968.3333333333 & 3469.85749529643 & 14.4006874636979 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 49959.0166666667 & 3448.27524368487 & 14.4881174315075 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 49893.9166666667 & 3411.97299072404 & 14.6231862920108 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 49456.4166666667 & 3061.65924193469 & 16.1534686777927 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 49351.6166666667 & 3022.32331761676 & 16.3290328268329 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 50046.35 & 2705.74378422825 & 18.4963374180954 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 50583.95 & 2572.98171503216 & 19.6596616697557 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 51875.3166666667 & 2224.09347717065 & 23.3242519701371 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 52123.3166666667 & 2150.56795881356 & 24.2370004877328 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 50965.2068965517 & 4010.71891810226 & 12.7072497318428 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 50701.9107142857 & 3902.08515788681 & 12.9935428528022 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 50493.5 & 3814.53850234194 & 13.2371189775643 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 50469.9807692308 & 3779.62971927800 & 13.3531548108559 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 50429.94 & 3737.24418281270 & 13.4938841384578 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 50461.6458333333 & 3719.19753049285 & 13.5678853891491 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 50471.152173913 & 3702.28924766805 & 13.6324173498068 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 50522.3636363636 & 3685.0894090276 & 13.7099424270672 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 50579.7380952381 & 3656.98023054175 & 13.8310121757878 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 50673.9 & 3621.86708062894 & 13.9910987542923 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 50781.1052631579 & 3570.75467751337 & 14.2213929125261 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 50893.5555555556 & 3515.72992137771 & 14.4759571109523 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 51029.6176470588 & 3444.90682539845 & 14.8130617846701 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 51184.03125 & 3344.39448732706 & 15.3044239978125 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 51368.3333333333 & 3204.92192647329 & 16.0279515419770 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 51641.4642857143 & 3108.07481051061 & 16.6152578152488 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 51971.7307692308 & 2965.44339637441 & 17.5257874868804 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 52254.875 & 2859.23758353573 & 18.2758072644602 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 52508.0454545455 & 2732.97299425872 & 19.2127933809999 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 52607.95 & 2670.14161212768 & 19.7023070840351 \tabularnewline
Median & 54227 &  &  \tabularnewline
Midrange & 66009 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 50217.2903225806 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 51368.3333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 50217.2903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 51368.3333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 51368.3333333333 &  &  \tabularnewline
Midmean - Closest Observation & 50217.2903225806 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 51368.3333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 51184.03125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66021&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]51466.6666666667[/C][C]4172.48807106761[/C][C]12.3347666404467[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]37671.7953065482[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21812.4682622998[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]60629.9226724451[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]51210.95[/C][C]4098.20598688921[/C][C]12.4959433868946[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]51077.05[/C][C]4026.37341227094[/C][C]12.6856217171352[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]50554.65[/C][C]3866.41005245[/C][C]13.0753462033768[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]50603.45[/C][C]3852.84161428417[/C][C]13.1340592388721[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]50303.1166666667[/C][C]3731.21635542784[/C][C]13.4816938700138[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]50417.9166666667[/C][C]3690.013010273[/C][C]13.6633438761064[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]50208.2666666667[/C][C]3648.77825662596[/C][C]13.7602954017530[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]50201.0666666667[/C][C]3643.64500865235[/C][C]13.7777051681646[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]50014.7666666667[/C][C]3608.44072655258[/C][C]13.8604927880995[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]49994.9333333333[/C][C]3597.01842089579[/C][C]13.8989928555558[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]50038.9333333333[/C][C]3516.31678832509[/C][C]14.2304963817461[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]49968.3333333333[/C][C]3469.85749529643[/C][C]14.4006874636979[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]49959.0166666667[/C][C]3448.27524368487[/C][C]14.4881174315075[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]49893.9166666667[/C][C]3411.97299072404[/C][C]14.6231862920108[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]49456.4166666667[/C][C]3061.65924193469[/C][C]16.1534686777927[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]49351.6166666667[/C][C]3022.32331761676[/C][C]16.3290328268329[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]50046.35[/C][C]2705.74378422825[/C][C]18.4963374180954[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]50583.95[/C][C]2572.98171503216[/C][C]19.6596616697557[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]51875.3166666667[/C][C]2224.09347717065[/C][C]23.3242519701371[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]52123.3166666667[/C][C]2150.56795881356[/C][C]24.2370004877328[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]50965.2068965517[/C][C]4010.71891810226[/C][C]12.7072497318428[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]50701.9107142857[/C][C]3902.08515788681[/C][C]12.9935428528022[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]50493.5[/C][C]3814.53850234194[/C][C]13.2371189775643[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]50469.9807692308[/C][C]3779.62971927800[/C][C]13.3531548108559[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]50429.94[/C][C]3737.24418281270[/C][C]13.4938841384578[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]50461.6458333333[/C][C]3719.19753049285[/C][C]13.5678853891491[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]50471.152173913[/C][C]3702.28924766805[/C][C]13.6324173498068[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]50522.3636363636[/C][C]3685.0894090276[/C][C]13.7099424270672[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]50579.7380952381[/C][C]3656.98023054175[/C][C]13.8310121757878[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]50673.9[/C][C]3621.86708062894[/C][C]13.9910987542923[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]50781.1052631579[/C][C]3570.75467751337[/C][C]14.2213929125261[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]50893.5555555556[/C][C]3515.72992137771[/C][C]14.4759571109523[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]51029.6176470588[/C][C]3444.90682539845[/C][C]14.8130617846701[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]51184.03125[/C][C]3344.39448732706[/C][C]15.3044239978125[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]51368.3333333333[/C][C]3204.92192647329[/C][C]16.0279515419770[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]51641.4642857143[/C][C]3108.07481051061[/C][C]16.6152578152488[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]51971.7307692308[/C][C]2965.44339637441[/C][C]17.5257874868804[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]52254.875[/C][C]2859.23758353573[/C][C]18.2758072644602[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]52508.0454545455[/C][C]2732.97299425872[/C][C]19.2127933809999[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]52607.95[/C][C]2670.14161212768[/C][C]19.7023070840351[/C][/ROW]
[ROW][C]Median[/C][C]54227[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]66009[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]50217.2903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]51368.3333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]50217.2903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]51368.3333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]51368.3333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]50217.2903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]51368.3333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]51184.03125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66021&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66021&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 Mean51466.66666666674172.4880710676112.3347666404467
Geometric Mean37671.7953065482
Harmonic Mean21812.4682622998
Quadratic Mean60629.9226724451
Winsorized Mean ( 1 / 20 )51210.954098.2059868892112.4959433868946
Winsorized Mean ( 2 / 20 )51077.054026.3734122709412.6856217171352
Winsorized Mean ( 3 / 20 )50554.653866.4100524513.0753462033768
Winsorized Mean ( 4 / 20 )50603.453852.8416142841713.1340592388721
Winsorized Mean ( 5 / 20 )50303.11666666673731.2163554278413.4816938700138
Winsorized Mean ( 6 / 20 )50417.91666666673690.01301027313.6633438761064
Winsorized Mean ( 7 / 20 )50208.26666666673648.7782566259613.7602954017530
Winsorized Mean ( 8 / 20 )50201.06666666673643.6450086523513.7777051681646
Winsorized Mean ( 9 / 20 )50014.76666666673608.4407265525813.8604927880995
Winsorized Mean ( 10 / 20 )49994.93333333333597.0184208957913.8989928555558
Winsorized Mean ( 11 / 20 )50038.93333333333516.3167883250914.2304963817461
Winsorized Mean ( 12 / 20 )49968.33333333333469.8574952964314.4006874636979
Winsorized Mean ( 13 / 20 )49959.01666666673448.2752436848714.4881174315075
Winsorized Mean ( 14 / 20 )49893.91666666673411.9729907240414.6231862920108
Winsorized Mean ( 15 / 20 )49456.41666666673061.6592419346916.1534686777927
Winsorized Mean ( 16 / 20 )49351.61666666673022.3233176167616.3290328268329
Winsorized Mean ( 17 / 20 )50046.352705.7437842282518.4963374180954
Winsorized Mean ( 18 / 20 )50583.952572.9817150321619.6596616697557
Winsorized Mean ( 19 / 20 )51875.31666666672224.0934771706523.3242519701371
Winsorized Mean ( 20 / 20 )52123.31666666672150.5679588135624.2370004877328
Trimmed Mean ( 1 / 20 )50965.20689655174010.7189181022612.7072497318428
Trimmed Mean ( 2 / 20 )50701.91071428573902.0851578868112.9935428528022
Trimmed Mean ( 3 / 20 )50493.53814.5385023419413.2371189775643
Trimmed Mean ( 4 / 20 )50469.98076923083779.6297192780013.3531548108559
Trimmed Mean ( 5 / 20 )50429.943737.2441828127013.4938841384578
Trimmed Mean ( 6 / 20 )50461.64583333333719.1975304928513.5678853891491
Trimmed Mean ( 7 / 20 )50471.1521739133702.2892476680513.6324173498068
Trimmed Mean ( 8 / 20 )50522.36363636363685.089409027613.7099424270672
Trimmed Mean ( 9 / 20 )50579.73809523813656.9802305417513.8310121757878
Trimmed Mean ( 10 / 20 )50673.93621.8670806289413.9910987542923
Trimmed Mean ( 11 / 20 )50781.10526315793570.7546775133714.2213929125261
Trimmed Mean ( 12 / 20 )50893.55555555563515.7299213777114.4759571109523
Trimmed Mean ( 13 / 20 )51029.61764705883444.9068253984514.8130617846701
Trimmed Mean ( 14 / 20 )51184.031253344.3944873270615.3044239978125
Trimmed Mean ( 15 / 20 )51368.33333333333204.9219264732916.0279515419770
Trimmed Mean ( 16 / 20 )51641.46428571433108.0748105106116.6152578152488
Trimmed Mean ( 17 / 20 )51971.73076923082965.4433963744117.5257874868804
Trimmed Mean ( 18 / 20 )52254.8752859.2375835357318.2758072644602
Trimmed Mean ( 19 / 20 )52508.04545454552732.9729942587219.2127933809999
Trimmed Mean ( 20 / 20 )52607.952670.1416121276819.7023070840351
Median54227
Midrange66009
Midmean - Weighted Average at Xnp50217.2903225806
Midmean - Weighted Average at X(n+1)p51368.3333333333
Midmean - Empirical Distribution Function50217.2903225806
Midmean - Empirical Distribution Function - Averaging51368.3333333333
Midmean - Empirical Distribution Function - Interpolation51368.3333333333
Midmean - Closest Observation50217.2903225806
Midmean - True Basic - Statistics Graphics Toolkit51368.3333333333
Midmean - MS Excel (old versions)51184.03125
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')