Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 18 Dec 2014 20:03:02 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/18/t14189329941tjtfyc78fevg1r.htm/, Retrieved Sun, 19 May 2024 18:06:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271264, Retrieved Sun, 19 May 2024 18:06:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-12-18 20:03:02] [4897fbbb7461c8caec7645a3718e7cbe] [Current]
Feedback Forum

Post a new message
Dataseries X:
18
39
46
31
67
35
52
77
37
32
36
69
21
26
54
36
23
112
35
47
37
109
20
22
23
32
30
43
16
49
43
46
19
23
59
32
19
22
48
23
33
34
48
18
33
67
80
32
43
38
29
32
35
29
12
37
51
14
20
11
35
8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271264&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271264&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271264&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean37.85483870967742.6249672531203714.4210708399042
Geometric Mean33.198790635758
Harmonic Mean28.9315571332704
Quadratic Mean43.0500458955958
Winsorized Mean ( 1 / 20 )37.85483870967742.5942668326201914.5917290518047
Winsorized Mean ( 2 / 20 )36.95161290322582.2252133652924316.6058740611464
Winsorized Mean ( 3 / 20 )36.90322580645162.1628209928169117.062542822089
Winsorized Mean ( 4 / 20 )36.51612903225811.992946570145918.3226833971694
Winsorized Mean ( 5 / 20 )36.51612903225811.9240939320293818.9783504975476
Winsorized Mean ( 6 / 20 )36.51612903225811.9240939320293818.9783504975476
Winsorized Mean ( 7 / 20 )35.72580645161291.6855012662967221.1959534922851
Winsorized Mean ( 8 / 20 )35.08064516129031.5474682735657722.6697023522526
Winsorized Mean ( 9 / 20 )34.93548387096771.4661473430705323.828085244013
Winsorized Mean ( 10 / 20 )34.77419354838711.4358150884377424.2191308814172
Winsorized Mean ( 11 / 20 )34.59677419354841.3419678356145825.7806284736355
Winsorized Mean ( 12 / 20 )34.59677419354841.2765342750501327.1021114510926
Winsorized Mean ( 13 / 20 )34.59677419354841.2765342750501327.1021114510926
Winsorized Mean ( 14 / 20 )34.59677419354841.2018537764459328.7861758822744
Winsorized Mean ( 15 / 20 )34.35483870967741.1614959568804329.5780958221744
Winsorized Mean ( 16 / 20 )34.35483870967741.1614959568804329.5780958221744
Winsorized Mean ( 17 / 20 )33.53225806451611.0316815715697332.5025269313436
Winsorized Mean ( 18 / 20 )34.40322580645160.89106846108312438.6089591417402
Winsorized Mean ( 19 / 20 )35.32258064516130.75634953459457646.701398003894
Winsorized Mean ( 20 / 20 )34.03225806451610.55189100519559461.6648174080222
Trimmed Mean ( 1 / 20 )37.11666666666672.3553151415884615.758683842891
Trimmed Mean ( 2 / 20 )36.32758620689662.0395941512703517.8111837515665
Trimmed Mean ( 3 / 20 )35.98214285714291.9109206102948718.8297424096496
Trimmed Mean ( 4 / 20 )35.62962962962961.7806507765947520.0093303515507
Trimmed Mean ( 5 / 20 )35.36538461538461.6897412151490420.9294679554025
Trimmed Mean ( 6 / 20 )35.081.599193674375721.9360547519015
Trimmed Mean ( 7 / 20 )34.77083333333331.481337683562523.4725908340576
Trimmed Mean ( 8 / 20 )34.58695652173911.4096205289746524.5363598293346
Trimmed Mean ( 9 / 20 )34.51.3587474022684525.3910329045721
Trimmed Mean ( 10 / 20 )34.42857142857141.3146820591086826.1877548187683
Trimmed Mean ( 11 / 20 )34.3751.2642457465589127.190125095191
Trimmed Mean ( 12 / 20 )34.34210526315791.2222896196695928.0965367867898
Trimmed Mean ( 13 / 20 )34.30555555555561.182423825154429.012909606313
Trimmed Mean ( 14 / 20 )34.26470588235291.1260240524602930.4298170252108
Trimmed Mean ( 15 / 20 )34.218751.0689291964466732.0121764039655
Trimmed Mean ( 16 / 20 )34.20.99931010685130834.2236106345002
Trimmed Mean ( 17 / 20 )34.17857142857140.89391471757534438.2347116079232
Trimmed Mean ( 18 / 20 )34.26923076923080.78555750376148643.6240893952886
Trimmed Mean ( 19 / 20 )34.250.68166994435978950.2442571854432
Trimmed Mean ( 20 / 20 )34.09090909090910.57324583134658559.4699642399976
Median34.5
Midrange60
Midmean - Weighted Average at Xnp33.8787878787879
Midmean - Weighted Average at X(n+1)p33.8787878787879
Midmean - Empirical Distribution Function33.8787878787879
Midmean - Empirical Distribution Function - Averaging33.8787878787879
Midmean - Empirical Distribution Function - Interpolation33.8787878787879
Midmean - Closest Observation33.8787878787879
Midmean - True Basic - Statistics Graphics Toolkit33.8787878787879
Midmean - MS Excel (old versions)33.8787878787879
Number of observations62

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 37.8548387096774 & 2.62496725312037 & 14.4210708399042 \tabularnewline
Geometric Mean & 33.198790635758 &  &  \tabularnewline
Harmonic Mean & 28.9315571332704 &  &  \tabularnewline
Quadratic Mean & 43.0500458955958 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 37.8548387096774 & 2.59426683262019 & 14.5917290518047 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 36.9516129032258 & 2.22521336529243 & 16.6058740611464 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 36.9032258064516 & 2.16282099281691 & 17.062542822089 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 36.5161290322581 & 1.9929465701459 & 18.3226833971694 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 36.5161290322581 & 1.92409393202938 & 18.9783504975476 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 36.5161290322581 & 1.92409393202938 & 18.9783504975476 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 35.7258064516129 & 1.68550126629672 & 21.1959534922851 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 35.0806451612903 & 1.54746827356577 & 22.6697023522526 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 34.9354838709677 & 1.46614734307053 & 23.828085244013 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 34.7741935483871 & 1.43581508843774 & 24.2191308814172 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 34.5967741935484 & 1.34196783561458 & 25.7806284736355 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 34.5967741935484 & 1.27653427505013 & 27.1021114510926 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 34.5967741935484 & 1.27653427505013 & 27.1021114510926 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 34.5967741935484 & 1.20185377644593 & 28.7861758822744 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 34.3548387096774 & 1.16149595688043 & 29.5780958221744 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 34.3548387096774 & 1.16149595688043 & 29.5780958221744 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 33.5322580645161 & 1.03168157156973 & 32.5025269313436 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 34.4032258064516 & 0.891068461083124 & 38.6089591417402 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 35.3225806451613 & 0.756349534594576 & 46.701398003894 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 34.0322580645161 & 0.551891005195594 & 61.6648174080222 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 37.1166666666667 & 2.35531514158846 & 15.758683842891 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 36.3275862068966 & 2.03959415127035 & 17.8111837515665 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 35.9821428571429 & 1.91092061029487 & 18.8297424096496 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 35.6296296296296 & 1.78065077659475 & 20.0093303515507 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 35.3653846153846 & 1.68974121514904 & 20.9294679554025 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 35.08 & 1.5991936743757 & 21.9360547519015 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 34.7708333333333 & 1.4813376835625 & 23.4725908340576 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 34.5869565217391 & 1.40962052897465 & 24.5363598293346 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 34.5 & 1.35874740226845 & 25.3910329045721 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 34.4285714285714 & 1.31468205910868 & 26.1877548187683 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 34.375 & 1.26424574655891 & 27.190125095191 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 34.3421052631579 & 1.22228961966959 & 28.0965367867898 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 34.3055555555556 & 1.1824238251544 & 29.012909606313 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 34.2647058823529 & 1.12602405246029 & 30.4298170252108 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 34.21875 & 1.06892919644667 & 32.0121764039655 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 34.2 & 0.999310106851308 & 34.2236106345002 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 34.1785714285714 & 0.893914717575344 & 38.2347116079232 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 34.2692307692308 & 0.785557503761486 & 43.6240893952886 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 34.25 & 0.681669944359789 & 50.2442571854432 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 34.0909090909091 & 0.573245831346585 & 59.4699642399976 \tabularnewline
Median & 34.5 &  &  \tabularnewline
Midrange & 60 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 33.8787878787879 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 33.8787878787879 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 33.8787878787879 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 33.8787878787879 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 33.8787878787879 &  &  \tabularnewline
Midmean - Closest Observation & 33.8787878787879 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 33.8787878787879 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 33.8787878787879 &  &  \tabularnewline
Number of observations & 62 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271264&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]37.8548387096774[/C][C]2.62496725312037[/C][C]14.4210708399042[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]33.198790635758[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]28.9315571332704[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]43.0500458955958[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]37.8548387096774[/C][C]2.59426683262019[/C][C]14.5917290518047[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]36.9516129032258[/C][C]2.22521336529243[/C][C]16.6058740611464[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]36.9032258064516[/C][C]2.16282099281691[/C][C]17.062542822089[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]36.5161290322581[/C][C]1.9929465701459[/C][C]18.3226833971694[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]36.5161290322581[/C][C]1.92409393202938[/C][C]18.9783504975476[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]36.5161290322581[/C][C]1.92409393202938[/C][C]18.9783504975476[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]35.7258064516129[/C][C]1.68550126629672[/C][C]21.1959534922851[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]35.0806451612903[/C][C]1.54746827356577[/C][C]22.6697023522526[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]34.9354838709677[/C][C]1.46614734307053[/C][C]23.828085244013[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]34.7741935483871[/C][C]1.43581508843774[/C][C]24.2191308814172[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]34.5967741935484[/C][C]1.34196783561458[/C][C]25.7806284736355[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]34.5967741935484[/C][C]1.27653427505013[/C][C]27.1021114510926[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]34.5967741935484[/C][C]1.27653427505013[/C][C]27.1021114510926[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]34.5967741935484[/C][C]1.20185377644593[/C][C]28.7861758822744[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]34.3548387096774[/C][C]1.16149595688043[/C][C]29.5780958221744[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]34.3548387096774[/C][C]1.16149595688043[/C][C]29.5780958221744[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]33.5322580645161[/C][C]1.03168157156973[/C][C]32.5025269313436[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]34.4032258064516[/C][C]0.891068461083124[/C][C]38.6089591417402[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]35.3225806451613[/C][C]0.756349534594576[/C][C]46.701398003894[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]34.0322580645161[/C][C]0.551891005195594[/C][C]61.6648174080222[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]37.1166666666667[/C][C]2.35531514158846[/C][C]15.758683842891[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]36.3275862068966[/C][C]2.03959415127035[/C][C]17.8111837515665[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]35.9821428571429[/C][C]1.91092061029487[/C][C]18.8297424096496[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]35.6296296296296[/C][C]1.78065077659475[/C][C]20.0093303515507[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]35.3653846153846[/C][C]1.68974121514904[/C][C]20.9294679554025[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]35.08[/C][C]1.5991936743757[/C][C]21.9360547519015[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]34.7708333333333[/C][C]1.4813376835625[/C][C]23.4725908340576[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]34.5869565217391[/C][C]1.40962052897465[/C][C]24.5363598293346[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]34.5[/C][C]1.35874740226845[/C][C]25.3910329045721[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]34.4285714285714[/C][C]1.31468205910868[/C][C]26.1877548187683[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]34.375[/C][C]1.26424574655891[/C][C]27.190125095191[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]34.3421052631579[/C][C]1.22228961966959[/C][C]28.0965367867898[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]34.3055555555556[/C][C]1.1824238251544[/C][C]29.012909606313[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]34.2647058823529[/C][C]1.12602405246029[/C][C]30.4298170252108[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]34.21875[/C][C]1.06892919644667[/C][C]32.0121764039655[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]34.2[/C][C]0.999310106851308[/C][C]34.2236106345002[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]34.1785714285714[/C][C]0.893914717575344[/C][C]38.2347116079232[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]34.2692307692308[/C][C]0.785557503761486[/C][C]43.6240893952886[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]34.25[/C][C]0.681669944359789[/C][C]50.2442571854432[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]34.0909090909091[/C][C]0.573245831346585[/C][C]59.4699642399976[/C][/ROW]
[ROW][C]Median[/C][C]34.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]60[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]33.8787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]33.8787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]33.8787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]33.8787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]33.8787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]33.8787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]33.8787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]33.8787878787879[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]62[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271264&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271264&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 Mean37.85483870967742.6249672531203714.4210708399042
Geometric Mean33.198790635758
Harmonic Mean28.9315571332704
Quadratic Mean43.0500458955958
Winsorized Mean ( 1 / 20 )37.85483870967742.5942668326201914.5917290518047
Winsorized Mean ( 2 / 20 )36.95161290322582.2252133652924316.6058740611464
Winsorized Mean ( 3 / 20 )36.90322580645162.1628209928169117.062542822089
Winsorized Mean ( 4 / 20 )36.51612903225811.992946570145918.3226833971694
Winsorized Mean ( 5 / 20 )36.51612903225811.9240939320293818.9783504975476
Winsorized Mean ( 6 / 20 )36.51612903225811.9240939320293818.9783504975476
Winsorized Mean ( 7 / 20 )35.72580645161291.6855012662967221.1959534922851
Winsorized Mean ( 8 / 20 )35.08064516129031.5474682735657722.6697023522526
Winsorized Mean ( 9 / 20 )34.93548387096771.4661473430705323.828085244013
Winsorized Mean ( 10 / 20 )34.77419354838711.4358150884377424.2191308814172
Winsorized Mean ( 11 / 20 )34.59677419354841.3419678356145825.7806284736355
Winsorized Mean ( 12 / 20 )34.59677419354841.2765342750501327.1021114510926
Winsorized Mean ( 13 / 20 )34.59677419354841.2765342750501327.1021114510926
Winsorized Mean ( 14 / 20 )34.59677419354841.2018537764459328.7861758822744
Winsorized Mean ( 15 / 20 )34.35483870967741.1614959568804329.5780958221744
Winsorized Mean ( 16 / 20 )34.35483870967741.1614959568804329.5780958221744
Winsorized Mean ( 17 / 20 )33.53225806451611.0316815715697332.5025269313436
Winsorized Mean ( 18 / 20 )34.40322580645160.89106846108312438.6089591417402
Winsorized Mean ( 19 / 20 )35.32258064516130.75634953459457646.701398003894
Winsorized Mean ( 20 / 20 )34.03225806451610.55189100519559461.6648174080222
Trimmed Mean ( 1 / 20 )37.11666666666672.3553151415884615.758683842891
Trimmed Mean ( 2 / 20 )36.32758620689662.0395941512703517.8111837515665
Trimmed Mean ( 3 / 20 )35.98214285714291.9109206102948718.8297424096496
Trimmed Mean ( 4 / 20 )35.62962962962961.7806507765947520.0093303515507
Trimmed Mean ( 5 / 20 )35.36538461538461.6897412151490420.9294679554025
Trimmed Mean ( 6 / 20 )35.081.599193674375721.9360547519015
Trimmed Mean ( 7 / 20 )34.77083333333331.481337683562523.4725908340576
Trimmed Mean ( 8 / 20 )34.58695652173911.4096205289746524.5363598293346
Trimmed Mean ( 9 / 20 )34.51.3587474022684525.3910329045721
Trimmed Mean ( 10 / 20 )34.42857142857141.3146820591086826.1877548187683
Trimmed Mean ( 11 / 20 )34.3751.2642457465589127.190125095191
Trimmed Mean ( 12 / 20 )34.34210526315791.2222896196695928.0965367867898
Trimmed Mean ( 13 / 20 )34.30555555555561.182423825154429.012909606313
Trimmed Mean ( 14 / 20 )34.26470588235291.1260240524602930.4298170252108
Trimmed Mean ( 15 / 20 )34.218751.0689291964466732.0121764039655
Trimmed Mean ( 16 / 20 )34.20.99931010685130834.2236106345002
Trimmed Mean ( 17 / 20 )34.17857142857140.89391471757534438.2347116079232
Trimmed Mean ( 18 / 20 )34.26923076923080.78555750376148643.6240893952886
Trimmed Mean ( 19 / 20 )34.250.68166994435978950.2442571854432
Trimmed Mean ( 20 / 20 )34.09090909090910.57324583134658559.4699642399976
Median34.5
Midrange60
Midmean - Weighted Average at Xnp33.8787878787879
Midmean - Weighted Average at X(n+1)p33.8787878787879
Midmean - Empirical Distribution Function33.8787878787879
Midmean - Empirical Distribution Function - Averaging33.8787878787879
Midmean - Empirical Distribution Function - Interpolation33.8787878787879
Midmean - Closest Observation33.8787878787879
Midmean - True Basic - Statistics Graphics Toolkit33.8787878787879
Midmean - MS Excel (old versions)33.8787878787879
Number of observations62



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')