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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, 26 Nov 2010 13:56:53 +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/2010/Nov/26/t1290779764svqj2v2vyit0kb3.htm/, Retrieved Fri, 03 May 2024 22:41:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101880, Retrieved Fri, 03 May 2024 22:41:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWorkshop 3
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Minitutorial Test...] [2010-11-26 13:56:53] [f76239c595e4d455b3b05a43389f68d5] [Current]
-    D    [Central Tendency] [] [2010-11-30 19:29:46] [f47feae0308dca73181bb669fbad1c56]
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Dataseries X:
6
7
4
3
0
6
3
1
6
5
7
4
3
6
6
5
2
3
-2
-4
0
1
4
-3
-3
0
6
-1
0
-1
1
-4
-1
-1
0
3
0
8
8
8
8
11
13
5
12
13
9
11
7
12
11
10
13
14
10
13
12
13
17
15
6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101880&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101880&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101880&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'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.426229508196720.6861068662453287.90872351692293
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean7.59529621477424
Winsorized Mean ( 1 / 20 )5.393442622950820.6776198655986077.95939271672071
Winsorized Mean ( 2 / 20 )5.393442622950820.6629453605738068.13557638940648
Winsorized Mean ( 3 / 20 )5.344262295081970.6528145226931988.18649418679309
Winsorized Mean ( 4 / 20 )5.409836065573770.6394913660108058.45959203377637
Winsorized Mean ( 5 / 20 )5.491803278688520.6244660892496668.79439792365229
Winsorized Mean ( 6 / 20 )5.491803278688520.6244660892496668.79439792365229
Winsorized Mean ( 7 / 20 )5.491803278688520.6244660892496668.79439792365229
Winsorized Mean ( 8 / 20 )5.360655737704920.5991947177448738.9464335698423
Winsorized Mean ( 9 / 20 )5.508196721311480.5743244788490969.59073994608327
Winsorized Mean ( 10 / 20 )5.508196721311480.5743244788490969.59073994608327
Winsorized Mean ( 11 / 20 )5.327868852459020.5415628625926719.8379509018629
Winsorized Mean ( 12 / 20 )5.327868852459020.5415628625926719.8379509018629
Winsorized Mean ( 13 / 20 )5.327868852459020.5415628625926719.8379509018629
Winsorized Mean ( 14 / 20 )5.09836065573770.50283617362343310.1392082017468
Winsorized Mean ( 15 / 20 )5.344262295081970.46275797466456511.5487200387110
Winsorized Mean ( 16 / 20 )5.081967213114750.42031414348919612.0908784342285
Winsorized Mean ( 17 / 20 )4.803278688524590.37896874168655412.6746038925221
Winsorized Mean ( 18 / 20 )5.09836065573770.33117188678562615.3949077780204
Winsorized Mean ( 19 / 20 )5.409836065573770.28474612331575018.9988049796024
Winsorized Mean ( 20 / 20 )5.409836065573770.28474612331575018.9988049796024
Trimmed Mean ( 1 / 20 )5.389830508474580.6620800993460348.14075292974121
Trimmed Mean ( 2 / 20 )5.38596491228070.642946297198128.37700588019882
Trimmed Mean ( 3 / 20 )5.381818181818180.6289807419934198.55641170310186
Trimmed Mean ( 4 / 20 )5.396226415094340.6162645692666928.75634700452671
Trimmed Mean ( 5 / 20 )5.39215686274510.6052569905469258.90887168089147
Trimmed Mean ( 6 / 20 )5.367346938775510.595971365642549.00604835769042
Trimmed Mean ( 7 / 20 )5.340425531914890.583679194565819.14959035997087
Trimmed Mean ( 8 / 20 )5.311111111111110.5674880163574529.35898372832903
Trimmed Mean ( 9 / 20 )5.302325581395350.5533897191923489.58153973141008
Trimmed Mean ( 10 / 20 )5.268292682926830.5410292700299589.73753727341796
Trimmed Mean ( 11 / 20 )5.230769230769230.5240009303253519.98236630519236
Trimmed Mean ( 12 / 20 )5.216216216216220.50986534042634310.2305761985203
Trimmed Mean ( 13 / 20 )5.20.48989794855663610.6144555520604
Trimmed Mean ( 14 / 20 )5.181818181818180.46149983062175911.2282125322493
Trimmed Mean ( 15 / 20 )5.193548387096770.43358806782055811.9780703680391
Trimmed Mean ( 16 / 20 )5.172413793103450.4064412581762412.7261041763152
Trimmed Mean ( 17 / 20 )5.185185185185190.3813196348513713.5980020730017
Trimmed Mean ( 18 / 20 )5.240.35721142198983514.6691837870434
Trimmed Mean ( 19 / 20 )5.260869565217390.33982901597161515.4809310505046
Trimmed Mean ( 20 / 20 )5.238095238095240.33025792160761315.860619520033
Median6
Midrange6.5
Midmean - Weighted Average at Xnp5.03333333333333
Midmean - Weighted Average at X(n+1)p5.34375
Midmean - Empirical Distribution Function5.34375
Midmean - Empirical Distribution Function - Averaging5.34375
Midmean - Empirical Distribution Function - Interpolation5.34375
Midmean - Closest Observation4.5
Midmean - True Basic - Statistics Graphics Toolkit5.34375
Midmean - MS Excel (old versions)5.34375
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.42622950819672 & 0.686106866245328 & 7.90872351692293 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 7.59529621477424 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 5.39344262295082 & 0.677619865598607 & 7.95939271672071 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 5.39344262295082 & 0.662945360573806 & 8.13557638940648 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 5.34426229508197 & 0.652814522693198 & 8.18649418679309 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 5.40983606557377 & 0.639491366010805 & 8.45959203377637 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 5.49180327868852 & 0.624466089249666 & 8.79439792365229 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 5.49180327868852 & 0.624466089249666 & 8.79439792365229 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 5.49180327868852 & 0.624466089249666 & 8.79439792365229 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 5.36065573770492 & 0.599194717744873 & 8.9464335698423 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 5.50819672131148 & 0.574324478849096 & 9.59073994608327 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 5.50819672131148 & 0.574324478849096 & 9.59073994608327 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 5.32786885245902 & 0.541562862592671 & 9.8379509018629 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 5.32786885245902 & 0.541562862592671 & 9.8379509018629 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 5.32786885245902 & 0.541562862592671 & 9.8379509018629 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 5.0983606557377 & 0.502836173623433 & 10.1392082017468 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 5.34426229508197 & 0.462757974664565 & 11.5487200387110 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 5.08196721311475 & 0.420314143489196 & 12.0908784342285 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 4.80327868852459 & 0.378968741686554 & 12.6746038925221 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 5.0983606557377 & 0.331171886785626 & 15.3949077780204 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 5.40983606557377 & 0.284746123315750 & 18.9988049796024 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 5.40983606557377 & 0.284746123315750 & 18.9988049796024 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 5.38983050847458 & 0.662080099346034 & 8.14075292974121 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 5.3859649122807 & 0.64294629719812 & 8.37700588019882 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 5.38181818181818 & 0.628980741993419 & 8.55641170310186 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 5.39622641509434 & 0.616264569266692 & 8.75634700452671 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 5.3921568627451 & 0.605256990546925 & 8.90887168089147 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 5.36734693877551 & 0.59597136564254 & 9.00604835769042 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 5.34042553191489 & 0.58367919456581 & 9.14959035997087 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 5.31111111111111 & 0.567488016357452 & 9.35898372832903 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 5.30232558139535 & 0.553389719192348 & 9.58153973141008 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 5.26829268292683 & 0.541029270029958 & 9.73753727341796 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 5.23076923076923 & 0.524000930325351 & 9.98236630519236 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 5.21621621621622 & 0.509865340426343 & 10.2305761985203 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 5.2 & 0.489897948556636 & 10.6144555520604 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 5.18181818181818 & 0.461499830621759 & 11.2282125322493 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 5.19354838709677 & 0.433588067820558 & 11.9780703680391 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 5.17241379310345 & 0.40644125817624 & 12.7261041763152 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 5.18518518518519 & 0.38131963485137 & 13.5980020730017 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 5.24 & 0.357211421989835 & 14.6691837870434 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 5.26086956521739 & 0.339829015971615 & 15.4809310505046 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 5.23809523809524 & 0.330257921607613 & 15.860619520033 \tabularnewline
Median & 6 &  &  \tabularnewline
Midrange & 6.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 5.03333333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 5.34375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 5.34375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 5.34375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 5.34375 &  &  \tabularnewline
Midmean - Closest Observation & 4.5 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 5.34375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 5.34375 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101880&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]5.42622950819672[/C][C]0.686106866245328[/C][C]7.90872351692293[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.59529621477424[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]5.39344262295082[/C][C]0.677619865598607[/C][C]7.95939271672071[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]5.39344262295082[/C][C]0.662945360573806[/C][C]8.13557638940648[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]5.34426229508197[/C][C]0.652814522693198[/C][C]8.18649418679309[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]5.40983606557377[/C][C]0.639491366010805[/C][C]8.45959203377637[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]5.49180327868852[/C][C]0.624466089249666[/C][C]8.79439792365229[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]5.49180327868852[/C][C]0.624466089249666[/C][C]8.79439792365229[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]5.49180327868852[/C][C]0.624466089249666[/C][C]8.79439792365229[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]5.36065573770492[/C][C]0.599194717744873[/C][C]8.9464335698423[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]5.50819672131148[/C][C]0.574324478849096[/C][C]9.59073994608327[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]5.50819672131148[/C][C]0.574324478849096[/C][C]9.59073994608327[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]5.32786885245902[/C][C]0.541562862592671[/C][C]9.8379509018629[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]5.32786885245902[/C][C]0.541562862592671[/C][C]9.8379509018629[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]5.32786885245902[/C][C]0.541562862592671[/C][C]9.8379509018629[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]5.0983606557377[/C][C]0.502836173623433[/C][C]10.1392082017468[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]5.34426229508197[/C][C]0.462757974664565[/C][C]11.5487200387110[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]5.08196721311475[/C][C]0.420314143489196[/C][C]12.0908784342285[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]4.80327868852459[/C][C]0.378968741686554[/C][C]12.6746038925221[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]5.0983606557377[/C][C]0.331171886785626[/C][C]15.3949077780204[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]5.40983606557377[/C][C]0.284746123315750[/C][C]18.9988049796024[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]5.40983606557377[/C][C]0.284746123315750[/C][C]18.9988049796024[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]5.38983050847458[/C][C]0.662080099346034[/C][C]8.14075292974121[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]5.3859649122807[/C][C]0.64294629719812[/C][C]8.37700588019882[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]5.38181818181818[/C][C]0.628980741993419[/C][C]8.55641170310186[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]5.39622641509434[/C][C]0.616264569266692[/C][C]8.75634700452671[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]5.3921568627451[/C][C]0.605256990546925[/C][C]8.90887168089147[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]5.36734693877551[/C][C]0.59597136564254[/C][C]9.00604835769042[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]5.34042553191489[/C][C]0.58367919456581[/C][C]9.14959035997087[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]5.31111111111111[/C][C]0.567488016357452[/C][C]9.35898372832903[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]5.30232558139535[/C][C]0.553389719192348[/C][C]9.58153973141008[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]5.26829268292683[/C][C]0.541029270029958[/C][C]9.73753727341796[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]5.23076923076923[/C][C]0.524000930325351[/C][C]9.98236630519236[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]5.21621621621622[/C][C]0.509865340426343[/C][C]10.2305761985203[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]5.2[/C][C]0.489897948556636[/C][C]10.6144555520604[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]5.18181818181818[/C][C]0.461499830621759[/C][C]11.2282125322493[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]5.19354838709677[/C][C]0.433588067820558[/C][C]11.9780703680391[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]5.17241379310345[/C][C]0.40644125817624[/C][C]12.7261041763152[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]5.18518518518519[/C][C]0.38131963485137[/C][C]13.5980020730017[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]5.24[/C][C]0.357211421989835[/C][C]14.6691837870434[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]5.26086956521739[/C][C]0.339829015971615[/C][C]15.4809310505046[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]5.23809523809524[/C][C]0.330257921607613[/C][C]15.860619520033[/C][/ROW]
[ROW][C]Median[/C][C]6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]5.03333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]5.34375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]5.34375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]5.34375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]5.34375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]5.34375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]5.34375[/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=101880&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101880&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 Mean5.426229508196720.6861068662453287.90872351692293
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean7.59529621477424
Winsorized Mean ( 1 / 20 )5.393442622950820.6776198655986077.95939271672071
Winsorized Mean ( 2 / 20 )5.393442622950820.6629453605738068.13557638940648
Winsorized Mean ( 3 / 20 )5.344262295081970.6528145226931988.18649418679309
Winsorized Mean ( 4 / 20 )5.409836065573770.6394913660108058.45959203377637
Winsorized Mean ( 5 / 20 )5.491803278688520.6244660892496668.79439792365229
Winsorized Mean ( 6 / 20 )5.491803278688520.6244660892496668.79439792365229
Winsorized Mean ( 7 / 20 )5.491803278688520.6244660892496668.79439792365229
Winsorized Mean ( 8 / 20 )5.360655737704920.5991947177448738.9464335698423
Winsorized Mean ( 9 / 20 )5.508196721311480.5743244788490969.59073994608327
Winsorized Mean ( 10 / 20 )5.508196721311480.5743244788490969.59073994608327
Winsorized Mean ( 11 / 20 )5.327868852459020.5415628625926719.8379509018629
Winsorized Mean ( 12 / 20 )5.327868852459020.5415628625926719.8379509018629
Winsorized Mean ( 13 / 20 )5.327868852459020.5415628625926719.8379509018629
Winsorized Mean ( 14 / 20 )5.09836065573770.50283617362343310.1392082017468
Winsorized Mean ( 15 / 20 )5.344262295081970.46275797466456511.5487200387110
Winsorized Mean ( 16 / 20 )5.081967213114750.42031414348919612.0908784342285
Winsorized Mean ( 17 / 20 )4.803278688524590.37896874168655412.6746038925221
Winsorized Mean ( 18 / 20 )5.09836065573770.33117188678562615.3949077780204
Winsorized Mean ( 19 / 20 )5.409836065573770.28474612331575018.9988049796024
Winsorized Mean ( 20 / 20 )5.409836065573770.28474612331575018.9988049796024
Trimmed Mean ( 1 / 20 )5.389830508474580.6620800993460348.14075292974121
Trimmed Mean ( 2 / 20 )5.38596491228070.642946297198128.37700588019882
Trimmed Mean ( 3 / 20 )5.381818181818180.6289807419934198.55641170310186
Trimmed Mean ( 4 / 20 )5.396226415094340.6162645692666928.75634700452671
Trimmed Mean ( 5 / 20 )5.39215686274510.6052569905469258.90887168089147
Trimmed Mean ( 6 / 20 )5.367346938775510.595971365642549.00604835769042
Trimmed Mean ( 7 / 20 )5.340425531914890.583679194565819.14959035997087
Trimmed Mean ( 8 / 20 )5.311111111111110.5674880163574529.35898372832903
Trimmed Mean ( 9 / 20 )5.302325581395350.5533897191923489.58153973141008
Trimmed Mean ( 10 / 20 )5.268292682926830.5410292700299589.73753727341796
Trimmed Mean ( 11 / 20 )5.230769230769230.5240009303253519.98236630519236
Trimmed Mean ( 12 / 20 )5.216216216216220.50986534042634310.2305761985203
Trimmed Mean ( 13 / 20 )5.20.48989794855663610.6144555520604
Trimmed Mean ( 14 / 20 )5.181818181818180.46149983062175911.2282125322493
Trimmed Mean ( 15 / 20 )5.193548387096770.43358806782055811.9780703680391
Trimmed Mean ( 16 / 20 )5.172413793103450.4064412581762412.7261041763152
Trimmed Mean ( 17 / 20 )5.185185185185190.3813196348513713.5980020730017
Trimmed Mean ( 18 / 20 )5.240.35721142198983514.6691837870434
Trimmed Mean ( 19 / 20 )5.260869565217390.33982901597161515.4809310505046
Trimmed Mean ( 20 / 20 )5.238095238095240.33025792160761315.860619520033
Median6
Midrange6.5
Midmean - Weighted Average at Xnp5.03333333333333
Midmean - Weighted Average at X(n+1)p5.34375
Midmean - Empirical Distribution Function5.34375
Midmean - Empirical Distribution Function - Averaging5.34375
Midmean - Empirical Distribution Function - Interpolation5.34375
Midmean - Closest Observation4.5
Midmean - True Basic - Statistics Graphics Toolkit5.34375
Midmean - MS Excel (old versions)5.34375
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')