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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 computationThu, 18 Dec 2008 07:38:56 -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/2008/Dec/18/t1229611180as1ejj8na95shn3.htm/, Retrieved Sat, 11 May 2024 22:22:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34803, Retrieved Sat, 11 May 2024 22:22:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Werkloosheid - Jo...] [2008-12-14 16:04:23] [44ec60eb6065a3f81a5f756bd5af1faf]
- RMPD    [Central Tendency] [Werkloosheid - Jo...] [2008-12-18 14:38:56] [924502d03698cd41cacbcd1327858815] [Current]
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Dataseries X:
21.1
21
20.4
19.5
18.6
18.8
23.7
24.8
25
23.6
22.3
21.8
20.8
19.7
18.3
17.4
17
18.1
23.9
25.6
25.3
23.6
21.9
21.4
20.6
20.5
20.2
20.6
19.7
19.3
22.8
23.5
23.8
22.6
22
21.7
20.7
20.2
19.1
19.5
18.7
18.6
22.2
23.2
23.5
21.3
20
18.7
18.9
18.3
18.4
19.9
19.2
18.5
20.9
20.5
19.4
18.1
17
17




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34803&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34803&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34803&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean20.71166666666670.28786268370602271.9498144046289
Geometric Mean20.5956336093196
Harmonic Mean20.4817732630759
Quadratic Mean20.8293582874429
Winsorized Mean ( 1 / 20 )20.70666666666670.28646359907846472.2837621718039
Winsorized Mean ( 2 / 20 )20.69666666666670.28381945668411672.9219444941067
Winsorized Mean ( 3 / 20 )20.70666666666670.27704928956996874.7400099773121
Winsorized Mean ( 4 / 20 )20.69333333333330.25429493382880881.3753267584328
Winsorized Mean ( 5 / 20 )20.6850.25253321088298581.9100185978498
Winsorized Mean ( 6 / 20 )20.6950.24707812300982183.7589331985388
Winsorized Mean ( 7 / 20 )20.68333333333330.24469705317856884.5262869522161
Winsorized Mean ( 8 / 20 )20.69666666666670.24252632994302185.3378133068239
Winsorized Mean ( 9 / 20 )20.69666666666670.237119801738887.2835862500641
Winsorized Mean ( 10 / 20 )20.71333333333330.234538453675288.3152975930255
Winsorized Mean ( 11 / 20 )20.65833333333330.22369889552001392.3488392077695
Winsorized Mean ( 12 / 20 )20.59833333333330.205592593497289100.190055404914
Winsorized Mean ( 13 / 20 )20.5550.197861804766132103.885638889707
Winsorized Mean ( 14 / 20 )20.50833333333330.182175982259575112.574298098812
Winsorized Mean ( 15 / 20 )20.50833333333330.174088289612017117.804209456244
Winsorized Mean ( 16 / 20 )20.50833333333330.157169376171143130.485555347637
Winsorized Mean ( 17 / 20 )20.50833333333330.148367608558281138.226487119508
Winsorized Mean ( 18 / 20 )20.50833333333330.139172121751064147.359493232534
Winsorized Mean ( 19 / 20 )20.50833333333330.129586296676201158.260046466007
Winsorized Mean ( 20 / 20 )20.44166666666670.109500449310707186.68112135927
Trimmed Mean ( 1 / 20 )20.69137931034480.27807875649539874.4083423383953
Trimmed Mean ( 2 / 20 )20.6750.26772550878081877.2246174604386
Trimmed Mean ( 3 / 20 )20.66296296296300.2566692027468280.5042550560498
Trimmed Mean ( 4 / 20 )20.64615384615380.24621511303908783.8541289822297
Trimmed Mean ( 5 / 20 )20.6320.24217450277830385.1947656062183
Trimmed Mean ( 6 / 20 )20.618750.23748191887126986.822399355703
Trimmed Mean ( 7 / 20 )20.60217391304350.23297050735852188.432540868096
Trimmed Mean ( 8 / 20 )20.58636363636360.22764979291554790.4299686492606
Trimmed Mean ( 9 / 20 )20.56666666666670.22109080929409293.0236165507411
Trimmed Mean ( 10 / 20 )20.5450.21375609153113496.1142199636802
Trimmed Mean ( 11 / 20 )20.51842105263160.204391866369012100.387659338593
Trimmed Mean ( 12 / 20 )20.49722222222220.194874241544738105.181793446604
Trimmed Mean ( 13 / 20 )20.48235294117650.187176724915266109.427883998124
Trimmed Mean ( 14 / 20 )20.4718750.178605393515263114.620698720672
Trimmed Mean ( 15 / 20 )20.46666666666670.171225020551423119.530817404808
Trimmed Mean ( 16 / 20 )20.46071428571430.162840143455119125.649080451428
Trimmed Mean ( 17 / 20 )20.45384615384620.156030644843177131.088647197504
Trimmed Mean ( 18 / 20 )20.44583333333330.148419104822555137.757422521701
Trimmed Mean ( 19 / 20 )20.43636363636360.139657195415793146.332335942446
Trimmed Mean ( 20 / 20 )20.4250.129141904813842158.159352144005
Median20.5
Midrange21.3
Midmean - Weighted Average at Xnp20.4129032258065
Midmean - Weighted Average at X(n+1)p20.4666666666667
Midmean - Empirical Distribution Function20.4129032258065
Midmean - Empirical Distribution Function - Averaging20.4666666666667
Midmean - Empirical Distribution Function - Interpolation20.4666666666667
Midmean - Closest Observation20.4129032258065
Midmean - True Basic - Statistics Graphics Toolkit20.4666666666667
Midmean - MS Excel (old versions)20.471875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 20.7116666666667 & 0.287862683706022 & 71.9498144046289 \tabularnewline
Geometric Mean & 20.5956336093196 &  &  \tabularnewline
Harmonic Mean & 20.4817732630759 &  &  \tabularnewline
Quadratic Mean & 20.8293582874429 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 20.7066666666667 & 0.286463599078464 & 72.2837621718039 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 20.6966666666667 & 0.283819456684116 & 72.9219444941067 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 20.7066666666667 & 0.277049289569968 & 74.7400099773121 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 20.6933333333333 & 0.254294933828808 & 81.3753267584328 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 20.685 & 0.252533210882985 & 81.9100185978498 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 20.695 & 0.247078123009821 & 83.7589331985388 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 20.6833333333333 & 0.244697053178568 & 84.5262869522161 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 20.6966666666667 & 0.242526329943021 & 85.3378133068239 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 20.6966666666667 & 0.2371198017388 & 87.2835862500641 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 20.7133333333333 & 0.2345384536752 & 88.3152975930255 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 20.6583333333333 & 0.223698895520013 & 92.3488392077695 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 20.5983333333333 & 0.205592593497289 & 100.190055404914 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 20.555 & 0.197861804766132 & 103.885638889707 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 20.5083333333333 & 0.182175982259575 & 112.574298098812 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 20.5083333333333 & 0.174088289612017 & 117.804209456244 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 20.5083333333333 & 0.157169376171143 & 130.485555347637 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 20.5083333333333 & 0.148367608558281 & 138.226487119508 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 20.5083333333333 & 0.139172121751064 & 147.359493232534 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 20.5083333333333 & 0.129586296676201 & 158.260046466007 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 20.4416666666667 & 0.109500449310707 & 186.68112135927 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 20.6913793103448 & 0.278078756495398 & 74.4083423383953 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 20.675 & 0.267725508780818 & 77.2246174604386 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 20.6629629629630 & 0.25666920274682 & 80.5042550560498 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 20.6461538461538 & 0.246215113039087 & 83.8541289822297 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 20.632 & 0.242174502778303 & 85.1947656062183 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 20.61875 & 0.237481918871269 & 86.822399355703 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 20.6021739130435 & 0.232970507358521 & 88.432540868096 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 20.5863636363636 & 0.227649792915547 & 90.4299686492606 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 20.5666666666667 & 0.221090809294092 & 93.0236165507411 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 20.545 & 0.213756091531134 & 96.1142199636802 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 20.5184210526316 & 0.204391866369012 & 100.387659338593 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 20.4972222222222 & 0.194874241544738 & 105.181793446604 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 20.4823529411765 & 0.187176724915266 & 109.427883998124 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 20.471875 & 0.178605393515263 & 114.620698720672 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 20.4666666666667 & 0.171225020551423 & 119.530817404808 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 20.4607142857143 & 0.162840143455119 & 125.649080451428 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 20.4538461538462 & 0.156030644843177 & 131.088647197504 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 20.4458333333333 & 0.148419104822555 & 137.757422521701 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 20.4363636363636 & 0.139657195415793 & 146.332335942446 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 20.425 & 0.129141904813842 & 158.159352144005 \tabularnewline
Median & 20.5 &  &  \tabularnewline
Midrange & 21.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 20.4129032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 20.4666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 20.4129032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 20.4666666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 20.4666666666667 &  &  \tabularnewline
Midmean - Closest Observation & 20.4129032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 20.4666666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 20.471875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34803&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]20.7116666666667[/C][C]0.287862683706022[/C][C]71.9498144046289[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]20.5956336093196[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]20.4817732630759[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]20.8293582874429[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]20.7066666666667[/C][C]0.286463599078464[/C][C]72.2837621718039[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]20.6966666666667[/C][C]0.283819456684116[/C][C]72.9219444941067[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]20.7066666666667[/C][C]0.277049289569968[/C][C]74.7400099773121[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]20.6933333333333[/C][C]0.254294933828808[/C][C]81.3753267584328[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]20.685[/C][C]0.252533210882985[/C][C]81.9100185978498[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]20.695[/C][C]0.247078123009821[/C][C]83.7589331985388[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]20.6833333333333[/C][C]0.244697053178568[/C][C]84.5262869522161[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]20.6966666666667[/C][C]0.242526329943021[/C][C]85.3378133068239[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]20.6966666666667[/C][C]0.2371198017388[/C][C]87.2835862500641[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]20.7133333333333[/C][C]0.2345384536752[/C][C]88.3152975930255[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]20.6583333333333[/C][C]0.223698895520013[/C][C]92.3488392077695[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]20.5983333333333[/C][C]0.205592593497289[/C][C]100.190055404914[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]20.555[/C][C]0.197861804766132[/C][C]103.885638889707[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]20.5083333333333[/C][C]0.182175982259575[/C][C]112.574298098812[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]20.5083333333333[/C][C]0.174088289612017[/C][C]117.804209456244[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]20.5083333333333[/C][C]0.157169376171143[/C][C]130.485555347637[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]20.5083333333333[/C][C]0.148367608558281[/C][C]138.226487119508[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]20.5083333333333[/C][C]0.139172121751064[/C][C]147.359493232534[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]20.5083333333333[/C][C]0.129586296676201[/C][C]158.260046466007[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]20.4416666666667[/C][C]0.109500449310707[/C][C]186.68112135927[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]20.6913793103448[/C][C]0.278078756495398[/C][C]74.4083423383953[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]20.675[/C][C]0.267725508780818[/C][C]77.2246174604386[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]20.6629629629630[/C][C]0.25666920274682[/C][C]80.5042550560498[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]20.6461538461538[/C][C]0.246215113039087[/C][C]83.8541289822297[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]20.632[/C][C]0.242174502778303[/C][C]85.1947656062183[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]20.61875[/C][C]0.237481918871269[/C][C]86.822399355703[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]20.6021739130435[/C][C]0.232970507358521[/C][C]88.432540868096[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]20.5863636363636[/C][C]0.227649792915547[/C][C]90.4299686492606[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]20.5666666666667[/C][C]0.221090809294092[/C][C]93.0236165507411[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]20.545[/C][C]0.213756091531134[/C][C]96.1142199636802[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]20.5184210526316[/C][C]0.204391866369012[/C][C]100.387659338593[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]20.4972222222222[/C][C]0.194874241544738[/C][C]105.181793446604[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]20.4823529411765[/C][C]0.187176724915266[/C][C]109.427883998124[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]20.471875[/C][C]0.178605393515263[/C][C]114.620698720672[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]20.4666666666667[/C][C]0.171225020551423[/C][C]119.530817404808[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]20.4607142857143[/C][C]0.162840143455119[/C][C]125.649080451428[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]20.4538461538462[/C][C]0.156030644843177[/C][C]131.088647197504[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]20.4458333333333[/C][C]0.148419104822555[/C][C]137.757422521701[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]20.4363636363636[/C][C]0.139657195415793[/C][C]146.332335942446[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]20.425[/C][C]0.129141904813842[/C][C]158.159352144005[/C][/ROW]
[ROW][C]Median[/C][C]20.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]20.4129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]20.4666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]20.4129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]20.4666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]20.4666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20.4129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]20.4666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]20.471875[/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=34803&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34803&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean20.71166666666670.28786268370602271.9498144046289
Geometric Mean20.5956336093196
Harmonic Mean20.4817732630759
Quadratic Mean20.8293582874429
Winsorized Mean ( 1 / 20 )20.70666666666670.28646359907846472.2837621718039
Winsorized Mean ( 2 / 20 )20.69666666666670.28381945668411672.9219444941067
Winsorized Mean ( 3 / 20 )20.70666666666670.27704928956996874.7400099773121
Winsorized Mean ( 4 / 20 )20.69333333333330.25429493382880881.3753267584328
Winsorized Mean ( 5 / 20 )20.6850.25253321088298581.9100185978498
Winsorized Mean ( 6 / 20 )20.6950.24707812300982183.7589331985388
Winsorized Mean ( 7 / 20 )20.68333333333330.24469705317856884.5262869522161
Winsorized Mean ( 8 / 20 )20.69666666666670.24252632994302185.3378133068239
Winsorized Mean ( 9 / 20 )20.69666666666670.237119801738887.2835862500641
Winsorized Mean ( 10 / 20 )20.71333333333330.234538453675288.3152975930255
Winsorized Mean ( 11 / 20 )20.65833333333330.22369889552001392.3488392077695
Winsorized Mean ( 12 / 20 )20.59833333333330.205592593497289100.190055404914
Winsorized Mean ( 13 / 20 )20.5550.197861804766132103.885638889707
Winsorized Mean ( 14 / 20 )20.50833333333330.182175982259575112.574298098812
Winsorized Mean ( 15 / 20 )20.50833333333330.174088289612017117.804209456244
Winsorized Mean ( 16 / 20 )20.50833333333330.157169376171143130.485555347637
Winsorized Mean ( 17 / 20 )20.50833333333330.148367608558281138.226487119508
Winsorized Mean ( 18 / 20 )20.50833333333330.139172121751064147.359493232534
Winsorized Mean ( 19 / 20 )20.50833333333330.129586296676201158.260046466007
Winsorized Mean ( 20 / 20 )20.44166666666670.109500449310707186.68112135927
Trimmed Mean ( 1 / 20 )20.69137931034480.27807875649539874.4083423383953
Trimmed Mean ( 2 / 20 )20.6750.26772550878081877.2246174604386
Trimmed Mean ( 3 / 20 )20.66296296296300.2566692027468280.5042550560498
Trimmed Mean ( 4 / 20 )20.64615384615380.24621511303908783.8541289822297
Trimmed Mean ( 5 / 20 )20.6320.24217450277830385.1947656062183
Trimmed Mean ( 6 / 20 )20.618750.23748191887126986.822399355703
Trimmed Mean ( 7 / 20 )20.60217391304350.23297050735852188.432540868096
Trimmed Mean ( 8 / 20 )20.58636363636360.22764979291554790.4299686492606
Trimmed Mean ( 9 / 20 )20.56666666666670.22109080929409293.0236165507411
Trimmed Mean ( 10 / 20 )20.5450.21375609153113496.1142199636802
Trimmed Mean ( 11 / 20 )20.51842105263160.204391866369012100.387659338593
Trimmed Mean ( 12 / 20 )20.49722222222220.194874241544738105.181793446604
Trimmed Mean ( 13 / 20 )20.48235294117650.187176724915266109.427883998124
Trimmed Mean ( 14 / 20 )20.4718750.178605393515263114.620698720672
Trimmed Mean ( 15 / 20 )20.46666666666670.171225020551423119.530817404808
Trimmed Mean ( 16 / 20 )20.46071428571430.162840143455119125.649080451428
Trimmed Mean ( 17 / 20 )20.45384615384620.156030644843177131.088647197504
Trimmed Mean ( 18 / 20 )20.44583333333330.148419104822555137.757422521701
Trimmed Mean ( 19 / 20 )20.43636363636360.139657195415793146.332335942446
Trimmed Mean ( 20 / 20 )20.4250.129141904813842158.159352144005
Median20.5
Midrange21.3
Midmean - Weighted Average at Xnp20.4129032258065
Midmean - Weighted Average at X(n+1)p20.4666666666667
Midmean - Empirical Distribution Function20.4129032258065
Midmean - Empirical Distribution Function - Averaging20.4666666666667
Midmean - Empirical Distribution Function - Interpolation20.4666666666667
Midmean - Closest Observation20.4129032258065
Midmean - True Basic - Statistics Graphics Toolkit20.4666666666667
Midmean - MS Excel (old versions)20.471875
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')