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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 computationTue, 20 Oct 2009 12:21:31 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t125606296552a2ulhtbl73a8i.htm/, Retrieved Thu, 02 May 2024 14:54:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48946, Retrieved Thu, 02 May 2024 14:54:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [ws3v3.1] [2009-10-20 18:21:31] [f47dffd5f5a8c03c3681db4cc9472742] [Current]
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Dataseries X:
48,9
57
61,5
62,6
63,3
63,1
65,3
60,9
58,8
51,2
34,9
14,1
13,7
9,8
2,9
5,2
-0,1
-8,4
-6,8
-1,8
-3,5
0,8
-2,3
1,6
2,4
7,3
5,6
5,2
0
8,1
6,9
11,8
31,9
5
4,1
10,3
9,4
18,1
16,7
20,1
16,8
22,8
15,8
15,9
25,1
29,3
27,3
29,4
30,5
34,5
35,9
36,5
24,5
24,2
29,2
30,2
31,4
30,5
31,3
21,9




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=48946&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=48946&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48946&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 Mean22.64333333333332.636106706629738.58968769222659
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean30.3762242551638
Winsorized Mean ( 1 / 20 )22.63666666666672.621955287412478.63350598514825
Winsorized Mean ( 2 / 20 )22.742.600325055734428.7450605261262
Winsorized Mean ( 3 / 20 )22.7752.583704502222008.81486252797614
Winsorized Mean ( 4 / 20 )22.7352.559261264572068.88342285124281
Winsorized Mean ( 5 / 20 )22.82666666666672.524032361064079.04372979474933
Winsorized Mean ( 6 / 20 )22.62666666666672.469564872428699.16220785259816
Winsorized Mean ( 7 / 20 )22.512.403559859874529.36527538830475
Winsorized Mean ( 8 / 20 )21.84333333333332.205536647183989.90386324399677
Winsorized Mean ( 9 / 20 )21.61833333333332.1101991922292810.2446884696677
Winsorized Mean ( 10 / 20 )19.6351.6899049299639311.6189968156488
Winsorized Mean ( 11 / 20 )19.7451.6350770554934512.0758834781894
Winsorized Mean ( 12 / 20 )19.7251.5730922891815612.5389973211695
Winsorized Mean ( 13 / 20 )19.68166666666671.5521308328908812.6804173009108
Winsorized Mean ( 14 / 20 )19.0751.4576926760648513.0857486720002
Winsorized Mean ( 15 / 20 )19.051.4231013716964413.3862565091136
Winsorized Mean ( 16 / 20 )19.371.3645311274354014.1953522426458
Winsorized Mean ( 17 / 20 )19.25666666666671.3137718302070514.6575426751477
Winsorized Mean ( 18 / 20 )19.49666666666671.2771060299270715.2662865962508
Winsorized Mean ( 19 / 20 )19.81333333333331.2018241001112816.4860509383185
Winsorized Mean ( 20 / 20 )19.681.14352216325417.2099856324592
Trimmed Mean ( 1 / 20 )22.44310344827592.568720486330968.73707496308116
Trimmed Mean ( 2 / 20 )22.23571428571432.502414974581418.88570221628959
Trimmed Mean ( 3 / 20 )21.95555555555562.433658785660429.02162443022904
Trimmed Mean ( 4 / 20 )21.64038461538462.354777979651029.18998937581016
Trimmed Mean ( 5 / 20 )21.3122.264333284763939.4120420096293
Trimmed Mean ( 6 / 20 )20.93333333333332.160358383498839.68975031792205
Trimmed Mean ( 7 / 20 )20.56521739130432.0442879473083510.0598437800222
Trimmed Mean ( 8 / 20 )20.18636363636361.9133297600542410.5503839734304
Trimmed Mean ( 9 / 20 )19.89047619047621.8058036825418311.014750043304
Trimmed Mean ( 10 / 20 )19.60251.6917086170117511.5873973820776
Trimmed Mean ( 11 / 20 )19.59736842105261.6654871983884511.7667481563445
Trimmed Mean ( 12 / 20 )19.5751.6412508537939511.9268787917155
Trimmed Mean ( 13 / 20 )19.55294117647061.6206017417128512.0652351982570
Trimmed Mean ( 14 / 20 )19.5343751.5929950575969212.2626714419743
Trimmed Mean ( 15 / 20 )19.61.5752467422123412.4424951817218
Trimmed Mean ( 16 / 20 )19.67857142857141.5530338728207112.6710510137361
Trimmed Mean ( 17 / 20 )19.72307692307691.5317190713735612.8764322986397
Trimmed Mean ( 18 / 20 )19.79166666666671.5074803417213513.1289716481922
Trimmed Mean ( 19 / 20 )19.83636363636361.4734379130952713.4626396267306
Trimmed Mean ( 20 / 20 )19.841.4388299339905913.7889819577035
Median19.1
Midrange28.45
Midmean - Weighted Average at Xnp18.7
Midmean - Weighted Average at X(n+1)p19.6
Midmean - Empirical Distribution Function18.7
Midmean - Empirical Distribution Function - Averaging19.6
Midmean - Empirical Distribution Function - Interpolation19.6
Midmean - Closest Observation18.7
Midmean - True Basic - Statistics Graphics Toolkit19.6
Midmean - MS Excel (old versions)19.1
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 22.6433333333333 & 2.63610670662973 & 8.58968769222659 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 30.3762242551638 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 22.6366666666667 & 2.62195528741247 & 8.63350598514825 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 22.74 & 2.60032505573442 & 8.7450605261262 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 22.775 & 2.58370450222200 & 8.81486252797614 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 22.735 & 2.55926126457206 & 8.88342285124281 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 22.8266666666667 & 2.52403236106407 & 9.04372979474933 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 22.6266666666667 & 2.46956487242869 & 9.16220785259816 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 22.51 & 2.40355985987452 & 9.36527538830475 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 21.8433333333333 & 2.20553664718398 & 9.90386324399677 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 21.6183333333333 & 2.11019919222928 & 10.2446884696677 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 19.635 & 1.68990492996393 & 11.6189968156488 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 19.745 & 1.63507705549345 & 12.0758834781894 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 19.725 & 1.57309228918156 & 12.5389973211695 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 19.6816666666667 & 1.55213083289088 & 12.6804173009108 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 19.075 & 1.45769267606485 & 13.0857486720002 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 19.05 & 1.42310137169644 & 13.3862565091136 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 19.37 & 1.36453112743540 & 14.1953522426458 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 19.2566666666667 & 1.31377183020705 & 14.6575426751477 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 19.4966666666667 & 1.27710602992707 & 15.2662865962508 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 19.8133333333333 & 1.20182410011128 & 16.4860509383185 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 19.68 & 1.143522163254 & 17.2099856324592 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 22.4431034482759 & 2.56872048633096 & 8.73707496308116 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 22.2357142857143 & 2.50241497458141 & 8.88570221628959 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 21.9555555555556 & 2.43365878566042 & 9.02162443022904 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 21.6403846153846 & 2.35477797965102 & 9.18998937581016 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 21.312 & 2.26433328476393 & 9.4120420096293 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 20.9333333333333 & 2.16035838349883 & 9.68975031792205 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 20.5652173913043 & 2.04428794730835 & 10.0598437800222 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 20.1863636363636 & 1.91332976005424 & 10.5503839734304 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 19.8904761904762 & 1.80580368254183 & 11.014750043304 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 19.6025 & 1.69170861701175 & 11.5873973820776 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 19.5973684210526 & 1.66548719838845 & 11.7667481563445 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 19.575 & 1.64125085379395 & 11.9268787917155 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 19.5529411764706 & 1.62060174171285 & 12.0652351982570 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 19.534375 & 1.59299505759692 & 12.2626714419743 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 19.6 & 1.57524674221234 & 12.4424951817218 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 19.6785714285714 & 1.55303387282071 & 12.6710510137361 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 19.7230769230769 & 1.53171907137356 & 12.8764322986397 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 19.7916666666667 & 1.50748034172135 & 13.1289716481922 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 19.8363636363636 & 1.47343791309527 & 13.4626396267306 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 19.84 & 1.43882993399059 & 13.7889819577035 \tabularnewline
Median & 19.1 &  &  \tabularnewline
Midrange & 28.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18.7 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 19.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18.7 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 19.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 19.6 &  &  \tabularnewline
Midmean - Closest Observation & 18.7 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 19.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 19.1 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48946&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]22.6433333333333[/C][C]2.63610670662973[/C][C]8.58968769222659[/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]30.3762242551638[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]22.6366666666667[/C][C]2.62195528741247[/C][C]8.63350598514825[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]22.74[/C][C]2.60032505573442[/C][C]8.7450605261262[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]22.775[/C][C]2.58370450222200[/C][C]8.81486252797614[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]22.735[/C][C]2.55926126457206[/C][C]8.88342285124281[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]22.8266666666667[/C][C]2.52403236106407[/C][C]9.04372979474933[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]22.6266666666667[/C][C]2.46956487242869[/C][C]9.16220785259816[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]22.51[/C][C]2.40355985987452[/C][C]9.36527538830475[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]21.8433333333333[/C][C]2.20553664718398[/C][C]9.90386324399677[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]21.6183333333333[/C][C]2.11019919222928[/C][C]10.2446884696677[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]19.635[/C][C]1.68990492996393[/C][C]11.6189968156488[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]19.745[/C][C]1.63507705549345[/C][C]12.0758834781894[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]19.725[/C][C]1.57309228918156[/C][C]12.5389973211695[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]19.6816666666667[/C][C]1.55213083289088[/C][C]12.6804173009108[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]19.075[/C][C]1.45769267606485[/C][C]13.0857486720002[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]19.05[/C][C]1.42310137169644[/C][C]13.3862565091136[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]19.37[/C][C]1.36453112743540[/C][C]14.1953522426458[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]19.2566666666667[/C][C]1.31377183020705[/C][C]14.6575426751477[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]19.4966666666667[/C][C]1.27710602992707[/C][C]15.2662865962508[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]19.8133333333333[/C][C]1.20182410011128[/C][C]16.4860509383185[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]19.68[/C][C]1.143522163254[/C][C]17.2099856324592[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]22.4431034482759[/C][C]2.56872048633096[/C][C]8.73707496308116[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]22.2357142857143[/C][C]2.50241497458141[/C][C]8.88570221628959[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]21.9555555555556[/C][C]2.43365878566042[/C][C]9.02162443022904[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]21.6403846153846[/C][C]2.35477797965102[/C][C]9.18998937581016[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]21.312[/C][C]2.26433328476393[/C][C]9.4120420096293[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]20.9333333333333[/C][C]2.16035838349883[/C][C]9.68975031792205[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]20.5652173913043[/C][C]2.04428794730835[/C][C]10.0598437800222[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]20.1863636363636[/C][C]1.91332976005424[/C][C]10.5503839734304[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]19.8904761904762[/C][C]1.80580368254183[/C][C]11.014750043304[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]19.6025[/C][C]1.69170861701175[/C][C]11.5873973820776[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]19.5973684210526[/C][C]1.66548719838845[/C][C]11.7667481563445[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]19.575[/C][C]1.64125085379395[/C][C]11.9268787917155[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]19.5529411764706[/C][C]1.62060174171285[/C][C]12.0652351982570[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]19.534375[/C][C]1.59299505759692[/C][C]12.2626714419743[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]19.6[/C][C]1.57524674221234[/C][C]12.4424951817218[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]19.6785714285714[/C][C]1.55303387282071[/C][C]12.6710510137361[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]19.7230769230769[/C][C]1.53171907137356[/C][C]12.8764322986397[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]19.7916666666667[/C][C]1.50748034172135[/C][C]13.1289716481922[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]19.8363636363636[/C][C]1.47343791309527[/C][C]13.4626396267306[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]19.84[/C][C]1.43882993399059[/C][C]13.7889819577035[/C][/ROW]
[ROW][C]Median[/C][C]19.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]28.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]19.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]19.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]19.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]19.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]19.1[/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=48946&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48946&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 Mean22.64333333333332.636106706629738.58968769222659
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean30.3762242551638
Winsorized Mean ( 1 / 20 )22.63666666666672.621955287412478.63350598514825
Winsorized Mean ( 2 / 20 )22.742.600325055734428.7450605261262
Winsorized Mean ( 3 / 20 )22.7752.583704502222008.81486252797614
Winsorized Mean ( 4 / 20 )22.7352.559261264572068.88342285124281
Winsorized Mean ( 5 / 20 )22.82666666666672.524032361064079.04372979474933
Winsorized Mean ( 6 / 20 )22.62666666666672.469564872428699.16220785259816
Winsorized Mean ( 7 / 20 )22.512.403559859874529.36527538830475
Winsorized Mean ( 8 / 20 )21.84333333333332.205536647183989.90386324399677
Winsorized Mean ( 9 / 20 )21.61833333333332.1101991922292810.2446884696677
Winsorized Mean ( 10 / 20 )19.6351.6899049299639311.6189968156488
Winsorized Mean ( 11 / 20 )19.7451.6350770554934512.0758834781894
Winsorized Mean ( 12 / 20 )19.7251.5730922891815612.5389973211695
Winsorized Mean ( 13 / 20 )19.68166666666671.5521308328908812.6804173009108
Winsorized Mean ( 14 / 20 )19.0751.4576926760648513.0857486720002
Winsorized Mean ( 15 / 20 )19.051.4231013716964413.3862565091136
Winsorized Mean ( 16 / 20 )19.371.3645311274354014.1953522426458
Winsorized Mean ( 17 / 20 )19.25666666666671.3137718302070514.6575426751477
Winsorized Mean ( 18 / 20 )19.49666666666671.2771060299270715.2662865962508
Winsorized Mean ( 19 / 20 )19.81333333333331.2018241001112816.4860509383185
Winsorized Mean ( 20 / 20 )19.681.14352216325417.2099856324592
Trimmed Mean ( 1 / 20 )22.44310344827592.568720486330968.73707496308116
Trimmed Mean ( 2 / 20 )22.23571428571432.502414974581418.88570221628959
Trimmed Mean ( 3 / 20 )21.95555555555562.433658785660429.02162443022904
Trimmed Mean ( 4 / 20 )21.64038461538462.354777979651029.18998937581016
Trimmed Mean ( 5 / 20 )21.3122.264333284763939.4120420096293
Trimmed Mean ( 6 / 20 )20.93333333333332.160358383498839.68975031792205
Trimmed Mean ( 7 / 20 )20.56521739130432.0442879473083510.0598437800222
Trimmed Mean ( 8 / 20 )20.18636363636361.9133297600542410.5503839734304
Trimmed Mean ( 9 / 20 )19.89047619047621.8058036825418311.014750043304
Trimmed Mean ( 10 / 20 )19.60251.6917086170117511.5873973820776
Trimmed Mean ( 11 / 20 )19.59736842105261.6654871983884511.7667481563445
Trimmed Mean ( 12 / 20 )19.5751.6412508537939511.9268787917155
Trimmed Mean ( 13 / 20 )19.55294117647061.6206017417128512.0652351982570
Trimmed Mean ( 14 / 20 )19.5343751.5929950575969212.2626714419743
Trimmed Mean ( 15 / 20 )19.61.5752467422123412.4424951817218
Trimmed Mean ( 16 / 20 )19.67857142857141.5530338728207112.6710510137361
Trimmed Mean ( 17 / 20 )19.72307692307691.5317190713735612.8764322986397
Trimmed Mean ( 18 / 20 )19.79166666666671.5074803417213513.1289716481922
Trimmed Mean ( 19 / 20 )19.83636363636361.4734379130952713.4626396267306
Trimmed Mean ( 20 / 20 )19.841.4388299339905913.7889819577035
Median19.1
Midrange28.45
Midmean - Weighted Average at Xnp18.7
Midmean - Weighted Average at X(n+1)p19.6
Midmean - Empirical Distribution Function18.7
Midmean - Empirical Distribution Function - Averaging19.6
Midmean - Empirical Distribution Function - Interpolation19.6
Midmean - Closest Observation18.7
Midmean - True Basic - Statistics Graphics Toolkit19.6
Midmean - MS Excel (old versions)19.1
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')