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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 20 Oct 2007 06:34:24 -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/2007/Oct/20/5m013sclokbndqj1192887077.htm/, Retrieved Thu, 02 May 2024 20:43:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1101, Retrieved Thu, 02 May 2024 20:43:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact230
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [vrouwen onder de ...] [2007-10-20 13:34:24] [a1ee67c0c4cd462b4e85e70c1c0a96bd] [Current]
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Dataseries X:
19,9
19
19
19
19,9
19,9
19,9
17,5
17,5
17,5
26,6
26,6
26,6
20,8
20,8
20,8
18,9
18,9
18,9
19,5
19,5
19,5
27,1
27,1
27,1
24,1
24,1
24,1
21,3
21,3
21,3
19,1
19,1
19,1
26,2
26,2
26,2
21,7
21,7
21,7
19,4
19,4
19,4
19,5
19,5
19,5
28,7
28,7
28,7
21,8
21,8
21,8
20
20
20
22,6
22,6
22,6
24,6
24,6
24,6




Summary of compuational 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 compuational 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=1101&T=0

[TABLE]
[ROW][C]Summary of compuational 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=1101&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1101&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 compuational 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 Mean21.88196721311480.40429732740129854.1234525436156
Geometric Mean21.6699538935565
Harmonic Mean21.4706341863928
Quadratic Mean22.1049286099833
Winsorized Mean ( 1 / 20 )21.88196721311480.40429732740129854.1234525436155
Winsorized Mean ( 2 / 20 )21.88196721311480.40429732740129854.1234525436156
Winsorized Mean ( 3 / 20 )21.8721311475410.3731210204319858.6194021505906
Winsorized Mean ( 4 / 20 )21.8721311475410.3731210204319858.6194021505906
Winsorized Mean ( 5 / 20 )21.8721311475410.3731210204319858.6194021505906
Winsorized Mean ( 6 / 20 )21.83278688524590.36065909089350360.5358008061214
Winsorized Mean ( 7 / 20 )21.83278688524590.36065909089350360.5358008061213
Winsorized Mean ( 8 / 20 )21.83278688524590.36065909089350360.5358008061213
Winsorized Mean ( 9 / 20 )21.78852459016390.34596107017999362.9797005160957
Winsorized Mean ( 10 / 20 )21.78852459016390.34596107017999362.9797005160957
Winsorized Mean ( 11 / 20 )21.78852459016390.34596107017999362.9797005160958
Winsorized Mean ( 12 / 20 )21.53278688524590.27516235953782578.254841692059
Winsorized Mean ( 13 / 20 )21.53278688524590.27516235953782578.254841692059
Winsorized Mean ( 14 / 20 )21.53278688524590.27516235953782578.254841692059
Winsorized Mean ( 15 / 20 )21.43442622950820.24959951798132985.8752709254494
Winsorized Mean ( 16 / 20 )21.43442622950820.24959951798132985.8752709254494
Winsorized Mean ( 17 / 20 )21.43442622950820.24959951798132985.8752709254494
Winsorized Mean ( 18 / 20 )20.99180327868850.175419794416266119.666103523503
Winsorized Mean ( 19 / 20 )20.99180327868850.175419794416266119.666103523503
Winsorized Mean ( 20 / 20 )20.99180327868850.175419794416266119.666103523503
Trimmed Mean ( 1 / 20 )21.84067796610170.39446135209142155.3683595371337
Trimmed Mean ( 2 / 20 )21.79649122807020.38227459419266657.0178912205836
Trimmed Mean ( 3 / 20 )21.74909090909090.36708766214462559.2476761055571
Trimmed Mean ( 4 / 20 )21.70188679245280.36309716906118259.768812983491
Trimmed Mean ( 5 / 20 )21.65098039215690.35767629739444760.5323320272466
Trimmed Mean ( 6 / 20 )21.59591836734690.35042441691470761.6278927064702
Trimmed Mean ( 7 / 20 )21.54468085106380.34472110636207462.498873592134
Trimmed Mean ( 8 / 20 )21.48888888888890.33690843737425463.7825786031532
Trimmed Mean ( 9 / 20 )21.42790697674420.32628187579748365.672991870514
Trimmed Mean ( 10 / 20 )21.36829268292680.31615909518496267.587151558698
Trimmed Mean ( 11 / 20 )21.30256410256410.30211774298666670.5108011597461
Trimmed Mean ( 12 / 20 )21.22972972972970.28241411208308475.1723402670618
Trimmed Mean ( 13 / 20 )21.18571428571430.27723553851829176.4177435510004
Trimmed Mean ( 14 / 20 )21.13636363636360.26921667310902278.5106040880472
Trimmed Mean ( 15 / 20 )21.08064516129030.25700589319374882.0239757903073
Trimmed Mean ( 16 / 20 )21.03103448275860.24750496080393784.9721735453155
Trimmed Mean ( 17 / 20 )20.97407407407410.23232950079565990.2772743118897
Trimmed Mean ( 18 / 20 )20.9080.207518673858523100.752378623305
Trimmed Mean ( 19 / 20 )20.89565217391300.203669718378967102.595772902443
Trimmed Mean ( 20 / 20 )20.88095238095240.195985792441703106.543194385703
Median20.8
Midrange23.1
Midmean - Weighted Average at Xnp21.0806451612903
Midmean - Weighted Average at X(n+1)p21.0806451612903
Midmean - Empirical Distribution Function21.0806451612903
Midmean - Empirical Distribution Function - Averaging21.0806451612903
Midmean - Empirical Distribution Function - Interpolation21.0806451612903
Midmean - Closest Observation20.9323529411765
Midmean - True Basic - Statistics Graphics Toolkit21.0806451612903
Midmean - MS Excel (old versions)21.0806451612903
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 21.8819672131148 & 0.404297327401298 & 54.1234525436156 \tabularnewline
Geometric Mean & 21.6699538935565 &  &  \tabularnewline
Harmonic Mean & 21.4706341863928 &  &  \tabularnewline
Quadratic Mean & 22.1049286099833 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 21.8819672131148 & 0.404297327401298 & 54.1234525436155 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 21.8819672131148 & 0.404297327401298 & 54.1234525436156 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 21.872131147541 & 0.37312102043198 & 58.6194021505906 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 21.872131147541 & 0.37312102043198 & 58.6194021505906 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 21.872131147541 & 0.37312102043198 & 58.6194021505906 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 21.8327868852459 & 0.360659090893503 & 60.5358008061214 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 21.8327868852459 & 0.360659090893503 & 60.5358008061213 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 21.8327868852459 & 0.360659090893503 & 60.5358008061213 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 21.7885245901639 & 0.345961070179993 & 62.9797005160957 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 21.7885245901639 & 0.345961070179993 & 62.9797005160957 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 21.7885245901639 & 0.345961070179993 & 62.9797005160958 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 21.5327868852459 & 0.275162359537825 & 78.254841692059 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 21.5327868852459 & 0.275162359537825 & 78.254841692059 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 21.5327868852459 & 0.275162359537825 & 78.254841692059 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 21.4344262295082 & 0.249599517981329 & 85.8752709254494 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 21.4344262295082 & 0.249599517981329 & 85.8752709254494 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 21.4344262295082 & 0.249599517981329 & 85.8752709254494 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 20.9918032786885 & 0.175419794416266 & 119.666103523503 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 20.9918032786885 & 0.175419794416266 & 119.666103523503 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 20.9918032786885 & 0.175419794416266 & 119.666103523503 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 21.8406779661017 & 0.394461352091421 & 55.3683595371337 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 21.7964912280702 & 0.382274594192666 & 57.0178912205836 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 21.7490909090909 & 0.367087662144625 & 59.2476761055571 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 21.7018867924528 & 0.363097169061182 & 59.768812983491 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 21.6509803921569 & 0.357676297394447 & 60.5323320272466 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 21.5959183673469 & 0.350424416914707 & 61.6278927064702 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 21.5446808510638 & 0.344721106362074 & 62.498873592134 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 21.4888888888889 & 0.336908437374254 & 63.7825786031532 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 21.4279069767442 & 0.326281875797483 & 65.672991870514 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 21.3682926829268 & 0.316159095184962 & 67.587151558698 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 21.3025641025641 & 0.302117742986666 & 70.5108011597461 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 21.2297297297297 & 0.282414112083084 & 75.1723402670618 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 21.1857142857143 & 0.277235538518291 & 76.4177435510004 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 21.1363636363636 & 0.269216673109022 & 78.5106040880472 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 21.0806451612903 & 0.257005893193748 & 82.0239757903073 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 21.0310344827586 & 0.247504960803937 & 84.9721735453155 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 20.9740740740741 & 0.232329500795659 & 90.2772743118897 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 20.908 & 0.207518673858523 & 100.752378623305 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 20.8956521739130 & 0.203669718378967 & 102.595772902443 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 20.8809523809524 & 0.195985792441703 & 106.543194385703 \tabularnewline
Median & 20.8 &  &  \tabularnewline
Midrange & 23.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 21.0806451612903 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 21.0806451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 21.0806451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 21.0806451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 21.0806451612903 &  &  \tabularnewline
Midmean - Closest Observation & 20.9323529411765 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 21.0806451612903 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 21.0806451612903 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1101&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]21.8819672131148[/C][C]0.404297327401298[/C][C]54.1234525436156[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21.6699538935565[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.4706341863928[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]22.1049286099833[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]21.8819672131148[/C][C]0.404297327401298[/C][C]54.1234525436155[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]21.8819672131148[/C][C]0.404297327401298[/C][C]54.1234525436156[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]21.872131147541[/C][C]0.37312102043198[/C][C]58.6194021505906[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]21.872131147541[/C][C]0.37312102043198[/C][C]58.6194021505906[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]21.872131147541[/C][C]0.37312102043198[/C][C]58.6194021505906[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]21.8327868852459[/C][C]0.360659090893503[/C][C]60.5358008061214[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]21.8327868852459[/C][C]0.360659090893503[/C][C]60.5358008061213[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]21.8327868852459[/C][C]0.360659090893503[/C][C]60.5358008061213[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]21.7885245901639[/C][C]0.345961070179993[/C][C]62.9797005160957[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]21.7885245901639[/C][C]0.345961070179993[/C][C]62.9797005160957[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]21.7885245901639[/C][C]0.345961070179993[/C][C]62.9797005160958[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]21.5327868852459[/C][C]0.275162359537825[/C][C]78.254841692059[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]21.5327868852459[/C][C]0.275162359537825[/C][C]78.254841692059[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]21.5327868852459[/C][C]0.275162359537825[/C][C]78.254841692059[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]21.4344262295082[/C][C]0.249599517981329[/C][C]85.8752709254494[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]21.4344262295082[/C][C]0.249599517981329[/C][C]85.8752709254494[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]21.4344262295082[/C][C]0.249599517981329[/C][C]85.8752709254494[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]20.9918032786885[/C][C]0.175419794416266[/C][C]119.666103523503[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]20.9918032786885[/C][C]0.175419794416266[/C][C]119.666103523503[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]20.9918032786885[/C][C]0.175419794416266[/C][C]119.666103523503[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]21.8406779661017[/C][C]0.394461352091421[/C][C]55.3683595371337[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]21.7964912280702[/C][C]0.382274594192666[/C][C]57.0178912205836[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]21.7490909090909[/C][C]0.367087662144625[/C][C]59.2476761055571[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]21.7018867924528[/C][C]0.363097169061182[/C][C]59.768812983491[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]21.6509803921569[/C][C]0.357676297394447[/C][C]60.5323320272466[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]21.5959183673469[/C][C]0.350424416914707[/C][C]61.6278927064702[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]21.5446808510638[/C][C]0.344721106362074[/C][C]62.498873592134[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]21.4888888888889[/C][C]0.336908437374254[/C][C]63.7825786031532[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]21.4279069767442[/C][C]0.326281875797483[/C][C]65.672991870514[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]21.3682926829268[/C][C]0.316159095184962[/C][C]67.587151558698[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]21.3025641025641[/C][C]0.302117742986666[/C][C]70.5108011597461[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]21.2297297297297[/C][C]0.282414112083084[/C][C]75.1723402670618[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]21.1857142857143[/C][C]0.277235538518291[/C][C]76.4177435510004[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]21.1363636363636[/C][C]0.269216673109022[/C][C]78.5106040880472[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]21.0806451612903[/C][C]0.257005893193748[/C][C]82.0239757903073[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]21.0310344827586[/C][C]0.247504960803937[/C][C]84.9721735453155[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]20.9740740740741[/C][C]0.232329500795659[/C][C]90.2772743118897[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]20.908[/C][C]0.207518673858523[/C][C]100.752378623305[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]20.8956521739130[/C][C]0.203669718378967[/C][C]102.595772902443[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]20.8809523809524[/C][C]0.195985792441703[/C][C]106.543194385703[/C][/ROW]
[ROW][C]Median[/C][C]20.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]23.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]21.0806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]21.0806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]21.0806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]21.0806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]21.0806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]20.9323529411765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]21.0806451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]21.0806451612903[/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=1101&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1101&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 Mean21.88196721311480.40429732740129854.1234525436156
Geometric Mean21.6699538935565
Harmonic Mean21.4706341863928
Quadratic Mean22.1049286099833
Winsorized Mean ( 1 / 20 )21.88196721311480.40429732740129854.1234525436155
Winsorized Mean ( 2 / 20 )21.88196721311480.40429732740129854.1234525436156
Winsorized Mean ( 3 / 20 )21.8721311475410.3731210204319858.6194021505906
Winsorized Mean ( 4 / 20 )21.8721311475410.3731210204319858.6194021505906
Winsorized Mean ( 5 / 20 )21.8721311475410.3731210204319858.6194021505906
Winsorized Mean ( 6 / 20 )21.83278688524590.36065909089350360.5358008061214
Winsorized Mean ( 7 / 20 )21.83278688524590.36065909089350360.5358008061213
Winsorized Mean ( 8 / 20 )21.83278688524590.36065909089350360.5358008061213
Winsorized Mean ( 9 / 20 )21.78852459016390.34596107017999362.9797005160957
Winsorized Mean ( 10 / 20 )21.78852459016390.34596107017999362.9797005160957
Winsorized Mean ( 11 / 20 )21.78852459016390.34596107017999362.9797005160958
Winsorized Mean ( 12 / 20 )21.53278688524590.27516235953782578.254841692059
Winsorized Mean ( 13 / 20 )21.53278688524590.27516235953782578.254841692059
Winsorized Mean ( 14 / 20 )21.53278688524590.27516235953782578.254841692059
Winsorized Mean ( 15 / 20 )21.43442622950820.24959951798132985.8752709254494
Winsorized Mean ( 16 / 20 )21.43442622950820.24959951798132985.8752709254494
Winsorized Mean ( 17 / 20 )21.43442622950820.24959951798132985.8752709254494
Winsorized Mean ( 18 / 20 )20.99180327868850.175419794416266119.666103523503
Winsorized Mean ( 19 / 20 )20.99180327868850.175419794416266119.666103523503
Winsorized Mean ( 20 / 20 )20.99180327868850.175419794416266119.666103523503
Trimmed Mean ( 1 / 20 )21.84067796610170.39446135209142155.3683595371337
Trimmed Mean ( 2 / 20 )21.79649122807020.38227459419266657.0178912205836
Trimmed Mean ( 3 / 20 )21.74909090909090.36708766214462559.2476761055571
Trimmed Mean ( 4 / 20 )21.70188679245280.36309716906118259.768812983491
Trimmed Mean ( 5 / 20 )21.65098039215690.35767629739444760.5323320272466
Trimmed Mean ( 6 / 20 )21.59591836734690.35042441691470761.6278927064702
Trimmed Mean ( 7 / 20 )21.54468085106380.34472110636207462.498873592134
Trimmed Mean ( 8 / 20 )21.48888888888890.33690843737425463.7825786031532
Trimmed Mean ( 9 / 20 )21.42790697674420.32628187579748365.672991870514
Trimmed Mean ( 10 / 20 )21.36829268292680.31615909518496267.587151558698
Trimmed Mean ( 11 / 20 )21.30256410256410.30211774298666670.5108011597461
Trimmed Mean ( 12 / 20 )21.22972972972970.28241411208308475.1723402670618
Trimmed Mean ( 13 / 20 )21.18571428571430.27723553851829176.4177435510004
Trimmed Mean ( 14 / 20 )21.13636363636360.26921667310902278.5106040880472
Trimmed Mean ( 15 / 20 )21.08064516129030.25700589319374882.0239757903073
Trimmed Mean ( 16 / 20 )21.03103448275860.24750496080393784.9721735453155
Trimmed Mean ( 17 / 20 )20.97407407407410.23232950079565990.2772743118897
Trimmed Mean ( 18 / 20 )20.9080.207518673858523100.752378623305
Trimmed Mean ( 19 / 20 )20.89565217391300.203669718378967102.595772902443
Trimmed Mean ( 20 / 20 )20.88095238095240.195985792441703106.543194385703
Median20.8
Midrange23.1
Midmean - Weighted Average at Xnp21.0806451612903
Midmean - Weighted Average at X(n+1)p21.0806451612903
Midmean - Empirical Distribution Function21.0806451612903
Midmean - Empirical Distribution Function - Averaging21.0806451612903
Midmean - Empirical Distribution Function - Interpolation21.0806451612903
Midmean - Closest Observation20.9323529411765
Midmean - True Basic - Statistics Graphics Toolkit21.0806451612903
Midmean - MS Excel (old versions)21.0806451612903
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')