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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, 21 Oct 2008 01:07:16 -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/2008/Oct/21/t122457310194xe662hmle87om.htm/, Retrieved Sun, 19 May 2024 18:48:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18343, Retrieved Sun, 19 May 2024 18:48:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Q9 Tijdreeks1] [2008-10-21 07:07:16] [d7f41258beeebb8716e3f5d39f3cdc01] [Current]
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Dataseries X:
4,6
7,6
6,8
7,8
12,2
6,3
7,1
10,5
8,9
7,7
11,1
7,2
5,1
8,5
7,4
7,3
12,9
7,7
8,1
10,2
8,8
8,9
10,2
6,5
5,2
8,8
8,4
7,4
11,5
5,7
5,9
6,7
5,9
6,7
6,2
4,1
4,3
6,3
6
7,5
10,7
7,3
7,1
8,9
7,9
7,6
8
5,8
6,4
7,1
7,9
8
12,1
11
12,4
12,9
41,7
9,2
7,3
7,1




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=18343&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=18343&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18343&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 Mean8.540.6254634439949413.65387550942
Geometric Mean7.92584627963415
Harmonic Mean7.54578597901999
Quadratic Mean9.7986053429387
Winsorized Mean ( 1 / 20 )8.063333333333330.28568449535304228.2246095412663
Winsorized Mean ( 2 / 20 )8.073333333333330.28352967607078828.4743856276889
Winsorized Mean ( 3 / 20 )8.073333333333330.27162273049448729.7225983946038
Winsorized Mean ( 4 / 20 )8.066666666666670.26684669064624230.2295923068449
Winsorized Mean ( 5 / 20 )8.10.25756355147972231.4485491191005
Winsorized Mean ( 6 / 20 )8.050.2407791026463633.4331339868115
Winsorized Mean ( 7 / 20 )8.0150.22790900404392535.167544317184
Winsorized Mean ( 8 / 20 )8.001666666666670.22487274074282635.5830886404222
Winsorized Mean ( 9 / 20 )7.971666666666670.21251908078730737.5103573624284
Winsorized Mean ( 10 / 20 )7.971666666666670.20019893590119339.8187264621678
Winsorized Mean ( 11 / 20 )7.9350.18588352163604842.6880227475805
Winsorized Mean ( 12 / 20 )7.9350.18588352163604842.6880227475805
Winsorized Mean ( 13 / 20 )7.740.14064419988201455.0324862773797
Winsorized Mean ( 14 / 20 )7.693333333333330.12496025733556761.5662411183563
Winsorized Mean ( 15 / 20 )7.743333333333330.11713063513608366.1085233964373
Winsorized Mean ( 16 / 20 )7.743333333333330.11713063513608366.1085233964373
Winsorized Mean ( 17 / 20 )7.743333333333330.10817872496401571.5790774563957
Winsorized Mean ( 18 / 20 )7.833333333333330.095629542591167281.913320100486
Winsorized Mean ( 19 / 20 )7.738333333333330.079762772091221197.0168554884645
Winsorized Mean ( 20 / 20 )7.7050.0744252933738613103.526632556158
Trimmed Mean ( 1 / 20 )8.04482758620690.27572894549558729.1765798173542
Trimmed Mean ( 2 / 20 )8.0250.26342215883678830.4644075328992
Trimmed Mean ( 3 / 20 )7.998148148148150.24952072494781232.0540434058974
Trimmed Mean ( 4 / 20 )7.969230769230770.23811949389981033.4673597642698
Trimmed Mean ( 5 / 20 )7.940.22566002964546435.1856729456013
Trimmed Mean ( 6 / 20 )7.90.21300784123015737.0878365527585
Trimmed Mean ( 7 / 20 )7.867391304347830.20256934991476338.8380142783608
Trimmed Mean ( 8 / 20 )7.838636363636360.19314948118856940.5832638814267
Trimmed Mean ( 9 / 20 )7.80952380952380.18161136806533843.0012938766818
Trimmed Mean ( 10 / 20 )7.78250.17010130842590645.7521466002713
Trimmed Mean ( 11 / 20 )7.752631578947370.15825941764454448.9868577449214
Trimmed Mean ( 12 / 20 )7.7250.14662201701318952.686493866096
Trimmed Mean ( 13 / 20 )7.694117647058820.12978394060258359.2840501785909
Trimmed Mean ( 14 / 20 )7.68750.12278275464701762.6105842151892
Trimmed Mean ( 15 / 20 )7.686666666666670.11780885876310565.246932593782
Trimmed Mean ( 16 / 20 )7.678571428571430.11284642638826368.0444359146322
Trimmed Mean ( 17 / 20 )7.669230769230770.1050668989474772.9937863024313
Trimmed Mean ( 18 / 20 )7.658333333333330.096480956044325579.376631900444
Trimmed Mean ( 19 / 20 )7.631818181818180.087134856827227687.5862824558336
Trimmed Mean ( 20 / 20 )7.6150.080549102383185294.5386078143268
Median7.6
Midrange22.9
Midmean - Weighted Average at Xnp7.6875
Midmean - Weighted Average at X(n+1)p7.7258064516129
Midmean - Empirical Distribution Function7.6875
Midmean - Empirical Distribution Function - Averaging7.7258064516129
Midmean - Empirical Distribution Function - Interpolation7.7258064516129
Midmean - Closest Observation7.6875
Midmean - True Basic - Statistics Graphics Toolkit7.7258064516129
Midmean - MS Excel (old versions)7.6875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.54 & 0.62546344399494 & 13.65387550942 \tabularnewline
Geometric Mean & 7.92584627963415 &  &  \tabularnewline
Harmonic Mean & 7.54578597901999 &  &  \tabularnewline
Quadratic Mean & 9.7986053429387 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.06333333333333 & 0.285684495353042 & 28.2246095412663 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.07333333333333 & 0.283529676070788 & 28.4743856276889 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.07333333333333 & 0.271622730494487 & 29.7225983946038 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.06666666666667 & 0.266846690646242 & 30.2295923068449 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.1 & 0.257563551479722 & 31.4485491191005 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.05 & 0.24077910264636 & 33.4331339868115 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.015 & 0.227909004043925 & 35.167544317184 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.00166666666667 & 0.224872740742826 & 35.5830886404222 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.97166666666667 & 0.212519080787307 & 37.5103573624284 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.97166666666667 & 0.200198935901193 & 39.8187264621678 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.935 & 0.185883521636048 & 42.6880227475805 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.935 & 0.185883521636048 & 42.6880227475805 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.74 & 0.140644199882014 & 55.0324862773797 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.69333333333333 & 0.124960257335567 & 61.5662411183563 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.74333333333333 & 0.117130635136083 & 66.1085233964373 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.74333333333333 & 0.117130635136083 & 66.1085233964373 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.74333333333333 & 0.108178724964015 & 71.5790774563957 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.83333333333333 & 0.0956295425911672 & 81.913320100486 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.73833333333333 & 0.0797627720912211 & 97.0168554884645 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.705 & 0.0744252933738613 & 103.526632556158 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.0448275862069 & 0.275728945495587 & 29.1765798173542 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.025 & 0.263422158836788 & 30.4644075328992 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.99814814814815 & 0.249520724947812 & 32.0540434058974 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.96923076923077 & 0.238119493899810 & 33.4673597642698 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.94 & 0.225660029645464 & 35.1856729456013 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.9 & 0.213007841230157 & 37.0878365527585 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.86739130434783 & 0.202569349914763 & 38.8380142783608 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.83863636363636 & 0.193149481188569 & 40.5832638814267 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.8095238095238 & 0.181611368065338 & 43.0012938766818 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.7825 & 0.170101308425906 & 45.7521466002713 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.75263157894737 & 0.158259417644544 & 48.9868577449214 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.725 & 0.146622017013189 & 52.686493866096 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.69411764705882 & 0.129783940602583 & 59.2840501785909 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.6875 & 0.122782754647017 & 62.6105842151892 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.68666666666667 & 0.117808858763105 & 65.246932593782 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.67857142857143 & 0.112846426388263 & 68.0444359146322 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.66923076923077 & 0.10506689894747 & 72.9937863024313 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.65833333333333 & 0.0964809560443255 & 79.376631900444 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.63181818181818 & 0.0871348568272276 & 87.5862824558336 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.615 & 0.0805491023831852 & 94.5386078143268 \tabularnewline
Median & 7.6 &  &  \tabularnewline
Midrange & 22.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.6875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.7258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.6875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.7258064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.7258064516129 &  &  \tabularnewline
Midmean - Closest Observation & 7.6875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.7258064516129 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.6875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18343&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]8.54[/C][C]0.62546344399494[/C][C]13.65387550942[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.92584627963415[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.54578597901999[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.7986053429387[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.06333333333333[/C][C]0.285684495353042[/C][C]28.2246095412663[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.07333333333333[/C][C]0.283529676070788[/C][C]28.4743856276889[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.07333333333333[/C][C]0.271622730494487[/C][C]29.7225983946038[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.06666666666667[/C][C]0.266846690646242[/C][C]30.2295923068449[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.1[/C][C]0.257563551479722[/C][C]31.4485491191005[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.05[/C][C]0.24077910264636[/C][C]33.4331339868115[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.015[/C][C]0.227909004043925[/C][C]35.167544317184[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.00166666666667[/C][C]0.224872740742826[/C][C]35.5830886404222[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.97166666666667[/C][C]0.212519080787307[/C][C]37.5103573624284[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.97166666666667[/C][C]0.200198935901193[/C][C]39.8187264621678[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.935[/C][C]0.185883521636048[/C][C]42.6880227475805[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.935[/C][C]0.185883521636048[/C][C]42.6880227475805[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.74[/C][C]0.140644199882014[/C][C]55.0324862773797[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.69333333333333[/C][C]0.124960257335567[/C][C]61.5662411183563[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.74333333333333[/C][C]0.117130635136083[/C][C]66.1085233964373[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.74333333333333[/C][C]0.117130635136083[/C][C]66.1085233964373[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.74333333333333[/C][C]0.108178724964015[/C][C]71.5790774563957[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.83333333333333[/C][C]0.0956295425911672[/C][C]81.913320100486[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.73833333333333[/C][C]0.0797627720912211[/C][C]97.0168554884645[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.705[/C][C]0.0744252933738613[/C][C]103.526632556158[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.0448275862069[/C][C]0.275728945495587[/C][C]29.1765798173542[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.025[/C][C]0.263422158836788[/C][C]30.4644075328992[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.99814814814815[/C][C]0.249520724947812[/C][C]32.0540434058974[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.96923076923077[/C][C]0.238119493899810[/C][C]33.4673597642698[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.94[/C][C]0.225660029645464[/C][C]35.1856729456013[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.9[/C][C]0.213007841230157[/C][C]37.0878365527585[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.86739130434783[/C][C]0.202569349914763[/C][C]38.8380142783608[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.83863636363636[/C][C]0.193149481188569[/C][C]40.5832638814267[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.8095238095238[/C][C]0.181611368065338[/C][C]43.0012938766818[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.7825[/C][C]0.170101308425906[/C][C]45.7521466002713[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.75263157894737[/C][C]0.158259417644544[/C][C]48.9868577449214[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.725[/C][C]0.146622017013189[/C][C]52.686493866096[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.69411764705882[/C][C]0.129783940602583[/C][C]59.2840501785909[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.6875[/C][C]0.122782754647017[/C][C]62.6105842151892[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.68666666666667[/C][C]0.117808858763105[/C][C]65.246932593782[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.67857142857143[/C][C]0.112846426388263[/C][C]68.0444359146322[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.66923076923077[/C][C]0.10506689894747[/C][C]72.9937863024313[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.65833333333333[/C][C]0.0964809560443255[/C][C]79.376631900444[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.63181818181818[/C][C]0.0871348568272276[/C][C]87.5862824558336[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.615[/C][C]0.0805491023831852[/C][C]94.5386078143268[/C][/ROW]
[ROW][C]Median[/C][C]7.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]22.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.7258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.7258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.7258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.6875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.7258064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.6875[/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=18343&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18343&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 Mean8.540.6254634439949413.65387550942
Geometric Mean7.92584627963415
Harmonic Mean7.54578597901999
Quadratic Mean9.7986053429387
Winsorized Mean ( 1 / 20 )8.063333333333330.28568449535304228.2246095412663
Winsorized Mean ( 2 / 20 )8.073333333333330.28352967607078828.4743856276889
Winsorized Mean ( 3 / 20 )8.073333333333330.27162273049448729.7225983946038
Winsorized Mean ( 4 / 20 )8.066666666666670.26684669064624230.2295923068449
Winsorized Mean ( 5 / 20 )8.10.25756355147972231.4485491191005
Winsorized Mean ( 6 / 20 )8.050.2407791026463633.4331339868115
Winsorized Mean ( 7 / 20 )8.0150.22790900404392535.167544317184
Winsorized Mean ( 8 / 20 )8.001666666666670.22487274074282635.5830886404222
Winsorized Mean ( 9 / 20 )7.971666666666670.21251908078730737.5103573624284
Winsorized Mean ( 10 / 20 )7.971666666666670.20019893590119339.8187264621678
Winsorized Mean ( 11 / 20 )7.9350.18588352163604842.6880227475805
Winsorized Mean ( 12 / 20 )7.9350.18588352163604842.6880227475805
Winsorized Mean ( 13 / 20 )7.740.14064419988201455.0324862773797
Winsorized Mean ( 14 / 20 )7.693333333333330.12496025733556761.5662411183563
Winsorized Mean ( 15 / 20 )7.743333333333330.11713063513608366.1085233964373
Winsorized Mean ( 16 / 20 )7.743333333333330.11713063513608366.1085233964373
Winsorized Mean ( 17 / 20 )7.743333333333330.10817872496401571.5790774563957
Winsorized Mean ( 18 / 20 )7.833333333333330.095629542591167281.913320100486
Winsorized Mean ( 19 / 20 )7.738333333333330.079762772091221197.0168554884645
Winsorized Mean ( 20 / 20 )7.7050.0744252933738613103.526632556158
Trimmed Mean ( 1 / 20 )8.04482758620690.27572894549558729.1765798173542
Trimmed Mean ( 2 / 20 )8.0250.26342215883678830.4644075328992
Trimmed Mean ( 3 / 20 )7.998148148148150.24952072494781232.0540434058974
Trimmed Mean ( 4 / 20 )7.969230769230770.23811949389981033.4673597642698
Trimmed Mean ( 5 / 20 )7.940.22566002964546435.1856729456013
Trimmed Mean ( 6 / 20 )7.90.21300784123015737.0878365527585
Trimmed Mean ( 7 / 20 )7.867391304347830.20256934991476338.8380142783608
Trimmed Mean ( 8 / 20 )7.838636363636360.19314948118856940.5832638814267
Trimmed Mean ( 9 / 20 )7.80952380952380.18161136806533843.0012938766818
Trimmed Mean ( 10 / 20 )7.78250.17010130842590645.7521466002713
Trimmed Mean ( 11 / 20 )7.752631578947370.15825941764454448.9868577449214
Trimmed Mean ( 12 / 20 )7.7250.14662201701318952.686493866096
Trimmed Mean ( 13 / 20 )7.694117647058820.12978394060258359.2840501785909
Trimmed Mean ( 14 / 20 )7.68750.12278275464701762.6105842151892
Trimmed Mean ( 15 / 20 )7.686666666666670.11780885876310565.246932593782
Trimmed Mean ( 16 / 20 )7.678571428571430.11284642638826368.0444359146322
Trimmed Mean ( 17 / 20 )7.669230769230770.1050668989474772.9937863024313
Trimmed Mean ( 18 / 20 )7.658333333333330.096480956044325579.376631900444
Trimmed Mean ( 19 / 20 )7.631818181818180.087134856827227687.5862824558336
Trimmed Mean ( 20 / 20 )7.6150.080549102383185294.5386078143268
Median7.6
Midrange22.9
Midmean - Weighted Average at Xnp7.6875
Midmean - Weighted Average at X(n+1)p7.7258064516129
Midmean - Empirical Distribution Function7.6875
Midmean - Empirical Distribution Function - Averaging7.7258064516129
Midmean - Empirical Distribution Function - Interpolation7.7258064516129
Midmean - Closest Observation7.6875
Midmean - True Basic - Statistics Graphics Toolkit7.7258064516129
Midmean - MS Excel (old versions)7.6875
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')