Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 02 Dec 2009 10:27:42 -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/2009/Dec/02/t1259775025xo1gl6omu1uhnqz.htm/, Retrieved Sun, 28 Apr 2024 09:38:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62468, Retrieved Sun, 28 Apr 2024 09:38:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper] [2009-12-02 17:27:42] [aef022288383377281176d9807aba5bf] [Current]
Feedback Forum

Post a new message
Dataseries X:
9
8.6
8.8
8.5
8.3
8.2
8
7.9
8
9.3
9.6
9
8.7
8.3
8.4
7.8
7.8
7.6
7.7
7.6
7.6
8.6
8.6
8.2
7.5
7.1
7
6.9
6.6
6.3
6.1
5.9
6
7.2
7.2
6.4
6.1
5.9
6.1
5.9
5.8
5.7
5.6
5.3
5.5
6.5
6.5
6.1
5.9
5.8
6.2
6.5
6.6
6.7
6.6
6.5
6.8
7.8
7.9
7.4




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=62468&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=62468&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62468&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 Mean7.20.14399466405681950.0018528267058
Geometric Mean7.11547906955358
Harmonic Mean7.03204024886433
Quadratic Mean7.28445834179408
Winsorized Mean ( 1 / 20 )7.198333333333330.14194953481130250.7105102028148
Winsorized Mean ( 2 / 20 )7.191666666666670.13892833714733551.7652972340685
Winsorized Mean ( 3 / 20 )7.196666666666670.13798318628978652.1561130756364
Winsorized Mean ( 4 / 20 )7.190.13394703397091153.6779336342857
Winsorized Mean ( 5 / 20 )7.181666666666670.13228738760373554.2883701670734
Winsorized Mean ( 6 / 20 )7.181666666666670.12864991401725855.8233304820031
Winsorized Mean ( 7 / 20 )7.181666666666670.12864991401725855.8233304820031
Winsorized Mean ( 8 / 20 )7.181666666666670.12864991401725855.8233304820031
Winsorized Mean ( 9 / 20 )7.166666666666670.12590164457012256.922740692836
Winsorized Mean ( 10 / 20 )7.166666666666670.12016153597108559.6419362381588
Winsorized Mean ( 11 / 20 )7.166666666666670.11405882778573962.833073123716
Winsorized Mean ( 12 / 20 )7.166666666666670.11405882778573962.833073123716
Winsorized Mean ( 13 / 20 )7.1450.11047982150805664.6724433699323
Winsorized Mean ( 14 / 20 )7.1450.11047982150805664.6724433699323
Winsorized Mean ( 15 / 20 )7.120.09865765724632572.1687520130651
Winsorized Mean ( 16 / 20 )7.146666666666670.094524282196007475.6066748208381
Winsorized Mean ( 17 / 20 )7.146666666666670.08601230586857183.0888858808988
Winsorized Mean ( 18 / 20 )7.176666666666670.08169692740409187.8450009652052
Winsorized Mean ( 19 / 20 )7.1450.077036384389287292.7483819060646
Winsorized Mean ( 20 / 20 )7.1450.077036384389287292.7483819060646
Trimmed Mean ( 1 / 20 )7.191379310344830.13916361700311751.6757142794279
Trimmed Mean ( 2 / 20 )7.183928571428570.13569869185873052.9402934768702
Trimmed Mean ( 3 / 20 )7.179629629629630.13336948224933353.832627288808
Trimmed Mean ( 4 / 20 )7.173076923076920.13084351541059654.8217991588449
Trimmed Mean ( 5 / 20 )7.1680.12915549874915555.4989920632158
Trimmed Mean ( 6 / 20 )7.164583333333330.12745773820977256.2114425845352
Trimmed Mean ( 7 / 20 )7.160869565217390.12624178400088256.7234503369136
Trimmed Mean ( 8 / 20 )7.156818181818180.12450314477093057.4830314124659
Trimmed Mean ( 9 / 20 )7.152380952380950.12208211547143358.5866400230804
Trimmed Mean ( 10 / 20 )7.150.11950753650733259.8288627559596
Trimmed Mean ( 11 / 20 )7.147368421052630.11744898969044760.8550864497899
Trimmed Mean ( 12 / 20 )7.144444444444440.11604900746684061.5640288563939
Trimmed Mean ( 13 / 20 )7.141176470588230.11384682199365062.7261819481138
Trimmed Mean ( 14 / 20 )7.1406250.11151986794997964.0300704373402
Trimmed Mean ( 15 / 20 )7.140.10791652798109466.162247188409
Trimmed Mean ( 16 / 20 )7.142857142857140.10608828451750467.3293679442859
Trimmed Mean ( 17 / 20 )7.14230769230770.10424425118597968.5151230024697
Trimmed Mean ( 18 / 20 )7.141666666666670.10372005708418268.8552134219356
Trimmed Mean ( 19 / 20 )7.136363636363640.10351933850023568.9374926439224
Trimmed Mean ( 20 / 20 )7.1350.1039420385042668.6440260617708
Median7.15
Midrange7.45
Midmean - Weighted Average at Xnp7.01764705882353
Midmean - Weighted Average at X(n+1)p7.14
Midmean - Empirical Distribution Function7.01764705882353
Midmean - Empirical Distribution Function - Averaging7.14
Midmean - Empirical Distribution Function - Interpolation7.14
Midmean - Closest Observation7.01764705882353
Midmean - True Basic - Statistics Graphics Toolkit7.14
Midmean - MS Excel (old versions)7.08333333333333
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.2 & 0.143994664056819 & 50.0018528267058 \tabularnewline
Geometric Mean & 7.11547906955358 &  &  \tabularnewline
Harmonic Mean & 7.03204024886433 &  &  \tabularnewline
Quadratic Mean & 7.28445834179408 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.19833333333333 & 0.141949534811302 & 50.7105102028148 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.19166666666667 & 0.138928337147335 & 51.7652972340685 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.19666666666667 & 0.137983186289786 & 52.1561130756364 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.19 & 0.133947033970911 & 53.6779336342857 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.18166666666667 & 0.132287387603735 & 54.2883701670734 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.18166666666667 & 0.128649914017258 & 55.8233304820031 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.18166666666667 & 0.128649914017258 & 55.8233304820031 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.18166666666667 & 0.128649914017258 & 55.8233304820031 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.16666666666667 & 0.125901644570122 & 56.922740692836 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.16666666666667 & 0.120161535971085 & 59.6419362381588 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.16666666666667 & 0.114058827785739 & 62.833073123716 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.16666666666667 & 0.114058827785739 & 62.833073123716 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.145 & 0.110479821508056 & 64.6724433699323 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.145 & 0.110479821508056 & 64.6724433699323 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.12 & 0.098657657246325 & 72.1687520130651 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.14666666666667 & 0.0945242821960074 & 75.6066748208381 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.14666666666667 & 0.086012305868571 & 83.0888858808988 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.17666666666667 & 0.081696927404091 & 87.8450009652052 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.145 & 0.0770363843892872 & 92.7483819060646 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.145 & 0.0770363843892872 & 92.7483819060646 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.19137931034483 & 0.139163617003117 & 51.6757142794279 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.18392857142857 & 0.135698691858730 & 52.9402934768702 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.17962962962963 & 0.133369482249333 & 53.832627288808 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.17307692307692 & 0.130843515410596 & 54.8217991588449 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.168 & 0.129155498749155 & 55.4989920632158 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.16458333333333 & 0.127457738209772 & 56.2114425845352 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.16086956521739 & 0.126241784000882 & 56.7234503369136 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.15681818181818 & 0.124503144770930 & 57.4830314124659 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.15238095238095 & 0.122082115471433 & 58.5866400230804 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.15 & 0.119507536507332 & 59.8288627559596 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.14736842105263 & 0.117448989690447 & 60.8550864497899 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.14444444444444 & 0.116049007466840 & 61.5640288563939 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.14117647058823 & 0.113846821993650 & 62.7261819481138 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.140625 & 0.111519867949979 & 64.0300704373402 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.14 & 0.107916527981094 & 66.162247188409 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.14285714285714 & 0.106088284517504 & 67.3293679442859 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.1423076923077 & 0.104244251185979 & 68.5151230024697 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.14166666666667 & 0.103720057084182 & 68.8552134219356 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.13636363636364 & 0.103519338500235 & 68.9374926439224 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.135 & 0.10394203850426 & 68.6440260617708 \tabularnewline
Median & 7.15 &  &  \tabularnewline
Midrange & 7.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.01764705882353 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.14 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.01764705882353 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.14 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.14 &  &  \tabularnewline
Midmean - Closest Observation & 7.01764705882353 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.14 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.08333333333333 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62468&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]7.2[/C][C]0.143994664056819[/C][C]50.0018528267058[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.11547906955358[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.03204024886433[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.28445834179408[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.19833333333333[/C][C]0.141949534811302[/C][C]50.7105102028148[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.19166666666667[/C][C]0.138928337147335[/C][C]51.7652972340685[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.19666666666667[/C][C]0.137983186289786[/C][C]52.1561130756364[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.19[/C][C]0.133947033970911[/C][C]53.6779336342857[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.18166666666667[/C][C]0.132287387603735[/C][C]54.2883701670734[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.18166666666667[/C][C]0.128649914017258[/C][C]55.8233304820031[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.18166666666667[/C][C]0.128649914017258[/C][C]55.8233304820031[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.18166666666667[/C][C]0.128649914017258[/C][C]55.8233304820031[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.16666666666667[/C][C]0.125901644570122[/C][C]56.922740692836[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.16666666666667[/C][C]0.120161535971085[/C][C]59.6419362381588[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.16666666666667[/C][C]0.114058827785739[/C][C]62.833073123716[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.16666666666667[/C][C]0.114058827785739[/C][C]62.833073123716[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.145[/C][C]0.110479821508056[/C][C]64.6724433699323[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.145[/C][C]0.110479821508056[/C][C]64.6724433699323[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.12[/C][C]0.098657657246325[/C][C]72.1687520130651[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.14666666666667[/C][C]0.0945242821960074[/C][C]75.6066748208381[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.14666666666667[/C][C]0.086012305868571[/C][C]83.0888858808988[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.17666666666667[/C][C]0.081696927404091[/C][C]87.8450009652052[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.145[/C][C]0.0770363843892872[/C][C]92.7483819060646[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.145[/C][C]0.0770363843892872[/C][C]92.7483819060646[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.19137931034483[/C][C]0.139163617003117[/C][C]51.6757142794279[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.18392857142857[/C][C]0.135698691858730[/C][C]52.9402934768702[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.17962962962963[/C][C]0.133369482249333[/C][C]53.832627288808[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.17307692307692[/C][C]0.130843515410596[/C][C]54.8217991588449[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.168[/C][C]0.129155498749155[/C][C]55.4989920632158[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.16458333333333[/C][C]0.127457738209772[/C][C]56.2114425845352[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.16086956521739[/C][C]0.126241784000882[/C][C]56.7234503369136[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.15681818181818[/C][C]0.124503144770930[/C][C]57.4830314124659[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.15238095238095[/C][C]0.122082115471433[/C][C]58.5866400230804[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.15[/C][C]0.119507536507332[/C][C]59.8288627559596[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.14736842105263[/C][C]0.117448989690447[/C][C]60.8550864497899[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.14444444444444[/C][C]0.116049007466840[/C][C]61.5640288563939[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.14117647058823[/C][C]0.113846821993650[/C][C]62.7261819481138[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.140625[/C][C]0.111519867949979[/C][C]64.0300704373402[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.14[/C][C]0.107916527981094[/C][C]66.162247188409[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.14285714285714[/C][C]0.106088284517504[/C][C]67.3293679442859[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.1423076923077[/C][C]0.104244251185979[/C][C]68.5151230024697[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.14166666666667[/C][C]0.103720057084182[/C][C]68.8552134219356[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.13636363636364[/C][C]0.103519338500235[/C][C]68.9374926439224[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.135[/C][C]0.10394203850426[/C][C]68.6440260617708[/C][/ROW]
[ROW][C]Median[/C][C]7.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.01764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.01764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.01764705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.08333333333333[/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=62468&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62468&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 Mean7.20.14399466405681950.0018528267058
Geometric Mean7.11547906955358
Harmonic Mean7.03204024886433
Quadratic Mean7.28445834179408
Winsorized Mean ( 1 / 20 )7.198333333333330.14194953481130250.7105102028148
Winsorized Mean ( 2 / 20 )7.191666666666670.13892833714733551.7652972340685
Winsorized Mean ( 3 / 20 )7.196666666666670.13798318628978652.1561130756364
Winsorized Mean ( 4 / 20 )7.190.13394703397091153.6779336342857
Winsorized Mean ( 5 / 20 )7.181666666666670.13228738760373554.2883701670734
Winsorized Mean ( 6 / 20 )7.181666666666670.12864991401725855.8233304820031
Winsorized Mean ( 7 / 20 )7.181666666666670.12864991401725855.8233304820031
Winsorized Mean ( 8 / 20 )7.181666666666670.12864991401725855.8233304820031
Winsorized Mean ( 9 / 20 )7.166666666666670.12590164457012256.922740692836
Winsorized Mean ( 10 / 20 )7.166666666666670.12016153597108559.6419362381588
Winsorized Mean ( 11 / 20 )7.166666666666670.11405882778573962.833073123716
Winsorized Mean ( 12 / 20 )7.166666666666670.11405882778573962.833073123716
Winsorized Mean ( 13 / 20 )7.1450.11047982150805664.6724433699323
Winsorized Mean ( 14 / 20 )7.1450.11047982150805664.6724433699323
Winsorized Mean ( 15 / 20 )7.120.09865765724632572.1687520130651
Winsorized Mean ( 16 / 20 )7.146666666666670.094524282196007475.6066748208381
Winsorized Mean ( 17 / 20 )7.146666666666670.08601230586857183.0888858808988
Winsorized Mean ( 18 / 20 )7.176666666666670.08169692740409187.8450009652052
Winsorized Mean ( 19 / 20 )7.1450.077036384389287292.7483819060646
Winsorized Mean ( 20 / 20 )7.1450.077036384389287292.7483819060646
Trimmed Mean ( 1 / 20 )7.191379310344830.13916361700311751.6757142794279
Trimmed Mean ( 2 / 20 )7.183928571428570.13569869185873052.9402934768702
Trimmed Mean ( 3 / 20 )7.179629629629630.13336948224933353.832627288808
Trimmed Mean ( 4 / 20 )7.173076923076920.13084351541059654.8217991588449
Trimmed Mean ( 5 / 20 )7.1680.12915549874915555.4989920632158
Trimmed Mean ( 6 / 20 )7.164583333333330.12745773820977256.2114425845352
Trimmed Mean ( 7 / 20 )7.160869565217390.12624178400088256.7234503369136
Trimmed Mean ( 8 / 20 )7.156818181818180.12450314477093057.4830314124659
Trimmed Mean ( 9 / 20 )7.152380952380950.12208211547143358.5866400230804
Trimmed Mean ( 10 / 20 )7.150.11950753650733259.8288627559596
Trimmed Mean ( 11 / 20 )7.147368421052630.11744898969044760.8550864497899
Trimmed Mean ( 12 / 20 )7.144444444444440.11604900746684061.5640288563939
Trimmed Mean ( 13 / 20 )7.141176470588230.11384682199365062.7261819481138
Trimmed Mean ( 14 / 20 )7.1406250.11151986794997964.0300704373402
Trimmed Mean ( 15 / 20 )7.140.10791652798109466.162247188409
Trimmed Mean ( 16 / 20 )7.142857142857140.10608828451750467.3293679442859
Trimmed Mean ( 17 / 20 )7.14230769230770.10424425118597968.5151230024697
Trimmed Mean ( 18 / 20 )7.141666666666670.10372005708418268.8552134219356
Trimmed Mean ( 19 / 20 )7.136363636363640.10351933850023568.9374926439224
Trimmed Mean ( 20 / 20 )7.1350.1039420385042668.6440260617708
Median7.15
Midrange7.45
Midmean - Weighted Average at Xnp7.01764705882353
Midmean - Weighted Average at X(n+1)p7.14
Midmean - Empirical Distribution Function7.01764705882353
Midmean - Empirical Distribution Function - Averaging7.14
Midmean - Empirical Distribution Function - Interpolation7.14
Midmean - Closest Observation7.01764705882353
Midmean - True Basic - Statistics Graphics Toolkit7.14
Midmean - MS Excel (old versions)7.08333333333333
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')