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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 computationFri, 05 Dec 2008 05:03:20 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/05/t1228478677odwt708ebnc9d5s.htm/, Retrieved Thu, 16 May 2024 18:18:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29206, Retrieved Thu, 16 May 2024 18:18:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact180
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Simple Regression] [simple linear reg...] [2008-12-05 11:36:25] [4ddbf81f78ea7c738951638c7e93f6ee]
- RM D    [Central Tendency] [central tendency ...] [2008-12-05 12:03:20] [e8f764b122b426f433a1e1038b457077] [Current]
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Dataseries X:
7,5
7,6
7,9
7,9
8,1
8,2
8
7,5
6,8
6,5
6,6
7,6
8
8
7,7
7,5
7,6
7,7
7,9
7,8
7,5
7,5
7,1
7,5
7,5
7,6
7,7
7,7
7,9
8,1
8,2
8,2
8,1
7,9
7,3
6,9
6,6
6,7
6,9
7
7,1
7,2
7,1
6,9
7
6,8
6,4
6,7
6,7
6,4
6,3
6,2
6,5
6,8
6,8
6,5
6,3
5,9
5,9
6,4
6,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29206&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29206&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.222950819672130.082528135378712987.5210712871044
Geometric Mean7.19416422895116
Harmonic Mean7.16494225401968
Quadratic Mean7.25118418819627
Winsorized Mean ( 1 / 20 )7.222950819672130.082528135378712987.5210712871043
Winsorized Mean ( 2 / 20 )7.23278688524590.080154267634881590.2358302142149
Winsorized Mean ( 3 / 20 )7.23278688524590.078187155020809892.5060757527355
Winsorized Mean ( 4 / 20 )7.23278688524590.078187155020809892.5060757527355
Winsorized Mean ( 5 / 20 )7.240983606557380.076621882233804394.5028155855297
Winsorized Mean ( 6 / 20 )7.231147540983610.07486019697239896.5953581934848
Winsorized Mean ( 7 / 20 )7.231147540983610.07486019697239896.5953581934848
Winsorized Mean ( 8 / 20 )7.23114754098360.07486019697239896.5953581934848
Winsorized Mean ( 9 / 20 )7.231147540983610.0697591870129908103.658712932491
Winsorized Mean ( 10 / 20 )7.231147540983610.0697591870129908103.658712932491
Winsorized Mean ( 11 / 20 )7.231147540983610.0697591870129908103.658712932491
Winsorized Mean ( 12 / 20 )7.250819672131150.0664322223654569109.146125388414
Winsorized Mean ( 13 / 20 )7.250819672131150.0664322223654569109.146125388414
Winsorized Mean ( 14 / 20 )7.250819672131150.059120278936489122.645220938833
Winsorized Mean ( 15 / 20 )7.226229508196720.0554613851460489130.292986537707
Winsorized Mean ( 16 / 20 )7.226229508196720.0554613851460489130.292986537707
Winsorized Mean ( 17 / 20 )7.254098360655740.0511920081328768141.703727304985
Winsorized Mean ( 18 / 20 )7.254098360655740.0511920081328768141.703727304985
Winsorized Mean ( 19 / 20 )7.222950819672130.0468338210088537154.225101947301
Winsorized Mean ( 20 / 20 )7.222950819672130.0468338210088537154.225101947301
Trimmed Mean ( 1 / 20 )7.228813559322030.080582727455086189.7067372576972
Trimmed Mean ( 2 / 20 )7.235087719298250.078179923423503492.544062496781
Trimmed Mean ( 3 / 20 )7.236363636363640.076776979765925694.25173611186
Trimmed Mean ( 4 / 20 )7.23773584905660.075918488825398995.3356153558629
Trimmed Mean ( 5 / 20 )7.239215686274510.074784838107500796.8005797628174
Trimmed Mean ( 6 / 20 )7.238775510204080.073818144266022898.0622797034463
Trimmed Mean ( 7 / 20 )7.24042553191490.073037669400222199.1327569920087
Trimmed Mean ( 8 / 20 )7.242222222222220.0719489780561344100.657749670494
Trimmed Mean ( 9 / 20 )7.244186046511630.0704598348221206102.812986502167
Trimmed Mean ( 10 / 20 )7.246341463414630.0697641987449998103.869055959508
Trimmed Mean ( 11 / 20 )7.248717948717950.068714020875921105.491104381843
Trimmed Mean ( 12 / 20 )7.251351351351350.0671851037246115107.930939290863
Trimmed Mean ( 13 / 20 )7.251428571428570.0658967142639169110.042339021435
Trimmed Mean ( 14 / 20 )7.251515151515150.0639781585779315113.343605266196
Trimmed Mean ( 15 / 20 )7.25161290322580.0632236119873722114.697858525928
Trimmed Mean ( 16 / 20 )7.25517241379310.0628913769368943115.360368418599
Trimmed Mean ( 17 / 20 )7.259259259259260.0620768890154496116.939804400517
Trimmed Mean ( 18 / 20 )7.260.061913918736689117.259578268268
Trimmed Mean ( 19 / 20 )7.260869565217390.0611933792289154118.654495906421
Trimmed Mean ( 20 / 20 )7.266666666666670.0610750254208603118.979347394340
Median7.3
Midrange7.05
Midmean - Weighted Average at Xnp7.234375
Midmean - Weighted Average at X(n+1)p7.234375
Midmean - Empirical Distribution Function7.234375
Midmean - Empirical Distribution Function - Averaging7.234375
Midmean - Empirical Distribution Function - Interpolation7.234375
Midmean - Closest Observation7.234375
Midmean - True Basic - Statistics Graphics Toolkit7.234375
Midmean - MS Excel (old versions)7.234375
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.22295081967213 & 0.0825281353787129 & 87.5210712871044 \tabularnewline
Geometric Mean & 7.19416422895116 &  &  \tabularnewline
Harmonic Mean & 7.16494225401968 &  &  \tabularnewline
Quadratic Mean & 7.25118418819627 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.22295081967213 & 0.0825281353787129 & 87.5210712871043 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.2327868852459 & 0.0801542676348815 & 90.2358302142149 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.2327868852459 & 0.0781871550208098 & 92.5060757527355 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.2327868852459 & 0.0781871550208098 & 92.5060757527355 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.24098360655738 & 0.0766218822338043 & 94.5028155855297 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.23114754098361 & 0.074860196972398 & 96.5953581934848 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.23114754098361 & 0.074860196972398 & 96.5953581934848 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.2311475409836 & 0.074860196972398 & 96.5953581934848 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.23114754098361 & 0.0697591870129908 & 103.658712932491 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.23114754098361 & 0.0697591870129908 & 103.658712932491 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.23114754098361 & 0.0697591870129908 & 103.658712932491 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.25081967213115 & 0.0664322223654569 & 109.146125388414 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.25081967213115 & 0.0664322223654569 & 109.146125388414 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.25081967213115 & 0.059120278936489 & 122.645220938833 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.22622950819672 & 0.0554613851460489 & 130.292986537707 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.22622950819672 & 0.0554613851460489 & 130.292986537707 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.25409836065574 & 0.0511920081328768 & 141.703727304985 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.25409836065574 & 0.0511920081328768 & 141.703727304985 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.22295081967213 & 0.0468338210088537 & 154.225101947301 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.22295081967213 & 0.0468338210088537 & 154.225101947301 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.22881355932203 & 0.0805827274550861 & 89.7067372576972 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.23508771929825 & 0.0781799234235034 & 92.544062496781 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.23636363636364 & 0.0767769797659256 & 94.25173611186 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.2377358490566 & 0.0759184888253989 & 95.3356153558629 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.23921568627451 & 0.0747848381075007 & 96.8005797628174 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.23877551020408 & 0.0738181442660228 & 98.0622797034463 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.2404255319149 & 0.0730376694002221 & 99.1327569920087 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.24222222222222 & 0.0719489780561344 & 100.657749670494 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.24418604651163 & 0.0704598348221206 & 102.812986502167 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.24634146341463 & 0.0697641987449998 & 103.869055959508 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.24871794871795 & 0.068714020875921 & 105.491104381843 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.25135135135135 & 0.0671851037246115 & 107.930939290863 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.25142857142857 & 0.0658967142639169 & 110.042339021435 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.25151515151515 & 0.0639781585779315 & 113.343605266196 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.2516129032258 & 0.0632236119873722 & 114.697858525928 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.2551724137931 & 0.0628913769368943 & 115.360368418599 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.25925925925926 & 0.0620768890154496 & 116.939804400517 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.26 & 0.061913918736689 & 117.259578268268 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.26086956521739 & 0.0611933792289154 & 118.654495906421 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.26666666666667 & 0.0610750254208603 & 118.979347394340 \tabularnewline
Median & 7.3 &  &  \tabularnewline
Midrange & 7.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.234375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.234375 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.234375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.234375 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.234375 &  &  \tabularnewline
Midmean - Closest Observation & 7.234375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.234375 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.234375 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29206&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]7.22295081967213[/C][C]0.0825281353787129[/C][C]87.5210712871044[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.19416422895116[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.16494225401968[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.25118418819627[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.22295081967213[/C][C]0.0825281353787129[/C][C]87.5210712871043[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.2327868852459[/C][C]0.0801542676348815[/C][C]90.2358302142149[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.2327868852459[/C][C]0.0781871550208098[/C][C]92.5060757527355[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.2327868852459[/C][C]0.0781871550208098[/C][C]92.5060757527355[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.24098360655738[/C][C]0.0766218822338043[/C][C]94.5028155855297[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.23114754098361[/C][C]0.074860196972398[/C][C]96.5953581934848[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.23114754098361[/C][C]0.074860196972398[/C][C]96.5953581934848[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.2311475409836[/C][C]0.074860196972398[/C][C]96.5953581934848[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.23114754098361[/C][C]0.0697591870129908[/C][C]103.658712932491[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.23114754098361[/C][C]0.0697591870129908[/C][C]103.658712932491[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.23114754098361[/C][C]0.0697591870129908[/C][C]103.658712932491[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.25081967213115[/C][C]0.0664322223654569[/C][C]109.146125388414[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.25081967213115[/C][C]0.0664322223654569[/C][C]109.146125388414[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.25081967213115[/C][C]0.059120278936489[/C][C]122.645220938833[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.22622950819672[/C][C]0.0554613851460489[/C][C]130.292986537707[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.22622950819672[/C][C]0.0554613851460489[/C][C]130.292986537707[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.25409836065574[/C][C]0.0511920081328768[/C][C]141.703727304985[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.25409836065574[/C][C]0.0511920081328768[/C][C]141.703727304985[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.22295081967213[/C][C]0.0468338210088537[/C][C]154.225101947301[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.22295081967213[/C][C]0.0468338210088537[/C][C]154.225101947301[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.22881355932203[/C][C]0.0805827274550861[/C][C]89.7067372576972[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.23508771929825[/C][C]0.0781799234235034[/C][C]92.544062496781[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.23636363636364[/C][C]0.0767769797659256[/C][C]94.25173611186[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.2377358490566[/C][C]0.0759184888253989[/C][C]95.3356153558629[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.23921568627451[/C][C]0.0747848381075007[/C][C]96.8005797628174[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.23877551020408[/C][C]0.0738181442660228[/C][C]98.0622797034463[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.2404255319149[/C][C]0.0730376694002221[/C][C]99.1327569920087[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.24222222222222[/C][C]0.0719489780561344[/C][C]100.657749670494[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.24418604651163[/C][C]0.0704598348221206[/C][C]102.812986502167[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.24634146341463[/C][C]0.0697641987449998[/C][C]103.869055959508[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.24871794871795[/C][C]0.068714020875921[/C][C]105.491104381843[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.25135135135135[/C][C]0.0671851037246115[/C][C]107.930939290863[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.25142857142857[/C][C]0.0658967142639169[/C][C]110.042339021435[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.25151515151515[/C][C]0.0639781585779315[/C][C]113.343605266196[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.2516129032258[/C][C]0.0632236119873722[/C][C]114.697858525928[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.2551724137931[/C][C]0.0628913769368943[/C][C]115.360368418599[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.25925925925926[/C][C]0.0620768890154496[/C][C]116.939804400517[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.26[/C][C]0.061913918736689[/C][C]117.259578268268[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.26086956521739[/C][C]0.0611933792289154[/C][C]118.654495906421[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.26666666666667[/C][C]0.0610750254208603[/C][C]118.979347394340[/C][/ROW]
[ROW][C]Median[/C][C]7.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.234375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.234375[/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=29206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29206&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 Mean7.222950819672130.082528135378712987.5210712871044
Geometric Mean7.19416422895116
Harmonic Mean7.16494225401968
Quadratic Mean7.25118418819627
Winsorized Mean ( 1 / 20 )7.222950819672130.082528135378712987.5210712871043
Winsorized Mean ( 2 / 20 )7.23278688524590.080154267634881590.2358302142149
Winsorized Mean ( 3 / 20 )7.23278688524590.078187155020809892.5060757527355
Winsorized Mean ( 4 / 20 )7.23278688524590.078187155020809892.5060757527355
Winsorized Mean ( 5 / 20 )7.240983606557380.076621882233804394.5028155855297
Winsorized Mean ( 6 / 20 )7.231147540983610.07486019697239896.5953581934848
Winsorized Mean ( 7 / 20 )7.231147540983610.07486019697239896.5953581934848
Winsorized Mean ( 8 / 20 )7.23114754098360.07486019697239896.5953581934848
Winsorized Mean ( 9 / 20 )7.231147540983610.0697591870129908103.658712932491
Winsorized Mean ( 10 / 20 )7.231147540983610.0697591870129908103.658712932491
Winsorized Mean ( 11 / 20 )7.231147540983610.0697591870129908103.658712932491
Winsorized Mean ( 12 / 20 )7.250819672131150.0664322223654569109.146125388414
Winsorized Mean ( 13 / 20 )7.250819672131150.0664322223654569109.146125388414
Winsorized Mean ( 14 / 20 )7.250819672131150.059120278936489122.645220938833
Winsorized Mean ( 15 / 20 )7.226229508196720.0554613851460489130.292986537707
Winsorized Mean ( 16 / 20 )7.226229508196720.0554613851460489130.292986537707
Winsorized Mean ( 17 / 20 )7.254098360655740.0511920081328768141.703727304985
Winsorized Mean ( 18 / 20 )7.254098360655740.0511920081328768141.703727304985
Winsorized Mean ( 19 / 20 )7.222950819672130.0468338210088537154.225101947301
Winsorized Mean ( 20 / 20 )7.222950819672130.0468338210088537154.225101947301
Trimmed Mean ( 1 / 20 )7.228813559322030.080582727455086189.7067372576972
Trimmed Mean ( 2 / 20 )7.235087719298250.078179923423503492.544062496781
Trimmed Mean ( 3 / 20 )7.236363636363640.076776979765925694.25173611186
Trimmed Mean ( 4 / 20 )7.23773584905660.075918488825398995.3356153558629
Trimmed Mean ( 5 / 20 )7.239215686274510.074784838107500796.8005797628174
Trimmed Mean ( 6 / 20 )7.238775510204080.073818144266022898.0622797034463
Trimmed Mean ( 7 / 20 )7.24042553191490.073037669400222199.1327569920087
Trimmed Mean ( 8 / 20 )7.242222222222220.0719489780561344100.657749670494
Trimmed Mean ( 9 / 20 )7.244186046511630.0704598348221206102.812986502167
Trimmed Mean ( 10 / 20 )7.246341463414630.0697641987449998103.869055959508
Trimmed Mean ( 11 / 20 )7.248717948717950.068714020875921105.491104381843
Trimmed Mean ( 12 / 20 )7.251351351351350.0671851037246115107.930939290863
Trimmed Mean ( 13 / 20 )7.251428571428570.0658967142639169110.042339021435
Trimmed Mean ( 14 / 20 )7.251515151515150.0639781585779315113.343605266196
Trimmed Mean ( 15 / 20 )7.25161290322580.0632236119873722114.697858525928
Trimmed Mean ( 16 / 20 )7.25517241379310.0628913769368943115.360368418599
Trimmed Mean ( 17 / 20 )7.259259259259260.0620768890154496116.939804400517
Trimmed Mean ( 18 / 20 )7.260.061913918736689117.259578268268
Trimmed Mean ( 19 / 20 )7.260869565217390.0611933792289154118.654495906421
Trimmed Mean ( 20 / 20 )7.266666666666670.0610750254208603118.979347394340
Median7.3
Midrange7.05
Midmean - Weighted Average at Xnp7.234375
Midmean - Weighted Average at X(n+1)p7.234375
Midmean - Empirical Distribution Function7.234375
Midmean - Empirical Distribution Function - Averaging7.234375
Midmean - Empirical Distribution Function - Interpolation7.234375
Midmean - Closest Observation7.234375
Midmean - True Basic - Statistics Graphics Toolkit7.234375
Midmean - MS Excel (old versions)7.234375
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')