Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 12 Mar 2017 10:19:07 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Mar/12/t14893140011y62h7u49lkbdxd.htm/, Retrieved Wed, 26 Aug 2026 23:11:49 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 26 Aug 2026 23:11:49 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsOpdracht5_oef2_inflatiecentrum_iko
Estimated Impact0
Dataseries X:
3,65
3,66
3,36
3,19
2,81
2,25
2,32
2,85
2,75
2,78
2,26
2,23
1,46
1,19
1,11
1
1,18
1,59
1,51
1,01
0,9
0,63
0,81
0,97
1,14
0,97
0,89
0,62
0,36
0,27
0,34
0,02
-0,12
0,09
-0,11
-0,38
-0,65
-0,4
-0,4
0,29
0,56
0,63
0,46
0,91
1,06
1,28
1,52
1,5
1,74
1,39
2,24
2,04
2,2
2,16
2,28
2,16
1,87
1,81
1,77
2,03
2,65




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' @ yule.wessa.net

\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' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.387868852459020.13499405264254410.2809629408935
Geometric MeanNaN
Harmonic Mean0.724697669431647
Quadratic Mean1.73769491181777
Winsorized Mean ( 1 / 20 )1.391803278688520.13397547043177910.3884933130146
Winsorized Mean ( 2 / 20 )1.382295081967210.13144642854067810.5160337737091
Winsorized Mean ( 3 / 20 )1.374918032786890.12919625917684610.642088567788
Winsorized Mean ( 4 / 20 )1.369672131147540.12060343886140911.3568248474366
Winsorized Mean ( 5 / 20 )1.36721311475410.11977030182528211.4152932230943
Winsorized Mean ( 6 / 20 )1.377049180327870.11662310137316711.8076878775641
Winsorized Mean ( 7 / 20 )1.38163934426230.11439987875148112.0772797955821
Winsorized Mean ( 8 / 20 )1.392131147540980.10753424025905812.9459337248046
Winsorized Mean ( 9 / 20 )1.346393442622950.098212447539720613.7089898108732
Winsorized Mean ( 10 / 20 )1.348032786885250.095683854343790214.0884039018933
Winsorized Mean ( 11 / 20 )1.348032786885250.094469996877064214.2694276643141
Winsorized Mean ( 12 / 20 )1.365737704918030.090800766413195515.0410371945887
Winsorized Mean ( 13 / 20 )1.384918032786890.086995893047595215.9193495723896
Winsorized Mean ( 14 / 20 )1.396393442622950.084475893928511116.5300818693279
Winsorized Mean ( 15 / 20 )1.391475409836070.082892990490364916.7864062040059
Winsorized Mean ( 16 / 20 )1.380983606557380.081201262782595517.0069227895477
Winsorized Mean ( 17 / 20 )1.431147540983610.073800091208147719.3922191362496
Winsorized Mean ( 18 / 20 )1.419344262295080.064787112010399421.9078180559623
Winsorized Mean ( 19 / 20 )1.419344262295080.063867121642597422.2233948515448
Winsorized Mean ( 20 / 20 )1.370163934426230.055268095621450424.7912275431189
Trimmed Mean ( 1 / 20 )1.383898305084750.12949256198311610.6870872264091
Trimmed Mean ( 2 / 20 )1.375438596491230.12397400239218611.0945728132588
Trimmed Mean ( 3 / 20 )1.371636363636360.11887258369348211.5387107861068
Trimmed Mean ( 4 / 20 )1.370377358490570.11364362672121412.058550030723
Trimmed Mean ( 5 / 20 )1.370588235294120.11058291601725312.3942131809969
Trimmed Mean ( 6 / 20 )1.371428571428570.1069816247175712.8192909300932
Trimmed Mean ( 7 / 20 )1.370212765957450.10338466711830213.2535394672164
Trimmed Mean ( 8 / 20 )1.3680.0994056072235113.7617991400032
Trimmed Mean ( 9 / 20 )1.363720930232560.096205427616997914.175093484971
Trimmed Mean ( 10 / 20 )1.366585365853660.09450681337942714.4601782346324
Trimmed Mean ( 11 / 20 )1.369487179487180.092787066841249614.7594619175779
Trimmed Mean ( 12 / 20 )1.37270270270270.090654649979249115.1421102283988
Trimmed Mean ( 13 / 20 )1.373714285714290.088612161953641815.5025479057035
Trimmed Mean ( 14 / 20 )1.372121212121210.086664580659362715.8325489107755
Trimmed Mean ( 15 / 20 )1.368709677419350.084429447463718416.2112831308949
Trimmed Mean ( 16 / 20 )1.365517241379310.081491010424609316.7566610631562
Trimmed Mean ( 17 / 20 )1.363333333333330.077533192965310117.5838667439288
Trimmed Mean ( 18 / 20 )1.35360.073900563822837918.3165043672061
Trimmed Mean ( 19 / 20 )1.343913043478260.071524171901391218.7896344375868
Trimmed Mean ( 20 / 20 )1.332380952380950.067576780888059119.716549602859
Median1.28
Midrange1.505
Midmean - Weighted Average at Xnp1.341
Midmean - Weighted Average at X(n+1)p1.36870967741935
Midmean - Empirical Distribution Function1.36870967741935
Midmean - Empirical Distribution Function - Averaging1.36870967741935
Midmean - Empirical Distribution Function - Interpolation1.36870967741935
Midmean - Closest Observation1.3453125
Midmean - True Basic - Statistics Graphics Toolkit1.36870967741935
Midmean - MS Excel (old versions)1.36870967741935
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.38786885245902 & 0.134994052642544 & 10.2809629408935 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0.724697669431647 &  &  \tabularnewline
Quadratic Mean & 1.73769491181777 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.39180327868852 & 0.133975470431779 & 10.3884933130146 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.38229508196721 & 0.131446428540678 & 10.5160337737091 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.37491803278689 & 0.129196259176846 & 10.642088567788 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.36967213114754 & 0.120603438861409 & 11.3568248474366 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.3672131147541 & 0.119770301825282 & 11.4152932230943 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.37704918032787 & 0.116623101373167 & 11.8076878775641 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.3816393442623 & 0.114399878751481 & 12.0772797955821 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.39213114754098 & 0.107534240259058 & 12.9459337248046 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.34639344262295 & 0.0982124475397206 & 13.7089898108732 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.34803278688525 & 0.0956838543437902 & 14.0884039018933 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.34803278688525 & 0.0944699968770642 & 14.2694276643141 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.36573770491803 & 0.0908007664131955 & 15.0410371945887 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.38491803278689 & 0.0869958930475952 & 15.9193495723896 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.39639344262295 & 0.0844758939285111 & 16.5300818693279 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.39147540983607 & 0.0828929904903649 & 16.7864062040059 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.38098360655738 & 0.0812012627825955 & 17.0069227895477 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.43114754098361 & 0.0738000912081477 & 19.3922191362496 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.41934426229508 & 0.0647871120103994 & 21.9078180559623 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.41934426229508 & 0.0638671216425974 & 22.2233948515448 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.37016393442623 & 0.0552680956214504 & 24.7912275431189 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.38389830508475 & 0.129492561983116 & 10.6870872264091 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.37543859649123 & 0.123974002392186 & 11.0945728132588 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.37163636363636 & 0.118872583693482 & 11.5387107861068 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.37037735849057 & 0.113643626721214 & 12.058550030723 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.37058823529412 & 0.110582916017253 & 12.3942131809969 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.37142857142857 & 0.10698162471757 & 12.8192909300932 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.37021276595745 & 0.103384667118302 & 13.2535394672164 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.368 & 0.09940560722351 & 13.7617991400032 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.36372093023256 & 0.0962054276169979 & 14.175093484971 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.36658536585366 & 0.094506813379427 & 14.4601782346324 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.36948717948718 & 0.0927870668412496 & 14.7594619175779 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.3727027027027 & 0.0906546499792491 & 15.1421102283988 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.37371428571429 & 0.0886121619536418 & 15.5025479057035 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.37212121212121 & 0.0866645806593627 & 15.8325489107755 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.36870967741935 & 0.0844294474637184 & 16.2112831308949 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.36551724137931 & 0.0814910104246093 & 16.7566610631562 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.36333333333333 & 0.0775331929653101 & 17.5838667439288 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.3536 & 0.0739005638228379 & 18.3165043672061 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.34391304347826 & 0.0715241719013912 & 18.7896344375868 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.33238095238095 & 0.0675767808880591 & 19.716549602859 \tabularnewline
Median & 1.28 &  &  \tabularnewline
Midrange & 1.505 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.341 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.36870967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.36870967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.36870967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.36870967741935 &  &  \tabularnewline
Midmean - Closest Observation & 1.3453125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.36870967741935 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.36870967741935 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1.38786885245902[/C][C]0.134994052642544[/C][C]10.2809629408935[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.724697669431647[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.73769491181777[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.39180327868852[/C][C]0.133975470431779[/C][C]10.3884933130146[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.38229508196721[/C][C]0.131446428540678[/C][C]10.5160337737091[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.37491803278689[/C][C]0.129196259176846[/C][C]10.642088567788[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.36967213114754[/C][C]0.120603438861409[/C][C]11.3568248474366[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.3672131147541[/C][C]0.119770301825282[/C][C]11.4152932230943[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.37704918032787[/C][C]0.116623101373167[/C][C]11.8076878775641[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.3816393442623[/C][C]0.114399878751481[/C][C]12.0772797955821[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.39213114754098[/C][C]0.107534240259058[/C][C]12.9459337248046[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.34639344262295[/C][C]0.0982124475397206[/C][C]13.7089898108732[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.34803278688525[/C][C]0.0956838543437902[/C][C]14.0884039018933[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.34803278688525[/C][C]0.0944699968770642[/C][C]14.2694276643141[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.36573770491803[/C][C]0.0908007664131955[/C][C]15.0410371945887[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.38491803278689[/C][C]0.0869958930475952[/C][C]15.9193495723896[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.39639344262295[/C][C]0.0844758939285111[/C][C]16.5300818693279[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.39147540983607[/C][C]0.0828929904903649[/C][C]16.7864062040059[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.38098360655738[/C][C]0.0812012627825955[/C][C]17.0069227895477[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.43114754098361[/C][C]0.0738000912081477[/C][C]19.3922191362496[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.41934426229508[/C][C]0.0647871120103994[/C][C]21.9078180559623[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.41934426229508[/C][C]0.0638671216425974[/C][C]22.2233948515448[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.37016393442623[/C][C]0.0552680956214504[/C][C]24.7912275431189[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.38389830508475[/C][C]0.129492561983116[/C][C]10.6870872264091[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.37543859649123[/C][C]0.123974002392186[/C][C]11.0945728132588[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.37163636363636[/C][C]0.118872583693482[/C][C]11.5387107861068[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.37037735849057[/C][C]0.113643626721214[/C][C]12.058550030723[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.37058823529412[/C][C]0.110582916017253[/C][C]12.3942131809969[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.37142857142857[/C][C]0.10698162471757[/C][C]12.8192909300932[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.37021276595745[/C][C]0.103384667118302[/C][C]13.2535394672164[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.368[/C][C]0.09940560722351[/C][C]13.7617991400032[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.36372093023256[/C][C]0.0962054276169979[/C][C]14.175093484971[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.36658536585366[/C][C]0.094506813379427[/C][C]14.4601782346324[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.36948717948718[/C][C]0.0927870668412496[/C][C]14.7594619175779[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.3727027027027[/C][C]0.0906546499792491[/C][C]15.1421102283988[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.37371428571429[/C][C]0.0886121619536418[/C][C]15.5025479057035[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.37212121212121[/C][C]0.0866645806593627[/C][C]15.8325489107755[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.36870967741935[/C][C]0.0844294474637184[/C][C]16.2112831308949[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.36551724137931[/C][C]0.0814910104246093[/C][C]16.7566610631562[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.36333333333333[/C][C]0.0775331929653101[/C][C]17.5838667439288[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.3536[/C][C]0.0739005638228379[/C][C]18.3165043672061[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.34391304347826[/C][C]0.0715241719013912[/C][C]18.7896344375868[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.33238095238095[/C][C]0.0675767808880591[/C][C]19.716549602859[/C][/ROW]
[ROW][C]Median[/C][C]1.28[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.505[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.341[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.36870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.36870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.36870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.36870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.3453125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.36870967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.36870967741935[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean1.387868852459020.13499405264254410.2809629408935
Geometric MeanNaN
Harmonic Mean0.724697669431647
Quadratic Mean1.73769491181777
Winsorized Mean ( 1 / 20 )1.391803278688520.13397547043177910.3884933130146
Winsorized Mean ( 2 / 20 )1.382295081967210.13144642854067810.5160337737091
Winsorized Mean ( 3 / 20 )1.374918032786890.12919625917684610.642088567788
Winsorized Mean ( 4 / 20 )1.369672131147540.12060343886140911.3568248474366
Winsorized Mean ( 5 / 20 )1.36721311475410.11977030182528211.4152932230943
Winsorized Mean ( 6 / 20 )1.377049180327870.11662310137316711.8076878775641
Winsorized Mean ( 7 / 20 )1.38163934426230.11439987875148112.0772797955821
Winsorized Mean ( 8 / 20 )1.392131147540980.10753424025905812.9459337248046
Winsorized Mean ( 9 / 20 )1.346393442622950.098212447539720613.7089898108732
Winsorized Mean ( 10 / 20 )1.348032786885250.095683854343790214.0884039018933
Winsorized Mean ( 11 / 20 )1.348032786885250.094469996877064214.2694276643141
Winsorized Mean ( 12 / 20 )1.365737704918030.090800766413195515.0410371945887
Winsorized Mean ( 13 / 20 )1.384918032786890.086995893047595215.9193495723896
Winsorized Mean ( 14 / 20 )1.396393442622950.084475893928511116.5300818693279
Winsorized Mean ( 15 / 20 )1.391475409836070.082892990490364916.7864062040059
Winsorized Mean ( 16 / 20 )1.380983606557380.081201262782595517.0069227895477
Winsorized Mean ( 17 / 20 )1.431147540983610.073800091208147719.3922191362496
Winsorized Mean ( 18 / 20 )1.419344262295080.064787112010399421.9078180559623
Winsorized Mean ( 19 / 20 )1.419344262295080.063867121642597422.2233948515448
Winsorized Mean ( 20 / 20 )1.370163934426230.055268095621450424.7912275431189
Trimmed Mean ( 1 / 20 )1.383898305084750.12949256198311610.6870872264091
Trimmed Mean ( 2 / 20 )1.375438596491230.12397400239218611.0945728132588
Trimmed Mean ( 3 / 20 )1.371636363636360.11887258369348211.5387107861068
Trimmed Mean ( 4 / 20 )1.370377358490570.11364362672121412.058550030723
Trimmed Mean ( 5 / 20 )1.370588235294120.11058291601725312.3942131809969
Trimmed Mean ( 6 / 20 )1.371428571428570.1069816247175712.8192909300932
Trimmed Mean ( 7 / 20 )1.370212765957450.10338466711830213.2535394672164
Trimmed Mean ( 8 / 20 )1.3680.0994056072235113.7617991400032
Trimmed Mean ( 9 / 20 )1.363720930232560.096205427616997914.175093484971
Trimmed Mean ( 10 / 20 )1.366585365853660.09450681337942714.4601782346324
Trimmed Mean ( 11 / 20 )1.369487179487180.092787066841249614.7594619175779
Trimmed Mean ( 12 / 20 )1.37270270270270.090654649979249115.1421102283988
Trimmed Mean ( 13 / 20 )1.373714285714290.088612161953641815.5025479057035
Trimmed Mean ( 14 / 20 )1.372121212121210.086664580659362715.8325489107755
Trimmed Mean ( 15 / 20 )1.368709677419350.084429447463718416.2112831308949
Trimmed Mean ( 16 / 20 )1.365517241379310.081491010424609316.7566610631562
Trimmed Mean ( 17 / 20 )1.363333333333330.077533192965310117.5838667439288
Trimmed Mean ( 18 / 20 )1.35360.073900563822837918.3165043672061
Trimmed Mean ( 19 / 20 )1.343913043478260.071524171901391218.7896344375868
Trimmed Mean ( 20 / 20 )1.332380952380950.067576780888059119.716549602859
Median1.28
Midrange1.505
Midmean - Weighted Average at Xnp1.341
Midmean - Weighted Average at X(n+1)p1.36870967741935
Midmean - Empirical Distribution Function1.36870967741935
Midmean - Empirical Distribution Function - Averaging1.36870967741935
Midmean - Empirical Distribution Function - Interpolation1.36870967741935
Midmean - Closest Observation1.3453125
Midmean - True Basic - Statistics Graphics Toolkit1.36870967741935
Midmean - MS Excel (old versions)1.36870967741935
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')