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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 computationMon, 02 Nov 2009 10:21:35 -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/Nov/02/t1257182549gjlrl6ozsqsmt48.htm/, Retrieved Fri, 03 May 2024 23:52:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=52823, Retrieved Fri, 03 May 2024 23:52:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 3 Part 2...] [2009-11-02 17:21:35] [fd0d141bb5380cffe1d2cd25afb62297] [Current]
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Dataseries X:
18.2
16.6
15.2
14.4
13.5
13
13
13.5
12.9
12.7
16
16.3
16.4
15.9
15
14.4
13.2
12.7
11.9
11.7
11.5
11.8
15.9
16.8
16.5
14.9
13.3
12
11.7
11.5
11.8
13.1
12.7
12.3
15
14.6
13.4
12.2
11.1
11
11.1
10.6
9.4
8.6
8
9.7
15.9
17.4
16.2
13.9
11.1
11.4
13.3
14.4
14.7
14.1
12.9
13.4
17
17.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52823&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=52823&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52823&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean13.50.29547433855711245.6892468764783
Geometric Mean13.3012598225565
Harmonic Mean13.0931422350993
Quadratic Mean13.6894484914477
Winsorized Mean ( 1 / 20 )13.49666666666670.28913436622542846.6795657771922
Winsorized Mean ( 2 / 20 )13.520.28122813788225948.0748480639599
Winsorized Mean ( 3 / 20 )13.520.27427150555072649.294220239366
Winsorized Mean ( 4 / 20 )13.56666666666670.25846861775726052.4886416942415
Winsorized Mean ( 5 / 20 )13.58333333333330.24880694608841954.593867039814
Winsorized Mean ( 6 / 20 )13.58333333333330.24503160947556255.4350247398919
Winsorized Mean ( 7 / 20 )13.57166666666670.24270243652059255.918955166794
Winsorized Mean ( 8 / 20 )13.55833333333330.24009522200761356.470650352648
Winsorized Mean ( 9 / 20 )13.58833333333330.22965328407214759.1689049352521
Winsorized Mean ( 10 / 20 )13.57166666666670.22065761583841961.5055438494577
Winsorized Mean ( 11 / 20 )13.55333333333330.21726947867877962.380291128563
Winsorized Mean ( 12 / 20 )13.59333333333330.21102208450932164.4166384999049
Winsorized Mean ( 13 / 20 )13.59333333333330.21102208450932164.4166384999049
Winsorized Mean ( 14 / 20 )13.45333333333330.17862416224324175.3164250814695
Winsorized Mean ( 15 / 20 )13.40333333333330.17050882089723878.6078588943572
Winsorized Mean ( 16 / 20 )13.430.16630412546564480.7556635314765
Winsorized Mean ( 17 / 20 )13.430.15740300573587985.3223859176832
Winsorized Mean ( 18 / 20 )13.430.13886749364397996.7108979040923
Winsorized Mean ( 19 / 20 )13.430.129259079389108103.899858048437
Winsorized Mean ( 20 / 20 )13.49666666666670.100055540132024134.891747611953
Trimmed Mean ( 1 / 20 )13.51379310344830.27865644592759748.4962515705075
Trimmed Mean ( 2 / 20 )13.53214285714290.26570302657335550.9295773994765
Trimmed Mean ( 3 / 20 )13.53888888888890.25504574981367653.0841580335283
Trimmed Mean ( 4 / 20 )13.54615384615380.24520225189073855.2448182743035
Trimmed Mean ( 5 / 20 )13.540.23919934475372756.6055062313838
Trimmed Mean ( 6 / 20 )13.52916666666670.23478446305033657.6237732722805
Trimmed Mean ( 7 / 20 )13.51739130434780.23012922955990758.7382634105111
Trimmed Mean ( 8 / 20 )13.50681818181820.22463025121241860.1291148850903
Trimmed Mean ( 9 / 20 )13.49761904761900.21804452696703961.9030398761599
Trimmed Mean ( 10 / 20 )13.48250.21206818871925863.5762491367743
Trimmed Mean ( 11 / 20 )13.46842105263160.2063744219528865.262065546605
Trimmed Mean ( 12 / 20 )13.45555555555560.19938176049918267.4863915428752
Trimmed Mean ( 13 / 20 )13.43529411764710.19120046469474470.2681038934544
Trimmed Mean ( 14 / 20 )13.41250.17936660511995674.7770187824544
Trimmed Mean ( 15 / 20 )13.40666666666670.17326700764628477.3757615416071
Trimmed Mean ( 16 / 20 )13.40714285714290.16666099763601380.4455934340681
Trimmed Mean ( 17 / 20 )13.40384615384620.15781983586265784.931314752544
Trimmed Mean ( 18 / 20 )13.40.14731903662027190.9590525937243
Trimmed Mean ( 19 / 20 )13.39545454545450.13840108486288796.7872076922328
Trimmed Mean ( 20 / 20 )13.390.127712670928884104.844726076210
Median13.3
Midrange13.1
Midmean - Weighted Average at Xnp13.3548387096774
Midmean - Weighted Average at X(n+1)p13.3548387096774
Midmean - Empirical Distribution Function13.3548387096774
Midmean - Empirical Distribution Function - Averaging13.3548387096774
Midmean - Empirical Distribution Function - Interpolation13.3548387096774
Midmean - Closest Observation13.3548387096774
Midmean - True Basic - Statistics Graphics Toolkit13.3548387096774
Midmean - MS Excel (old versions)13.4125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13.5 & 0.295474338557112 & 45.6892468764783 \tabularnewline
Geometric Mean & 13.3012598225565 &  &  \tabularnewline
Harmonic Mean & 13.0931422350993 &  &  \tabularnewline
Quadratic Mean & 13.6894484914477 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 13.4966666666667 & 0.289134366225428 & 46.6795657771922 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 13.52 & 0.281228137882259 & 48.0748480639599 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 13.52 & 0.274271505550726 & 49.294220239366 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 13.5666666666667 & 0.258468617757260 & 52.4886416942415 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 13.5833333333333 & 0.248806946088419 & 54.593867039814 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 13.5833333333333 & 0.245031609475562 & 55.4350247398919 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 13.5716666666667 & 0.242702436520592 & 55.918955166794 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 13.5583333333333 & 0.240095222007613 & 56.470650352648 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 13.5883333333333 & 0.229653284072147 & 59.1689049352521 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 13.5716666666667 & 0.220657615838419 & 61.5055438494577 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 13.5533333333333 & 0.217269478678779 & 62.380291128563 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 13.5933333333333 & 0.211022084509321 & 64.4166384999049 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 13.5933333333333 & 0.211022084509321 & 64.4166384999049 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 13.4533333333333 & 0.178624162243241 & 75.3164250814695 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 13.4033333333333 & 0.170508820897238 & 78.6078588943572 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 13.43 & 0.166304125465644 & 80.7556635314765 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 13.43 & 0.157403005735879 & 85.3223859176832 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 13.43 & 0.138867493643979 & 96.7108979040923 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 13.43 & 0.129259079389108 & 103.899858048437 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 13.4966666666667 & 0.100055540132024 & 134.891747611953 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 13.5137931034483 & 0.278656445927597 & 48.4962515705075 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 13.5321428571429 & 0.265703026573355 & 50.9295773994765 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 13.5388888888889 & 0.255045749813676 & 53.0841580335283 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 13.5461538461538 & 0.245202251890738 & 55.2448182743035 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 13.54 & 0.239199344753727 & 56.6055062313838 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 13.5291666666667 & 0.234784463050336 & 57.6237732722805 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 13.5173913043478 & 0.230129229559907 & 58.7382634105111 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 13.5068181818182 & 0.224630251212418 & 60.1291148850903 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 13.4976190476190 & 0.218044526967039 & 61.9030398761599 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 13.4825 & 0.212068188719258 & 63.5762491367743 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 13.4684210526316 & 0.20637442195288 & 65.262065546605 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 13.4555555555556 & 0.199381760499182 & 67.4863915428752 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 13.4352941176471 & 0.191200464694744 & 70.2681038934544 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 13.4125 & 0.179366605119956 & 74.7770187824544 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 13.4066666666667 & 0.173267007646284 & 77.3757615416071 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 13.4071428571429 & 0.166660997636013 & 80.4455934340681 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 13.4038461538462 & 0.157819835862657 & 84.931314752544 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 13.4 & 0.147319036620271 & 90.9590525937243 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 13.3954545454545 & 0.138401084862887 & 96.7872076922328 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 13.39 & 0.127712670928884 & 104.844726076210 \tabularnewline
Median & 13.3 &  &  \tabularnewline
Midrange & 13.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13.3548387096774 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13.3548387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13.3548387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13.3548387096774 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13.3548387096774 &  &  \tabularnewline
Midmean - Closest Observation & 13.3548387096774 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13.3548387096774 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13.4125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=52823&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]13.5[/C][C]0.295474338557112[/C][C]45.6892468764783[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13.3012598225565[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13.0931422350993[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13.6894484914477[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]13.4966666666667[/C][C]0.289134366225428[/C][C]46.6795657771922[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]13.52[/C][C]0.281228137882259[/C][C]48.0748480639599[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]13.52[/C][C]0.274271505550726[/C][C]49.294220239366[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]13.5666666666667[/C][C]0.258468617757260[/C][C]52.4886416942415[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]13.5833333333333[/C][C]0.248806946088419[/C][C]54.593867039814[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]13.5833333333333[/C][C]0.245031609475562[/C][C]55.4350247398919[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]13.5716666666667[/C][C]0.242702436520592[/C][C]55.918955166794[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]13.5583333333333[/C][C]0.240095222007613[/C][C]56.470650352648[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]13.5883333333333[/C][C]0.229653284072147[/C][C]59.1689049352521[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]13.5716666666667[/C][C]0.220657615838419[/C][C]61.5055438494577[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]13.5533333333333[/C][C]0.217269478678779[/C][C]62.380291128563[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]13.5933333333333[/C][C]0.211022084509321[/C][C]64.4166384999049[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]13.5933333333333[/C][C]0.211022084509321[/C][C]64.4166384999049[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]13.4533333333333[/C][C]0.178624162243241[/C][C]75.3164250814695[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]13.4033333333333[/C][C]0.170508820897238[/C][C]78.6078588943572[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]13.43[/C][C]0.166304125465644[/C][C]80.7556635314765[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]13.43[/C][C]0.157403005735879[/C][C]85.3223859176832[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]13.43[/C][C]0.138867493643979[/C][C]96.7108979040923[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]13.43[/C][C]0.129259079389108[/C][C]103.899858048437[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]13.4966666666667[/C][C]0.100055540132024[/C][C]134.891747611953[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]13.5137931034483[/C][C]0.278656445927597[/C][C]48.4962515705075[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]13.5321428571429[/C][C]0.265703026573355[/C][C]50.9295773994765[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]13.5388888888889[/C][C]0.255045749813676[/C][C]53.0841580335283[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]13.5461538461538[/C][C]0.245202251890738[/C][C]55.2448182743035[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]13.54[/C][C]0.239199344753727[/C][C]56.6055062313838[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]13.5291666666667[/C][C]0.234784463050336[/C][C]57.6237732722805[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]13.5173913043478[/C][C]0.230129229559907[/C][C]58.7382634105111[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]13.5068181818182[/C][C]0.224630251212418[/C][C]60.1291148850903[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]13.4976190476190[/C][C]0.218044526967039[/C][C]61.9030398761599[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]13.4825[/C][C]0.212068188719258[/C][C]63.5762491367743[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]13.4684210526316[/C][C]0.20637442195288[/C][C]65.262065546605[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]13.4555555555556[/C][C]0.199381760499182[/C][C]67.4863915428752[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]13.4352941176471[/C][C]0.191200464694744[/C][C]70.2681038934544[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]13.4125[/C][C]0.179366605119956[/C][C]74.7770187824544[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]13.4066666666667[/C][C]0.173267007646284[/C][C]77.3757615416071[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]13.4071428571429[/C][C]0.166660997636013[/C][C]80.4455934340681[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]13.4038461538462[/C][C]0.157819835862657[/C][C]84.931314752544[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]13.4[/C][C]0.147319036620271[/C][C]90.9590525937243[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]13.3954545454545[/C][C]0.138401084862887[/C][C]96.7872076922328[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]13.39[/C][C]0.127712670928884[/C][C]104.844726076210[/C][/ROW]
[ROW][C]Median[/C][C]13.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]13.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13.3548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13.3548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13.3548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13.3548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13.3548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13.3548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13.3548387096774[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13.4125[/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=52823&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=52823&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 Mean13.50.29547433855711245.6892468764783
Geometric Mean13.3012598225565
Harmonic Mean13.0931422350993
Quadratic Mean13.6894484914477
Winsorized Mean ( 1 / 20 )13.49666666666670.28913436622542846.6795657771922
Winsorized Mean ( 2 / 20 )13.520.28122813788225948.0748480639599
Winsorized Mean ( 3 / 20 )13.520.27427150555072649.294220239366
Winsorized Mean ( 4 / 20 )13.56666666666670.25846861775726052.4886416942415
Winsorized Mean ( 5 / 20 )13.58333333333330.24880694608841954.593867039814
Winsorized Mean ( 6 / 20 )13.58333333333330.24503160947556255.4350247398919
Winsorized Mean ( 7 / 20 )13.57166666666670.24270243652059255.918955166794
Winsorized Mean ( 8 / 20 )13.55833333333330.24009522200761356.470650352648
Winsorized Mean ( 9 / 20 )13.58833333333330.22965328407214759.1689049352521
Winsorized Mean ( 10 / 20 )13.57166666666670.22065761583841961.5055438494577
Winsorized Mean ( 11 / 20 )13.55333333333330.21726947867877962.380291128563
Winsorized Mean ( 12 / 20 )13.59333333333330.21102208450932164.4166384999049
Winsorized Mean ( 13 / 20 )13.59333333333330.21102208450932164.4166384999049
Winsorized Mean ( 14 / 20 )13.45333333333330.17862416224324175.3164250814695
Winsorized Mean ( 15 / 20 )13.40333333333330.17050882089723878.6078588943572
Winsorized Mean ( 16 / 20 )13.430.16630412546564480.7556635314765
Winsorized Mean ( 17 / 20 )13.430.15740300573587985.3223859176832
Winsorized Mean ( 18 / 20 )13.430.13886749364397996.7108979040923
Winsorized Mean ( 19 / 20 )13.430.129259079389108103.899858048437
Winsorized Mean ( 20 / 20 )13.49666666666670.100055540132024134.891747611953
Trimmed Mean ( 1 / 20 )13.51379310344830.27865644592759748.4962515705075
Trimmed Mean ( 2 / 20 )13.53214285714290.26570302657335550.9295773994765
Trimmed Mean ( 3 / 20 )13.53888888888890.25504574981367653.0841580335283
Trimmed Mean ( 4 / 20 )13.54615384615380.24520225189073855.2448182743035
Trimmed Mean ( 5 / 20 )13.540.23919934475372756.6055062313838
Trimmed Mean ( 6 / 20 )13.52916666666670.23478446305033657.6237732722805
Trimmed Mean ( 7 / 20 )13.51739130434780.23012922955990758.7382634105111
Trimmed Mean ( 8 / 20 )13.50681818181820.22463025121241860.1291148850903
Trimmed Mean ( 9 / 20 )13.49761904761900.21804452696703961.9030398761599
Trimmed Mean ( 10 / 20 )13.48250.21206818871925863.5762491367743
Trimmed Mean ( 11 / 20 )13.46842105263160.2063744219528865.262065546605
Trimmed Mean ( 12 / 20 )13.45555555555560.19938176049918267.4863915428752
Trimmed Mean ( 13 / 20 )13.43529411764710.19120046469474470.2681038934544
Trimmed Mean ( 14 / 20 )13.41250.17936660511995674.7770187824544
Trimmed Mean ( 15 / 20 )13.40666666666670.17326700764628477.3757615416071
Trimmed Mean ( 16 / 20 )13.40714285714290.16666099763601380.4455934340681
Trimmed Mean ( 17 / 20 )13.40384615384620.15781983586265784.931314752544
Trimmed Mean ( 18 / 20 )13.40.14731903662027190.9590525937243
Trimmed Mean ( 19 / 20 )13.39545454545450.13840108486288796.7872076922328
Trimmed Mean ( 20 / 20 )13.390.127712670928884104.844726076210
Median13.3
Midrange13.1
Midmean - Weighted Average at Xnp13.3548387096774
Midmean - Weighted Average at X(n+1)p13.3548387096774
Midmean - Empirical Distribution Function13.3548387096774
Midmean - Empirical Distribution Function - Averaging13.3548387096774
Midmean - Empirical Distribution Function - Interpolation13.3548387096774
Midmean - Closest Observation13.3548387096774
Midmean - True Basic - Statistics Graphics Toolkit13.3548387096774
Midmean - MS Excel (old versions)13.4125
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')