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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 15 Nov 2011 10:42:56 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/15/t1321371920u7lfmksexvmuisc.htm/, Retrieved Fri, 29 Mar 2024 15:05:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143083, Retrieved Fri, 29 Mar 2024 15:05:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-06 21:28:17] [74be16979710d4c4e7c6647856088456]
- RM D    [Central Tendency] [WS6 - tutorial 3] [2011-11-15 15:42:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
29
44
36
37
53
68
75
18
31
25
34
14
11
11
22
16
27
9
29
30
40
32
41
147
22
29
46
23
4
31
39
15
32
27
32
34
17
46
42
43
34
19




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143083&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143083&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143083&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean33.66666666666673.555216786029229.46965225832784
Geometric Mean28.2601545649184
Harmonic Mean22.8373013107813
Quadratic Mean40.6407020936729
Winsorized Mean ( 1 / 14 )32.07142857142862.4398436901682813.1448701819159
Winsorized Mean ( 2 / 14 )31.83333333333332.2820606930100513.9493806763505
Winsorized Mean ( 3 / 14 )30.76190476190481.9187350422558116.032388049649
Winsorized Mean ( 4 / 14 )30.38095238095241.6775321945022718.1105033217955
Winsorized Mean ( 5 / 14 )30.51.6497104944344518.4880923670525
Winsorized Mean ( 6 / 14 )30.35714285714291.553842574493419.5368201100039
Winsorized Mean ( 7 / 14 )30.35714285714291.4815244011444220.4904778036009
Winsorized Mean ( 8 / 14 )30.35714285714291.4009377266746221.6691593631368
Winsorized Mean ( 9 / 14 )30.35714285714291.3123293776919523.1322588468859
Winsorized Mean ( 10 / 14 )30.83333333333331.1204552888002927.5185753876423
Winsorized Mean ( 11 / 14 )30.57142857142861.0691225668199628.5948772574893
Winsorized Mean ( 12 / 14 )30.28571428571430.906349850463533.4150375489403
Winsorized Mean ( 13 / 14 )30.59523809523810.73177391249772141.8096868072396
Winsorized Mean ( 14 / 14 )30.59523809523810.49275768099843462.0898248267698
Trimmed Mean ( 1 / 14 )31.5752.2454762215482214.061605149499
Trimmed Mean ( 2 / 14 )31.02631578947371.970438298176515.7458956305236
Trimmed Mean ( 3 / 14 )30.55555555555561.7096571848164117.8723289247235
Trimmed Mean ( 4 / 14 )30.47058823529411.5787330454292219.3006590465141
Trimmed Mean ( 5 / 14 )30.51.5173725168325420.1005354068675
Trimmed Mean ( 6 / 14 )30.51.4397876599509821.1836792663151
Trimmed Mean ( 7 / 14 )30.53571428571431.3661459934002122.3517211434436
Trimmed Mean ( 8 / 14 )30.57692307692311.2844311245097823.8058098199645
Trimmed Mean ( 9 / 14 )30.6251.1914740900440825.7034544484865
Trimmed Mean ( 10 / 14 )30.68181818181821.0818982108708528.3592466218438
Trimmed Mean ( 11 / 14 )30.650.99809028175126330.7086448594821
Trimmed Mean ( 12 / 14 )30.66666666666670.87447463219520635.0686749936744
Trimmed Mean ( 13 / 14 )30.750.7541
Trimmed Mean ( 14 / 14 )30.78571428571430.63918364339546548.1641146543968
Median31
Midrange75.5
Midmean - Weighted Average at Xnp30.2380952380952
Midmean - Weighted Average at X(n+1)p30.6818181818182
Midmean - Empirical Distribution Function30.6818181818182
Midmean - Empirical Distribution Function - Averaging30.6818181818182
Midmean - Empirical Distribution Function - Interpolation30.2380952380952
Midmean - Closest Observation30.6818181818182
Midmean - True Basic - Statistics Graphics Toolkit30.6818181818182
Midmean - MS Excel (old versions)30.6818181818182
Number of observations42

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 33.6666666666667 & 3.55521678602922 & 9.46965225832784 \tabularnewline
Geometric Mean & 28.2601545649184 &  &  \tabularnewline
Harmonic Mean & 22.8373013107813 &  &  \tabularnewline
Quadratic Mean & 40.6407020936729 &  &  \tabularnewline
Winsorized Mean ( 1 / 14 ) & 32.0714285714286 & 2.43984369016828 & 13.1448701819159 \tabularnewline
Winsorized Mean ( 2 / 14 ) & 31.8333333333333 & 2.28206069301005 & 13.9493806763505 \tabularnewline
Winsorized Mean ( 3 / 14 ) & 30.7619047619048 & 1.91873504225581 & 16.032388049649 \tabularnewline
Winsorized Mean ( 4 / 14 ) & 30.3809523809524 & 1.67753219450227 & 18.1105033217955 \tabularnewline
Winsorized Mean ( 5 / 14 ) & 30.5 & 1.64971049443445 & 18.4880923670525 \tabularnewline
Winsorized Mean ( 6 / 14 ) & 30.3571428571429 & 1.5538425744934 & 19.5368201100039 \tabularnewline
Winsorized Mean ( 7 / 14 ) & 30.3571428571429 & 1.48152440114442 & 20.4904778036009 \tabularnewline
Winsorized Mean ( 8 / 14 ) & 30.3571428571429 & 1.40093772667462 & 21.6691593631368 \tabularnewline
Winsorized Mean ( 9 / 14 ) & 30.3571428571429 & 1.31232937769195 & 23.1322588468859 \tabularnewline
Winsorized Mean ( 10 / 14 ) & 30.8333333333333 & 1.12045528880029 & 27.5185753876423 \tabularnewline
Winsorized Mean ( 11 / 14 ) & 30.5714285714286 & 1.06912256681996 & 28.5948772574893 \tabularnewline
Winsorized Mean ( 12 / 14 ) & 30.2857142857143 & 0.9063498504635 & 33.4150375489403 \tabularnewline
Winsorized Mean ( 13 / 14 ) & 30.5952380952381 & 0.731773912497721 & 41.8096868072396 \tabularnewline
Winsorized Mean ( 14 / 14 ) & 30.5952380952381 & 0.492757680998434 & 62.0898248267698 \tabularnewline
Trimmed Mean ( 1 / 14 ) & 31.575 & 2.24547622154822 & 14.061605149499 \tabularnewline
Trimmed Mean ( 2 / 14 ) & 31.0263157894737 & 1.9704382981765 & 15.7458956305236 \tabularnewline
Trimmed Mean ( 3 / 14 ) & 30.5555555555556 & 1.70965718481641 & 17.8723289247235 \tabularnewline
Trimmed Mean ( 4 / 14 ) & 30.4705882352941 & 1.57873304542922 & 19.3006590465141 \tabularnewline
Trimmed Mean ( 5 / 14 ) & 30.5 & 1.51737251683254 & 20.1005354068675 \tabularnewline
Trimmed Mean ( 6 / 14 ) & 30.5 & 1.43978765995098 & 21.1836792663151 \tabularnewline
Trimmed Mean ( 7 / 14 ) & 30.5357142857143 & 1.36614599340021 & 22.3517211434436 \tabularnewline
Trimmed Mean ( 8 / 14 ) & 30.5769230769231 & 1.28443112450978 & 23.8058098199645 \tabularnewline
Trimmed Mean ( 9 / 14 ) & 30.625 & 1.19147409004408 & 25.7034544484865 \tabularnewline
Trimmed Mean ( 10 / 14 ) & 30.6818181818182 & 1.08189821087085 & 28.3592466218438 \tabularnewline
Trimmed Mean ( 11 / 14 ) & 30.65 & 0.998090281751263 & 30.7086448594821 \tabularnewline
Trimmed Mean ( 12 / 14 ) & 30.6666666666667 & 0.874474632195206 & 35.0686749936744 \tabularnewline
Trimmed Mean ( 13 / 14 ) & 30.75 & 0.75 & 41 \tabularnewline
Trimmed Mean ( 14 / 14 ) & 30.7857142857143 & 0.639183643395465 & 48.1641146543968 \tabularnewline
Median & 31 &  &  \tabularnewline
Midrange & 75.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 30.2380952380952 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 30.6818181818182 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 30.6818181818182 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 30.6818181818182 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 30.2380952380952 &  &  \tabularnewline
Midmean - Closest Observation & 30.6818181818182 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 30.6818181818182 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 30.6818181818182 &  &  \tabularnewline
Number of observations & 42 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143083&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]33.6666666666667[/C][C]3.55521678602922[/C][C]9.46965225832784[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]28.2601545649184[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]22.8373013107813[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]40.6407020936729[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 14 )[/C][C]32.0714285714286[/C][C]2.43984369016828[/C][C]13.1448701819159[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 14 )[/C][C]31.8333333333333[/C][C]2.28206069301005[/C][C]13.9493806763505[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 14 )[/C][C]30.7619047619048[/C][C]1.91873504225581[/C][C]16.032388049649[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 14 )[/C][C]30.3809523809524[/C][C]1.67753219450227[/C][C]18.1105033217955[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 14 )[/C][C]30.5[/C][C]1.64971049443445[/C][C]18.4880923670525[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 14 )[/C][C]30.3571428571429[/C][C]1.5538425744934[/C][C]19.5368201100039[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 14 )[/C][C]30.3571428571429[/C][C]1.48152440114442[/C][C]20.4904778036009[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 14 )[/C][C]30.3571428571429[/C][C]1.40093772667462[/C][C]21.6691593631368[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 14 )[/C][C]30.3571428571429[/C][C]1.31232937769195[/C][C]23.1322588468859[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 14 )[/C][C]30.8333333333333[/C][C]1.12045528880029[/C][C]27.5185753876423[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 14 )[/C][C]30.5714285714286[/C][C]1.06912256681996[/C][C]28.5948772574893[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 14 )[/C][C]30.2857142857143[/C][C]0.9063498504635[/C][C]33.4150375489403[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 14 )[/C][C]30.5952380952381[/C][C]0.731773912497721[/C][C]41.8096868072396[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 14 )[/C][C]30.5952380952381[/C][C]0.492757680998434[/C][C]62.0898248267698[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 14 )[/C][C]31.575[/C][C]2.24547622154822[/C][C]14.061605149499[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 14 )[/C][C]31.0263157894737[/C][C]1.9704382981765[/C][C]15.7458956305236[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 14 )[/C][C]30.5555555555556[/C][C]1.70965718481641[/C][C]17.8723289247235[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 14 )[/C][C]30.4705882352941[/C][C]1.57873304542922[/C][C]19.3006590465141[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 14 )[/C][C]30.5[/C][C]1.51737251683254[/C][C]20.1005354068675[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 14 )[/C][C]30.5[/C][C]1.43978765995098[/C][C]21.1836792663151[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 14 )[/C][C]30.5357142857143[/C][C]1.36614599340021[/C][C]22.3517211434436[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 14 )[/C][C]30.5769230769231[/C][C]1.28443112450978[/C][C]23.8058098199645[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 14 )[/C][C]30.625[/C][C]1.19147409004408[/C][C]25.7034544484865[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 14 )[/C][C]30.6818181818182[/C][C]1.08189821087085[/C][C]28.3592466218438[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 14 )[/C][C]30.65[/C][C]0.998090281751263[/C][C]30.7086448594821[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 14 )[/C][C]30.6666666666667[/C][C]0.874474632195206[/C][C]35.0686749936744[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 14 )[/C][C]30.75[/C][C]0.75[/C][C]41[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 14 )[/C][C]30.7857142857143[/C][C]0.639183643395465[/C][C]48.1641146543968[/C][/ROW]
[ROW][C]Median[/C][C]31[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]75.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]30.2380952380952[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]30.6818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]30.6818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]30.6818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]30.2380952380952[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]30.6818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]30.6818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]30.6818181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]42[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143083&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143083&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 Mean33.66666666666673.555216786029229.46965225832784
Geometric Mean28.2601545649184
Harmonic Mean22.8373013107813
Quadratic Mean40.6407020936729
Winsorized Mean ( 1 / 14 )32.07142857142862.4398436901682813.1448701819159
Winsorized Mean ( 2 / 14 )31.83333333333332.2820606930100513.9493806763505
Winsorized Mean ( 3 / 14 )30.76190476190481.9187350422558116.032388049649
Winsorized Mean ( 4 / 14 )30.38095238095241.6775321945022718.1105033217955
Winsorized Mean ( 5 / 14 )30.51.6497104944344518.4880923670525
Winsorized Mean ( 6 / 14 )30.35714285714291.553842574493419.5368201100039
Winsorized Mean ( 7 / 14 )30.35714285714291.4815244011444220.4904778036009
Winsorized Mean ( 8 / 14 )30.35714285714291.4009377266746221.6691593631368
Winsorized Mean ( 9 / 14 )30.35714285714291.3123293776919523.1322588468859
Winsorized Mean ( 10 / 14 )30.83333333333331.1204552888002927.5185753876423
Winsorized Mean ( 11 / 14 )30.57142857142861.0691225668199628.5948772574893
Winsorized Mean ( 12 / 14 )30.28571428571430.906349850463533.4150375489403
Winsorized Mean ( 13 / 14 )30.59523809523810.73177391249772141.8096868072396
Winsorized Mean ( 14 / 14 )30.59523809523810.49275768099843462.0898248267698
Trimmed Mean ( 1 / 14 )31.5752.2454762215482214.061605149499
Trimmed Mean ( 2 / 14 )31.02631578947371.970438298176515.7458956305236
Trimmed Mean ( 3 / 14 )30.55555555555561.7096571848164117.8723289247235
Trimmed Mean ( 4 / 14 )30.47058823529411.5787330454292219.3006590465141
Trimmed Mean ( 5 / 14 )30.51.5173725168325420.1005354068675
Trimmed Mean ( 6 / 14 )30.51.4397876599509821.1836792663151
Trimmed Mean ( 7 / 14 )30.53571428571431.3661459934002122.3517211434436
Trimmed Mean ( 8 / 14 )30.57692307692311.2844311245097823.8058098199645
Trimmed Mean ( 9 / 14 )30.6251.1914740900440825.7034544484865
Trimmed Mean ( 10 / 14 )30.68181818181821.0818982108708528.3592466218438
Trimmed Mean ( 11 / 14 )30.650.99809028175126330.7086448594821
Trimmed Mean ( 12 / 14 )30.66666666666670.87447463219520635.0686749936744
Trimmed Mean ( 13 / 14 )30.750.7541
Trimmed Mean ( 14 / 14 )30.78571428571430.63918364339546548.1641146543968
Median31
Midrange75.5
Midmean - Weighted Average at Xnp30.2380952380952
Midmean - Weighted Average at X(n+1)p30.6818181818182
Midmean - Empirical Distribution Function30.6818181818182
Midmean - Empirical Distribution Function - Averaging30.6818181818182
Midmean - Empirical Distribution Function - Interpolation30.2380952380952
Midmean - Closest Observation30.6818181818182
Midmean - True Basic - Statistics Graphics Toolkit30.6818181818182
Midmean - MS Excel (old versions)30.6818181818182
Number of observations42



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')