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R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 22 Apr 2009 14:13:34 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Apr/22/t1240431231mpno38npad7pmcz.htm/, Retrieved Wed, 22 Apr 2009 22:13:53 +0200

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Apr/22/t1240431231mpno38npad7pmcz.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

16,32 16,36 16,65 17,29 17,30 17,37 17,41 17,67 17,84 17,85 17,87 17,99 18,07 18,10 18,10 18,14 18,15 18,16 18,24 18,32 18,38 18,39 18,39 18,40 18,41 18,50 18,60 18,60 18,62 18,70 18,80 18,81 18,88 19,00 19,16 19,44 20,01 20,19 20,21 20,30 20,45 20,61 20,76 20,85 20,91 21,05 21,10 21,22 21,77 21,83 21,84 21,89 21,90 22,00 22,00 22,00 22,10 22,15 22,37 22,40 22,63 22,63 22,71 22,81 23,01 23,37 23,55 23,96 25,10 25,42 25,66 25,72 25,85 26,15 26,17 26,20 26,27 26,39 26,63 26,82 26,88 27,00 27,00 27,38

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	21.0654761904762	0.343605273805698	61.3071969389746
Geometric Mean	20.8414562223154
Harmonic Mean	20.6271887364392
Quadratic Mean	21.2967989993578
Winsorized Mean ( 1 / 28 )	21.0614285714286	0.34255298231511	61.4837110133651
Winsorized Mean ( 2 / 28 )	21.0683333333333	0.341443807367474	61.7036621509403
Winsorized Mean ( 3 / 28 )	21.0869047619048	0.337218167156215	62.5319357486938
Winsorized Mean ( 4 / 28 )	21.0845238095238	0.336564619513829	62.6462871824752
Winsorized Mean ( 5 / 28 )	21.0773809523810	0.333708758136002	63.1610062322395
Winsorized Mean ( 6 / 28 )	21.0630952380952	0.329941056654138	63.8389640006963
Winsorized Mean ( 7 / 28 )	21.0747619047619	0.325193727343871	64.8067909454991
Winsorized Mean ( 8 / 28 )	21.0842857142857	0.321909565529888	65.4975433227011
Winsorized Mean ( 9 / 28 )	21.0821428571429	0.321165095685993	65.6426963587448
Winsorized Mean ( 10 / 28 )	21.0821428571429	0.320422889648668	65.7947466869757
Winsorized Mean ( 11 / 28 )	21.0585714285714	0.311151238186773	67.6795360072799
Winsorized Mean ( 12 / 28 )	21.0514285714286	0.306374527662992	68.7114190987342
Winsorized Mean ( 13 / 28 )	21.0467857142857	0.304130446953336	69.2031525456411
Winsorized Mean ( 14 / 28 )	21.0067857142857	0.296892645084913	70.755493819248
Winsorized Mean ( 15 / 28 )	20.9567857142857	0.285940294466933	73.2907747519622
Winsorized Mean ( 16 / 28 )	20.7415476190476	0.249756478873271	83.0470853553798
Winsorized Mean ( 17 / 28 )	20.6605952380952	0.236955756900641	87.1917842737138
Winsorized Mean ( 18 / 28 )	20.6391666666667	0.229181624713940	90.0559400974142
Winsorized Mean ( 19 / 28 )	20.5758333333333	0.215504398945385	95.4775560685787
Winsorized Mean ( 20 / 28 )	20.5425	0.207326358717199	99.0829151059403
Winsorized Mean ( 21 / 28 )	20.52	0.203745690428854	100.713786666155
Winsorized Mean ( 22 / 28 )	20.4990476190476	0.201051069104483	101.959406186468
Winsorized Mean ( 23 / 28 )	20.5017857142857	0.200705308323621	102.148696940433
Winsorized Mean ( 24 / 28 )	20.4389285714286	0.192100971031017	106.396799879416
Winsorized Mean ( 25 / 28 )	20.4567857142857	0.187615954637974	109.035426937753
Winsorized Mean ( 26 / 28 )	20.4196428571429	0.175505453674016	116.347625841134
Winsorized Mean ( 27 / 28 )	20.4035714285714	0.173604809928543	117.528837115572
Winsorized Mean ( 28 / 28 )	20.3769047619048	0.168877191813506	120.661082429694
Trimmed Mean ( 1 / 28 )	21.0463414634146	0.338426202970195	62.1888650426638
Trimmed Mean ( 2 / 28 )	21.0305	0.333587988696433	63.0433370283541
Trimmed Mean ( 3 / 28 )	21.0101282051282	0.328580712309507	63.942061776705
Trimmed Mean ( 4 / 28 )	20.9818421052632	0.324465536813805	64.6658573089185
Trimmed Mean ( 5 / 28 )	20.9527027027027	0.319773226830290	65.5236303251325
Trimmed Mean ( 6 / 28 )	20.9236111111111	0.31500449021538	66.4232154176752
Trimmed Mean ( 7 / 28 )	20.8957142857143	0.31026980654615	67.346914990925
Trimmed Mean ( 8 / 28 )	20.8641176470588	0.305644602679713	68.2626732621301
Trimmed Mean ( 9 / 28 )	20.8290909090909	0.300705210545275	69.2674758489256
Trimmed Mean ( 10 / 28 )	20.7921875	0.294808710911442	70.5277243529138
Trimmed Mean ( 11 / 28 )	20.7529032258065	0.287721991374130	72.1283177788837
Trimmed Mean ( 12 / 28 )	20.714	0.280930676854167	73.7334926607279
Trimmed Mean ( 13 / 28 )	20.6732758620690	0.273467283210905	75.5968890294097
Trimmed Mean ( 14 / 28 )	20.6301785714286	0.264602064744355	77.9668087297822
Trimmed Mean ( 15 / 28 )	20.5883333333333	0.255070967502406	80.7160984839998
Trimmed Mean ( 16 / 28 )	20.5486538461538	0.245451691979271	83.7177111327033
Trimmed Mean ( 17 / 28 )	20.5284	0.241054208485501	85.160927614482
Trimmed Mean ( 18 / 28 )	20.5147916666667	0.237837291211284	86.2555722956088
Trimmed Mean ( 19 / 28 )	20.5021739130435	0.234963233436644	87.256944898027
Trimmed Mean ( 20 / 28 )	20.4947727272727	0.233579664540215	87.742110459895
Trimmed Mean ( 21 / 28 )	20.49	0.232884502785459	87.9835272631947
Trimmed Mean ( 22 / 28 )	20.487	0.232122646626569	88.259376229493
Trimmed Mean ( 23 / 28 )	20.4857894736842	0.23105966284094	88.6601721036289
Trimmed Mean ( 24 / 28 )	20.4841666666667	0.229070022911828	89.4231659222878
Trimmed Mean ( 25 / 28 )	20.4888235294118	0.227641462435874	90.0047966225987
Trimmed Mean ( 26 / 28 )	20.4921875	0.225957074844713	90.6906212787678
Trimmed Mean ( 27 / 28 )	20.5	0.225698405211341	90.829175247402
Trimmed Mean ( 28 / 28 )	20.5107142857143	0.224623099121858	91.3116877378102
Median	20.685
Midrange	21.85
Midmean - Weighted Average at Xnp	20.4409302325581
Midmean - Weighted Average at X(n+1)p	20.49
Midmean - Empirical Distribution Function	20.4409302325581
Midmean - Empirical Distribution Function - Averaging	20.49
Midmean - Empirical Distribution Function - Interpolation	20.49
Midmean - Closest Observation	20.4409302325581
Midmean - True Basic - Statistics Graphics Toolkit	20.49
Midmean - MS Excel (old versions)	20.4947727272727
Number of observations	84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240431231mpno38npad7pmcz/107jt1240431213.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240431231mpno38npad7pmcz/107jt1240431213.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240431231mpno38npad7pmcz/213iv1240431213.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240431231mpno38npad7pmcz/213iv1240431213.ps (open in new window)

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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')

mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')

mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')

mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')

mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')

mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')

mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')

mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')

mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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