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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: Thu, 16 Oct 2008 08:31:36 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Oct/16/t1224167527yjk3c53bitur65z.htm/, Retrieved Thu, 16 Oct 2008 14:32:09 +0000

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/2008/Oct/16/t1224167527yjk3c53bitur65z.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

2 1.8 1.4 1.5 1.6 1.3 1.1 0.8 1.1 1.3 1.5 1.8 2.7 3 3.2 3.2 3.3 3.2 2.9 2.7 2.6 2.3 2.2 2.1 2.4 2.5 2.4 2.3 2.1 2.3 2.2 2.1 2 2.1 2.1 2.5 2.2 2.3 2.3 2.2 2.2 1.6 1.8 1.7 1.9 1.8 1.9 1.5 1 0.8 1.1 1.5 1.7 2.3 2.4 3 3 3.2 3.2 3.2 3.5 4 4.3 4.1 4 4.1 4.2 4.5 5.6 6.5 7.6 8.5 8.7 8.3 8.3 8.5 8.7 8.7 8.5 7.9

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	'George Udny Yule' @ 72.249.76.132

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	3.19875	0.247535279099231	12.9224004418283
Geometric Mean	2.65137546868119
Harmonic Mean	2.26601250174919
Quadratic Mean	3.88234787210008
Winsorized Mean ( 1 / 26 )	3.19875	0.247535279099231	12.9224004418283
Winsorized Mean ( 2 / 26 )	3.20375	0.246946182255122	12.9734745066445
Winsorized Mean ( 3 / 26 )	3.2	0.244444604270501	13.0909005316349
Winsorized Mean ( 4 / 26 )	3.2	0.244444604270501	13.0909005316349
Winsorized Mean ( 5 / 26 )	3.2	0.244444604270501	13.0909005316349
Winsorized Mean ( 6 / 26 )	3.2	0.238786489026855	13.4010932236627
Winsorized Mean ( 7 / 26 )	3.2	0.238786489026855	13.4010932236627
Winsorized Mean ( 8 / 26 )	3.17	0.227106176027587	13.9582289458078
Winsorized Mean ( 9 / 26 )	3.1475	0.217181128105237	14.4925115154336
Winsorized Mean ( 10 / 26 )	3.01	0.182602494194564	16.4838931323294
Winsorized Mean ( 11 / 26 )	2.88625	0.153706770705651	18.7776373594315
Winsorized Mean ( 12 / 26 )	2.72125	0.119342790902955	22.8019638170925
Winsorized Mean ( 13 / 26 )	2.705	0.111248666611267	24.3148981681911
Winsorized Mean ( 14 / 26 )	2.6875	0.108110571035492	24.8588086646744
Winsorized Mean ( 15 / 26 )	2.6875	0.102475298042312	26.2258324819931
Winsorized Mean ( 16 / 26 )	2.6875	0.102475298042312	26.2258324819931
Winsorized Mean ( 17 / 26 )	2.6875	0.0962488697944493	27.9224057980054
Winsorized Mean ( 18 / 26 )	2.6875	0.0962488697944493	27.9224057980054
Winsorized Mean ( 19 / 26 )	2.56875	0.076753628331339	33.4674732106595
Winsorized Mean ( 20 / 26 )	2.51875	0.0693343976863695	36.3275673265878
Winsorized Mean ( 21 / 26 )	2.51875	0.0622645882962074	40.4523673716063
Winsorized Mean ( 22 / 26 )	2.51875	0.0622645882962074	40.4523673716063
Winsorized Mean ( 23 / 26 )	2.5475	0.0587575742491602	43.3561125106592
Winsorized Mean ( 24 / 26 )	2.5475	0.0587575742491602	43.3561125106592
Winsorized Mean ( 25 / 26 )	2.57875	0.0551951013121704	46.7206316990923
Winsorized Mean ( 26 / 26 )	2.57875	0.0551951013121704	46.7206316990923
Trimmed Mean ( 1 / 26 )	3.15897435897436	0.241784325377229	13.0652570386677
Trimmed Mean ( 2 / 26 )	3.11710526315789	0.234972101053114	13.2658526233005
Trimmed Mean ( 3 / 26 )	3.07027027027027	0.227218013494008	13.5124421829840
Trimmed Mean ( 4 / 26 )	3.02222222222222	0.219083864133261	13.7948188661850
Trimmed Mean ( 5 / 26 )	2.97142857142857	0.209249302579462	14.2004228200483
Trimmed Mean ( 6 / 26 )	2.91764705882353	0.197225500513974	14.7934574952026
Trimmed Mean ( 7 / 26 )	2.86060606060606	0.184111028474564	15.5373965606915
Trimmed Mean ( 8 / 26 )	2.8	0.167527538603288	16.7136700231149
Trimmed Mean ( 9 / 26 )	2.74032258064516	0.149889077221204	18.2823367215814
Trimmed Mean ( 10 / 26 )	2.68	0.129749868009904	20.6551269847568
Trimmed Mean ( 11 / 26 )	2.63448275862069	0.114696045459944	22.9692553745520
Trimmed Mean ( 12 / 26 )	2.60178571428571	0.104057023310229	25.0034609055548
Trimmed Mean ( 13 / 26 )	2.58703703703704	0.0998267645629407	25.9152647925989
Trimmed Mean ( 14 / 26 )	2.57307692307692	0.0963166043322798	26.7147802906355
Trimmed Mean ( 15 / 26 )	2.56	0.0925820099772551	27.6511603132069
Trimmed Mean ( 16 / 26 )	2.54583333333333	0.089023381926047	28.5973558659925
Trimmed Mean ( 17 / 26 )	2.53043478260870	0.0843772049040166	29.9895544713432
Trimmed Mean ( 18 / 26 )	2.51363636363636	0.0797452941271262	31.5208112422188
Trimmed Mean ( 19 / 26 )	2.49523809523810	0.0734856706940635	33.9554374570017
Trimmed Mean ( 20 / 26 )	2.4875	0.070727673835309	35.1701090268033
Trimmed Mean ( 21 / 26 )	2.48421052631579	0.0688790883821133	36.0662515237483
Trimmed Mean ( 22 / 26 )	2.48055555555556	0.0679424878691407	36.5096368024259
Trimmed Mean ( 23 / 26 )	2.47647058823529	0.0664960593540338	37.2423661235358
Trimmed Mean ( 24 / 26 )	2.46875	0.0651359465445775	37.9014988031293
Trimmed Mean ( 25 / 26 )	2.46	0.0629906032036051	39.0534440835329
Trimmed Mean ( 26 / 26 )	2.44642857142857	0.0605272562804103	40.4186266116999
Median	2.3
Midrange	4.75
Midmean - Weighted Average at Xnp	2.43953488372093
Midmean - Weighted Average at X(n+1)p	2.43953488372093
Midmean - Empirical Distribution Function	2.43953488372093
Midmean - Empirical Distribution Function - Averaging	2.43953488372093
Midmean - Empirical Distribution Function - Interpolation	2.43953488372093
Midmean - Closest Observation	2.43953488372093
Midmean - True Basic - Statistics Graphics Toolkit	2.43953488372093
Midmean - MS Excel (old versions)	2.46363636363636
Number of observations	80

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/16/t1224167527yjk3c53bitur65z/130nh1224167494.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/16/t1224167527yjk3c53bitur65z/130nh1224167494.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/16/t1224167527yjk3c53bitur65z/2xevw1224167494.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/16/t1224167527yjk3c53bitur65z/2xevw1224167494.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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