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*The author of this computation has been verified*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Tue, 29 Dec 2009 10:08:39 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/29/t12621065492ii9pu7jo5wx24d.htm/, Retrieved Tue, 29 Dec 2009 18:09:11 +0100
 
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/Dec/29/t12621065492ii9pu7jo5wx24d.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 «
262.262 261.631 258.953 259.966 262.850 262.204 263.418 262.752 266.433 267.722 266.003 262.971 265.521 264.676 270.223 269.508 268.457 265.814 266.680 263.018 269.285 269.829 270.911 266.844 271.244 269.907 271.296 270.157 271.322 267.179 264.101 265.518 269.419 268.714 272.482 268.351 268.175 270.674 272.764 272.599 270.333 270.846 270.491 269.160 274.027 273.784 276.663 274.525 271.344 271.115 270.798 273.911 273.985 271.917 273.338 270.601 273.547 275.363 281.229 277.793 279.913 282.500 280.041 282.166 290.304 283.519 287.816 285.226 287.595 289.741 289.148 288.301 290.155 289.648 288.225 289.351 294.735 305.333 309.030 310.215 321.935 325.734 320.846 323.023 319.753 321.753 320.757 324.479 324.641 322.767
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean279.7250333333331.93399938871967144.635533477865
Geometric Mean279.162328410012
Harmonic Mean278.630651557574
Quadratic Mean280.31943519296
Winsorized Mean ( 1 / 30 )279.7241444444441.92946124022830144.975259731751
Winsorized Mean ( 2 / 30 )279.7575444444441.92443369429440145.371360558628
Winsorized Mean ( 3 / 30 )279.7281111111111.90992074306896146.460585930717
Winsorized Mean ( 4 / 30 )279.7193111111111.90676322538065146.698503195262
Winsorized Mean ( 5 / 30 )279.7003111111111.89233479020319147.806990897778
Winsorized Mean ( 6 / 30 )279.6947111111111.88863936340553148.093233960122
Winsorized Mean ( 7 / 30 )279.6335777777781.87013696708286149.525720682355
Winsorized Mean ( 8 / 30 )279.6298444444441.86776102771660149.713930366296
Winsorized Mean ( 9 / 30 )279.5694444444441.83904333609563152.01895407097
Winsorized Mean ( 10 / 30 )278.5855555555561.58140316493461176.163524730947
Winsorized Mean ( 11 / 30 )278.5111.54186156103855180.632948532943
Winsorized Mean ( 12 / 30 )278.1303333333331.42277191087048195.484835769049
Winsorized Mean ( 13 / 30 )276.5999444444441.11550186780164247.960090815043
Winsorized Mean ( 14 / 30 )275.9562555555560.990914494782629278.486445610113
Winsorized Mean ( 15 / 30 )275.9629222222220.9832768489113280.656381290552
Winsorized Mean ( 16 / 30 )275.9657666666670.96278894575598286.631631868165
Winsorized Mean ( 17 / 30 )275.9948555555560.954813328758198289.056349804528
Winsorized Mean ( 18 / 30 )275.9682555555560.941715868862893293.048322408311
Winsorized Mean ( 19 / 30 )275.9961222222220.927251290919192297.649757865125
Winsorized Mean ( 20 / 30 )275.9285666666670.884722496827118311.88148561411
Winsorized Mean ( 21 / 30 )276.0165333333330.87107792783112316.867784746402
Winsorized Mean ( 22 / 30 )275.9595777777780.851043504138902324.260248078619
Winsorized Mean ( 23 / 30 )275.9301888888890.839498939628019328.684380484332
Winsorized Mean ( 24 / 30 )275.3669888888890.735596324544079374.345248475189
Winsorized Mean ( 25 / 30 )275.0167111111110.652582979688703421.427955786252
Winsorized Mean ( 26 / 30 )274.7584444444440.606249968863375453.209828545763
Winsorized Mean ( 27 / 30 )274.6984444444440.587842695994206467.299238922843
Winsorized Mean ( 28 / 30 )274.4346222222220.543755640107997504.70211613385
Winsorized Mean ( 29 / 30 )274.1552555555560.47997706732596571.18407152851
Winsorized Mean ( 30 / 30 )274.1385888888890.471474340136188581.449647524195
Trimmed Mean ( 1 / 30 )279.438251.89195806426595147.697908995894
Trimmed Mean ( 2 / 30 )279.1390581395351.84837478887583151.018646120631
Trimmed Mean ( 3 / 30 )278.8077261904761.80054946363963154.845913328532
Trimmed Mean ( 4 / 30 )278.4711.75094509301674159.040395447362
Trimmed Mean ( 5 / 30 )278.11991251.69363912446603164.214388108024
Trimmed Mean ( 6 / 30 )277.7552051282051.63024116718656170.376758186980
Trimmed Mean ( 7 / 30 )277.3724078947371.55557605059513178.308484364118
Trimmed Mean ( 8 / 30 )276.9795405405411.47069238520089188.332749477523
Trimmed Mean ( 9 / 30 )276.5654305555561.36755118002180202.234062312130
Trimmed Mean ( 10 / 30 )276.1362857142861.24690345004084221.457632269155
Trimmed Mean ( 11 / 30 )275.8121176470591.1661920565992236.506599480167
Trimmed Mean ( 12 / 30 )275.4775454545451.07540300445749256.162149736151
Trimmed Mean ( 13 / 30 )275.4775454545450.991609546437836277.808484644127
Trimmed Mean ( 14 / 30 )275.0066290322580.960218324766995286.400104995904
Trimmed Mean ( 15 / 30 )274.9048833333330.945990888470253290.599927212700
Trimmed Mean ( 16 / 30 )274.7954310344830.9293619379354295.681821922842
Trimmed Mean ( 17 / 30 )274.6778750.911927284802828301.205896103207
Trimmed Mean ( 18 / 30 )274.5487592592590.891059748359716308.114870820565
Trimmed Mean ( 19 / 30 )274.4122692307690.866885727383034316.549529612362
Trimmed Mean ( 20 / 30 )274.262220.838454868652659327.104332330637
Trimmed Mean ( 21 / 30 )274.1060.810320410426142338.268660733659
Trimmed Mean ( 22 / 30 )273.9280.775641375869901353.163212435364
Trimmed Mean ( 23 / 30 )273.7391136363640.734171646531469372.854379394275
Trimmed Mean ( 24 / 30 )273.5349761904760.680816706115879401.774770996761
Trimmed Mean ( 25 / 30 )273.3632250.639042162333898427.77024915168
Trimmed Mean ( 26 / 30 )273.3632250.605408007715412451.535528959342
Trimmed Mean ( 27 / 30 )273.0573611111110.572364547160006477.068963243765
Trimmed Mean ( 28 / 30 )272.8964705882350.530439220748082514.472648163851
Trimmed Mean ( 29 / 30 )272.741968750.485698433926339561.545909351983
Trimmed Mean ( 30 / 30 )272.5957666666670.444135799578725613.766705870662
Median271.6305
Midrange292.3435
Midmean - Weighted Average at Xnp273.619377777778
Midmean - Weighted Average at X(n+1)p273.928
Midmean - Empirical Distribution Function273.928
Midmean - Empirical Distribution Function - Averaging273.928
Midmean - Empirical Distribution Function - Interpolation273.739113636364
Midmean - Closest Observation273.928
Midmean - True Basic - Statistics Graphics Toolkit273.928
Midmean - MS Excel (old versions)273.928
Number of observations90
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2009/Dec/29/t12621065492ii9pu7jo5wx24d/1d0141262106516.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/29/t12621065492ii9pu7jo5wx24d/1d0141262106516.ps (open in new window)


http://www.freestatistics.org/blog/date/2009/Dec/29/t12621065492ii9pu7jo5wx24d/2av9a1262106516.png (open in new window)
http://www.freestatistics.org/blog/date/2009/Dec/29/t12621065492ii9pu7jo5wx24d/2av9a1262106516.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')
 





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