Centr. Ten. Frankrijk
| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 3 seconds |
| R Server | 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 |
| Central Tendency - Ungrouped Data | |||
| Measure | Value | S.E. | Value/S.E. |
| Arithmetic Mean | 2224.50447761194 | 32.7728199422777 | 67.876505028555 |
| Geometric Mean | 2207.94748443037 | ||
| Harmonic Mean | 2190.6152658002 | ||
| Quadratic Mean | 2240.38121329731 | ||
| Winsorized Mean ( 1 / 22 ) | 2223.35074626866 | 32.3840548351703 | 68.6557244787645 |
| Winsorized Mean ( 2 / 22 ) | 2225.98656716418 | 30.5502265960904 | 72.8631769771897 |
| Winsorized Mean ( 3 / 22 ) | 2231.95522388060 | 28.8608492129641 | 77.3350502409339 |
| Winsorized Mean ( 4 / 22 ) | 2234.80895522388 | 27.9728227714104 | 79.8921500874757 |
| Winsorized Mean ( 5 / 22 ) | 2237.31641791045 | 27.4991067325022 | 81.359603410902 |
| Winsorized Mean ( 6 / 22 ) | 2230.2776119403 | 26.0198539355645 | 85.7144554870812 |
| Winsorized Mean ( 7 / 22 ) | 2229.97462686567 | 25.5580576691474 | 87.2513340306608 |
| Winsorized Mean ( 8 / 22 ) | 2231.95671641791 | 25.0938533401813 | 88.9443596469901 |
| Winsorized Mean ( 9 / 22 ) | 2231.27164179105 | 24.3933730282989 | 91.4704021949951 |
| Winsorized Mean ( 10 / 22 ) | 2224.03283582090 | 23.0027235116952 | 96.6856309293176 |
| Winsorized Mean ( 11 / 22 ) | 2228.82686567164 | 21.9449040354632 | 101.564666770465 |
| Winsorized Mean ( 12 / 22 ) | 2229.84776119403 | 21.6291675312951 | 103.094479154950 |
| Winsorized Mean ( 13 / 22 ) | 2229.26567164179 | 21.1894853677557 | 105.206220583068 |
| Winsorized Mean ( 14 / 22 ) | 2229.55820895522 | 20.5710587570619 | 108.383250239360 |
| Winsorized Mean ( 15 / 22 ) | 2226.80447761194 | 19.4728852100220 | 114.354111041844 |
| Winsorized Mean ( 16 / 22 ) | 2225.80149253731 | 19.2669871940027 | 115.524107122994 |
| Winsorized Mean ( 17 / 22 ) | 2232.75373134328 | 17.8923923465314 | 124.787881245859 |
| Winsorized Mean ( 18 / 22 ) | 2234.47313432836 | 15.3951547444941 | 145.141323449672 |
| Winsorized Mean ( 19 / 22 ) | 2234.01940298507 | 14.6191850305674 | 152.814223112571 |
| Winsorized Mean ( 20 / 22 ) | 2233.18358208955 | 13.4861985496557 | 165.590293948813 |
| Winsorized Mean ( 21 / 22 ) | 2225.09701492537 | 12.1518553806029 | 183.107595114828 |
| Winsorized Mean ( 22 / 22 ) | 2224.34179104478 | 11.7472902943361 | 189.349350813033 |
| Trimmed Mean ( 1 / 22 ) | 2226.26769230769 | 30.5799580944156 | 72.8015285512849 |
| Trimmed Mean ( 2 / 22 ) | 2229.36984126984 | 28.3605018052714 | 78.6082649939383 |
| Trimmed Mean ( 3 / 22 ) | 2231.22786885246 | 26.8996467495797 | 82.9463631855063 |
| Trimmed Mean ( 4 / 22 ) | 2230.95254237288 | 25.9441331356612 | 85.9906372938841 |
| Trimmed Mean ( 5 / 22 ) | 2229.81929824561 | 25.1176694986585 | 88.7749278795435 |
| Trimmed Mean ( 6 / 22 ) | 2227.99272727273 | 24.2522405302619 | 91.8675008394642 |
| Trimmed Mean ( 7 / 22 ) | 2227.51132075472 | 23.6306342926074 | 94.2637126525025 |
| Trimmed Mean ( 8 / 22 ) | 2227.04901960784 | 22.9757615457731 | 96.9303679084167 |
| Trimmed Mean ( 9 / 22 ) | 2226.21020408163 | 22.2660568915430 | 99.9822382079324 |
| Trimmed Mean ( 10 / 22 ) | 2225.40851063830 | 21.5393821765940 | 103.318121773083 |
| Trimmed Mean ( 11 / 22 ) | 2225.61333333333 | 20.9540164178709 | 106.214163860022 |
| Trimmed Mean ( 12 / 22 ) | 2225.15813953488 | 20.4425896357074 | 108.849132090788 |
| Trimmed Mean ( 13 / 22 ) | 2224.51951219512 | 19.8329733510957 | 112.162683467339 |
| Trimmed Mean ( 14 / 22 ) | 2223.89230769231 | 19.1212560868864 | 116.304718559650 |
| Trimmed Mean ( 15 / 22 ) | 2223.15945945946 | 18.3132959540491 | 121.395922669393 |
| Trimmed Mean ( 16 / 22 ) | 2222.69428571429 | 17.5051079905925 | 126.974040200654 |
| Trimmed Mean ( 17 / 22 ) | 2222.3 | 16.4224624440817 | 135.320753971392 |
| Trimmed Mean ( 18 / 22 ) | 2220.97096774194 | 15.3031855518156 | 145.131283955348 |
| Trimmed Mean ( 19 / 22 ) | 2219.23793103448 | 14.5076295655309 | 152.970402298335 |
| Trimmed Mean ( 20 / 22 ) | 2217.30740740741 | 13.5708459993285 | 163.387559443024 |
| Trimmed Mean ( 21 / 22 ) | 2215.18 | 12.5551768871118 | 176.435586684082 |
| Trimmed Mean ( 22 / 22 ) | 2213.80434782609 | 11.5610930563910 | 191.487460314342 |
| Median | 2211.7 | ||
| Midrange | 2167.2 | ||
| Midmean - Weighted Average at Xnp | 2216.62941176471 | ||
| Midmean - Weighted Average at X(n+1)p | 2222.69428571429 | ||
| Midmean - Empirical Distribution Function | 2222.69428571429 | ||
| Midmean - Empirical Distribution Function - Averaging | 2222.69428571429 | ||
| Midmean - Empirical Distribution Function - Interpolation | 2222.3 | ||
| Midmean - Closest Observation | 2216.62941176471 | ||
| Midmean - True Basic - Statistics Graphics Toolkit | 2222.69428571429 | ||
| Midmean - MS Excel (old versions) | 2222.69428571429 | ||
| Number of observations | 67 | ||
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/12/t1197455746gtimvkmfim4sfm6/1hhk61197456575.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/12/t1197455746gtimvkmfim4sfm6/1hhk61197456575.ps (open in new window) |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/12/t1197455746gtimvkmfim4sfm6/2kgsi1197456575.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/12/t1197455746gtimvkmfim4sfm6/2kgsi1197456575.ps (open in new window) |
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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