Central tendency van de Olieprijs
| Summary of compuational 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 | 43.6661428571429 | 1.94077617066775 | 22.4993193533075 |
| Geometric Mean | 40.6650118372803 | ||
| Harmonic Mean | 37.8273752848949 | ||
| Quadratic Mean | 46.5470543643741 | ||
| Winsorized Mean ( 1 / 23 ) | 43.7042857142857 | 1.92478810719936 | 22.7060243934472 |
| Winsorized Mean ( 2 / 23 ) | 43.6728571428571 | 1.9048678205542 | 22.9269751274138 |
| Winsorized Mean ( 3 / 23 ) | 43.5657142857143 | 1.87525002966675 | 23.2319496581777 |
| Winsorized Mean ( 4 / 23 ) | 43.5657142857143 | 1.87328376743917 | 23.2563347011061 |
| Winsorized Mean ( 5 / 23 ) | 43.5871428571429 | 1.8676896650687 | 23.3374653575221 |
| Winsorized Mean ( 6 / 23 ) | 43.4414285714286 | 1.83712293392595 | 23.646446173634 |
| Winsorized Mean ( 7 / 23 ) | 43.2814285714286 | 1.80173862761062 | 24.0220351099573 |
| Winsorized Mean ( 8 / 23 ) | 43.2471428571429 | 1.78844661356142 | 24.1813999530144 |
| Winsorized Mean ( 9 / 23 ) | 43.2728571428571 | 1.78064463799670 | 24.3017928560642 |
| Winsorized Mean ( 10 / 23 ) | 43.3157142857143 | 1.77001671011785 | 24.4719239304979 |
| Winsorized Mean ( 11 / 23 ) | 43.2371428571429 | 1.74185019956271 | 24.82253805063 |
| Winsorized Mean ( 12 / 23 ) | 42.5685714285714 | 1.61404875594637 | 26.3737828685430 |
| Winsorized Mean ( 13 / 23 ) | 42.55 | 1.57896728311875 | 26.9479934479427 |
| Winsorized Mean ( 14 / 23 ) | 42.55 | 1.57322939352075 | 27.0462782956125 |
| Winsorized Mean ( 15 / 23 ) | 42.4428571428571 | 1.55760283441137 | 27.2488314769256 |
| Winsorized Mean ( 16 / 23 ) | 42.6485714285714 | 1.52278994098904 | 28.0068644273231 |
| Winsorized Mean ( 17 / 23 ) | 42.6485714285714 | 1.52278994098904 | 28.0068644273231 |
| Winsorized Mean ( 18 / 23 ) | 42.6485714285714 | 1.51557783069664 | 28.1401394008038 |
| Winsorized Mean ( 19 / 23 ) | 42.35 | 1.46533689482007 | 28.9012036410919 |
| Winsorized Mean ( 20 / 23 ) | 42.2357142857143 | 1.38669518760627 | 30.4578213461765 |
| Winsorized Mean ( 21 / 23 ) | 42.1757142857143 | 1.36221478974224 | 30.9611337384576 |
| Winsorized Mean ( 22 / 23 ) | 42.1128571428571 | 1.33672744206237 | 31.5044457214727 |
| Winsorized Mean ( 23 / 23 ) | 42.2771428571428 | 1.31491707762478 | 32.151945986975 |
| Trimmed Mean ( 1 / 23 ) | 43.5661764705882 | 1.90406156420235 | 22.8806553788291 |
| Trimmed Mean ( 2 / 23 ) | 43.419696969697 | 1.87848351734254 | 23.1142283490047 |
| Trimmed Mean ( 3 / 23 ) | 43.28125 | 1.85944856963964 | 23.2763899505904 |
| Trimmed Mean ( 4 / 23 ) | 43.1741935483871 | 1.84854329071320 | 23.3557925125626 |
| Trimmed Mean ( 5 / 23 ) | 43.06 | 1.83450789288014 | 23.4722347977454 |
| Trimmed Mean ( 6 / 23 ) | 42.9327586206897 | 1.81758964315259 | 23.6207104185647 |
| Trimmed Mean ( 7 / 23 ) | 42.8267857142857 | 1.80381718461954 | 23.7423094088766 |
| Trimmed Mean ( 8 / 23 ) | 42.7425925925926 | 1.79396963657865 | 23.8257056981794 |
| Trimmed Mean ( 9 / 23 ) | 42.6576923076923 | 1.78274016330143 | 23.9281602478149 |
| Trimmed Mean ( 10 / 23 ) | 42.562 | 1.76819726021177 | 24.0708437671160 |
| Trimmed Mean ( 11 / 23 ) | 42.4520833333333 | 1.74989865355814 | 24.2597382694214 |
| Trimmed Mean ( 12 / 23 ) | 42.3434782608696 | 1.73059050594439 | 24.4676473812981 |
| Trimmed Mean ( 13 / 23 ) | 42.3136363636364 | 1.73071552406935 | 24.4486374422448 |
| Trimmed Mean ( 14 / 23 ) | 42.2833333333333 | 1.73381989731182 | 24.3873849866939 |
| Trimmed Mean ( 15 / 23 ) | 42.25 | 1.73427366012551 | 24.3617838242105 |
| Trimmed Mean ( 16 / 23 ) | 42.2263157894737 | 1.73316197036297 | 24.3637447114249 |
| Trimmed Mean ( 17 / 23 ) | 42.175 | 1.73353650366060 | 24.3288790925035 |
| Trimmed Mean ( 18 / 23 ) | 42.1176470588235 | 1.72776152970646 | 24.3770024593493 |
| Trimmed Mean ( 19 / 23 ) | 42.053125 | 1.71504246382466 | 24.5201654693835 |
| Trimmed Mean ( 20 / 23 ) | 42.0166666666667 | 1.70368149938332 | 24.662277944484 |
| Trimmed Mean ( 21 / 23 ) | 41.9892857142857 | 1.70079610433202 | 24.6880185151747 |
| Trimmed Mean ( 22 / 23 ) | 41.9653846153846 | 1.69347110359115 | 24.7806912833608 |
| Trimmed Mean ( 23 / 23 ) | 41.9458333333333 | 1.67918824382871 | 24.9798278945145 |
| Median | 40.35 | ||
| Midrange | 47.065 | ||
| Midmean - Weighted Average at Xnp | 41.3555555555555 | ||
| Midmean - Weighted Average at X(n+1)p | 42.2263157894737 | ||
| Midmean - Empirical Distribution Function | 42.2263157894737 | ||
| Midmean - Empirical Distribution Function - Averaging | 42.2263157894737 | ||
| Midmean - Empirical Distribution Function - Interpolation | 42.1176470588235 | ||
| Midmean - Closest Observation | 42.2263157894737 | ||
| Midmean - True Basic - Statistics Graphics Toolkit | 42.2263157894737 | ||
| Midmean - MS Excel (old versions) | 42.2263157894737 | ||
| Number of observations | 70 | ||
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197554977i58hcdpn78246ab/13emf1197552628.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197554977i58hcdpn78246ab/13emf1197552628.ps (open in new window) |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197554977i58hcdpn78246ab/2z7cs1197552628.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197554977i58hcdpn78246ab/2z7cs1197552628.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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.