PAPER_Central Tendency_Consumptiegoederen
| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 2 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 | 114.445 | 1.15752615862865 | 98.8703357992234 |
| Geometric Mean | 114.099730748685 | ||
| Harmonic Mean | 113.755068114603 | ||
| Quadratic Mean | 114.789852193766 | ||
| Winsorized Mean ( 1 / 20 ) | 114.453333333333 | 1.14849069875311 | 99.6554290405595 |
| Winsorized Mean ( 2 / 20 ) | 114.506666666667 | 1.1353509790256 | 100.855743097998 |
| Winsorized Mean ( 3 / 20 ) | 114.471666666667 | 1.12338042031105 | 101.899289498896 |
| Winsorized Mean ( 4 / 20 ) | 114.505 | 1.10834386809487 | 103.311799971269 |
| Winsorized Mean ( 5 / 20 ) | 114.521666666667 | 1.09159628013049 | 104.912107847213 |
| Winsorized Mean ( 6 / 20 ) | 114.521666666667 | 1.06396574980627 | 107.636610189302 |
| Winsorized Mean ( 7 / 20 ) | 114.51 | 1.02161581333518 | 112.087145192251 |
| Winsorized Mean ( 8 / 20 ) | 114.47 | 1.00399287592854 | 114.014753236305 |
| Winsorized Mean ( 9 / 20 ) | 114.485 | 0.990371228121822 | 115.598067420753 |
| Winsorized Mean ( 10 / 20 ) | 114.468333333333 | 0.95118270615568 | 120.343160775043 |
| Winsorized Mean ( 11 / 20 ) | 114.395 | 0.89909692607965 | 127.233223339778 |
| Winsorized Mean ( 12 / 20 ) | 114.755 | 0.841791286852905 | 136.322389875309 |
| Winsorized Mean ( 13 / 20 ) | 114.365 | 0.758674226477283 | 150.743225496173 |
| Winsorized Mean ( 14 / 20 ) | 114.178333333333 | 0.727906570596729 | 156.858500727272 |
| Winsorized Mean ( 15 / 20 ) | 114.053333333333 | 0.692422533008896 | 164.716380383693 |
| Winsorized Mean ( 16 / 20 ) | 114.16 | 0.65150932977177 | 175.223891329371 |
| Winsorized Mean ( 17 / 20 ) | 114.16 | 0.625793056171561 | 182.424523369437 |
| Winsorized Mean ( 18 / 20 ) | 114.19 | 0.62136945531624 | 183.771505057139 |
| Winsorized Mean ( 19 / 20 ) | 114.19 | 0.592994412183923 | 192.565052307074 |
| Winsorized Mean ( 20 / 20 ) | 114.423333333333 | 0.559667812424168 | 204.448658281268 |
| Trimmed Mean ( 1 / 20 ) | 114.458620689655 | 1.12645693649636 | 101.609406432933 |
| Trimmed Mean ( 2 / 20 ) | 114.464285714286 | 1.09908884510073 | 104.144706976618 |
| Trimmed Mean ( 3 / 20 ) | 114.440740740741 | 1.07368146273828 | 106.587237194983 |
| Trimmed Mean ( 4 / 20 ) | 114.428846153846 | 1.04749336847637 | 109.240640177311 |
| Trimmed Mean ( 5 / 20 ) | 114.406 | 1.02022170459690 | 112.138370987905 |
| Trimmed Mean ( 6 / 20 ) | 114.377083333333 | 0.991154314796021 | 115.397856444657 |
| Trimmed Mean ( 7 / 20 ) | 114.345652173913 | 0.962458137726887 | 118.805844838065 |
| Trimmed Mean ( 8 / 20 ) | 114.313636363636 | 0.93762435910407 | 121.918373017598 |
| Trimmed Mean ( 9 / 20 ) | 114.285714285714 | 0.909681897590243 | 125.632613541567 |
| Trimmed Mean ( 10 / 20 ) | 114.2525 | 0.876041413229025 | 130.419062700328 |
| Trimmed Mean ( 11 / 20 ) | 114.218421052632 | 0.841803044097628 | 135.683069636637 |
| Trimmed Mean ( 12 / 20 ) | 114.191666666667 | 0.809941943833601 | 140.987471430578 |
| Trimmed Mean ( 13 / 20 ) | 114.108823529412 | 0.781120449046786 | 146.083518449249 |
| Trimmed Mean ( 14 / 20 ) | 114.071875 | 0.764750570434464 | 149.162196682239 |
| Trimmed Mean ( 15 / 20 ) | 114.056666666667 | 0.748618395389606 | 152.356216957917 |
| Trimmed Mean ( 16 / 20 ) | 114.057142857143 | 0.733665663720505 | 155.462015598148 |
| Trimmed Mean ( 17 / 20 ) | 114.042307692308 | 0.721540511724166 | 158.053921906334 |
| Trimmed Mean ( 18 / 20 ) | 114.025 | 0.70800930354978 | 161.050143590356 |
| Trimmed Mean ( 19 / 20 ) | 114 | 0.683826767258381 | 166.708888066860 |
| Trimmed Mean ( 20 / 20 ) | 113.97 | 0.652448828402819 | 174.680365782856 |
| Median | 112.85 | ||
| Midrange | 114.05 | ||
| Midmean - Weighted Average at Xnp | 113.646875 | ||
| Midmean - Weighted Average at X(n+1)p | 114.056666666667 | ||
| Midmean - Empirical Distribution Function | 113.646875 | ||
| Midmean - Empirical Distribution Function - Averaging | 114.056666666667 | ||
| Midmean - Empirical Distribution Function - Interpolation | 114.056666666667 | ||
| Midmean - Closest Observation | 113.646875 | ||
| Midmean - True Basic - Statistics Graphics Toolkit | 114.056666666667 | ||
| Midmean - MS Excel (old versions) | 113.872727272727 | ||
| Number of observations | 60 | ||
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/11/t1194777581rl2k0569zq3vo03/1ok6k1194777799.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/11/t1194777581rl2k0569zq3vo03/1ok6k1194777799.ps (open in new window) |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/11/t1194777581rl2k0569zq3vo03/28ycj1194777799.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/11/t1194777581rl2k0569zq3vo03/28ycj1194777799.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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