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Central tendency: Personenwagens

*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: Fri, 12 Dec 2008 04:40:19 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/12/t1229082079pdcqxiz17nrmmpr.htm/, Retrieved Fri, 12 Dec 2008 12:41:23 +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/2008/Dec/12/t1229082079pdcqxiz17nrmmpr.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},
}
 
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean24898.6826923077680.43097755021236.5925178508944
Geometric Mean23892.5623549308
Harmonic Mean22813.9645909685
Quadratic Mean25838.5756240325
Winsorized Mean ( 1 / 34 )24891.8365384615672.85017981102536.9946197316208
Winsorized Mean ( 2 / 34 )24880.6826923077663.66228821418637.4899751487429
Winsorized Mean ( 3 / 34 )24863.2884615385646.1270292404338.4804958411461
Winsorized Mean ( 4 / 34 )24876.9038461538641.37384669524138.7869009226603
Winsorized Mean ( 5 / 34 )24862.3365384615628.94535014953139.5302016821502
Winsorized Mean ( 6 / 34 )24848.3173076923623.04395767953339.8821254927782
Winsorized Mean ( 7 / 34 )24921.8173076923600.12091648858541.5279931476382
Winsorized Mean ( 8 / 34 )25011.4326923077572.41635472130943.6944760330703
Winsorized Mean ( 9 / 34 )24986.0769230769567.41368826621744.0350267182029
Winsorized Mean ( 10 / 34 )24965.5563.00840405105344.3430325735176
Winsorized Mean ( 11 / 34 )24939.6923076923557.82330084518644.7089468473349
Winsorized Mean ( 12 / 34 )24735.5769230769521.53019128380347.4288494443392
Winsorized Mean ( 13 / 34 )24684.5769230769508.42631144501948.5509431109494
Winsorized Mean ( 14 / 34 )24685.5192307692505.43577626854148.8400710630616
Winsorized Mean ( 15 / 34 )24708.4519230769501.56047695048649.2631558078611
Winsorized Mean ( 16 / 34 )24657.0673076923493.06553384085550.0076878536207
Winsorized Mean ( 17 / 34 )24662.4615384615490.09575524941550.3217203460792
Winsorized Mean ( 18 / 34 )24606.7307692308479.52544304606351.3147552983274
Winsorized Mean ( 19 / 34 )24529.0865384615467.17584603495952.5050401185039
Winsorized Mean ( 20 / 34 )24526.5865384615453.33855487296954.1021412690879
Winsorized Mean ( 21 / 34 )24538.0961538462444.08428841009755.2554926941844
Winsorized Mean ( 22 / 34 )24525.6153846154440.30760860941955.7010937468745
Winsorized Mean ( 23 / 34 )24602.3557692308425.57397539781257.8098220085786
Winsorized Mean ( 24 / 34 )24708.7403846154409.57893572800160.3271756168249
Winsorized Mean ( 25 / 34 )24679.6538461538400.08753891100661.685634882129
Winsorized Mean ( 26 / 34 )24627.6538461538392.00484809219962.8248705749718
Winsorized Mean ( 27 / 34 )24717.7403846154378.69403894146165.2710046709668
Winsorized Mean ( 28 / 34 )24739.8173076923371.12114663884266.6623757006441
Winsorized Mean ( 29 / 34 )24684.6057692308361.05575122490768.3678509080288
Winsorized Mean ( 30 / 34 )24675.6634615385359.58187033445168.6232135079206
Winsorized Mean ( 31 / 34 )24613.6634615385346.53610376385471.0277030133384
Winsorized Mean ( 32 / 34 )24553.3557692308321.19027050215676.4448927137285
Winsorized Mean ( 33 / 34 )24524.1634615385301.14407443625581.436646254614
Winsorized Mean ( 34 / 34 )24377.0480769231256.67945911410094.9707785775213
Trimmed Mean ( 1 / 34 )24872.2254901961652.4791344929938.1195722212988
Trimmed Mean ( 2 / 34 )24851.83629.41560390202739.4839750491288
Trimmed Mean ( 3 / 34 )24836.5204081633608.85634120942440.7920862889074
Trimmed Mean ( 4 / 34 )24826.8541666667593.07584719135841.8611789440419
Trimmed Mean ( 5 / 34 )24813.0106382979576.76725771403143.0208377927731
Trimmed Mean ( 6 / 34 )24801.8586956522561.78310425880144.1484596237100
Trimmed Mean ( 7 / 34 )24792.9111111111546.18079889333545.3932308886475
Trimmed Mean ( 8 / 34 )24771.1477272727533.54471170526646.4275011706170
Trimmed Mean ( 9 / 34 )24734.8255813953524.66665000068847.143887611997
Trimmed Mean ( 10 / 34 )24700.2619047619515.37098277912347.927149044299
Trimmed Mean ( 11 / 34 )24666.6219512195505.40936319221748.805233435769
Trimmed Mean ( 12 / 34 )24634.35494.7594972895749.7905550776768
Trimmed Mean ( 13 / 34 )24623.1025641026488.4746080952750.4081525549844
Trimmed Mean ( 14 / 34 )24616.6315789474483.0963250148450.9559487503681
Trimmed Mean ( 15 / 34 )24616.6315789474477.13186456858851.5929314450737
Trimmed Mean ( 16 / 34 )24600.2083333333470.58504273740152.2757973569103
Trimmed Mean ( 17 / 34 )24594.9285714286464.03123213648853.0027439277931
Trimmed Mean ( 18 / 34 )24588.8529411765456.59168589842453.8530457312064
Trimmed Mean ( 19 / 34 )24587.2878787879449.22608081609154.7325476609041
Trimmed Mean ( 20 / 34 )24592.265625442.14811991182555.6199710402575
Trimmed Mean ( 21 / 34 )24597.7741935484435.57703870490656.4716961818844
Trimmed Mean ( 22 / 34 )24602.7428.86739703233257.3666829659826
Trimmed Mean ( 23 / 34 )24608.9827586207421.11186513691658.4381129955091
Trimmed Mean ( 24 / 34 )24609.5178571429413.80734035208659.4709553392745
Trimmed Mean ( 25 / 34 )24601.5555555556407.16123110001360.4221465022355
Trimmed Mean ( 26 / 34 )24595.3076923077400.23910607915261.4515356414065
Trimmed Mean ( 27 / 34 )24592.72392.71493638152262.6223189436019
Trimmed Mean ( 28 / 34 )24582.6875385.28133793161863.8045113525926
Trimmed Mean ( 29 / 34 )24570376.90170812101865.1894100519993
Trimmed Mean ( 30 / 34 )24570367.83301050692266.7966150350109
Trimmed Mean ( 31 / 34 )24551.1666666667356.05324269518968.9536387334197
Trimmed Mean ( 32 / 34 )24545.925343.28409851268571.5032391723003
Trimmed Mean ( 33 / 34 )24545.2894736842332.07762059407773.914313857626
Trimmed Mean ( 34 / 34 )24547.1388888889321.58646953092076.3313796276765
Median24734.5
Midrange26248
Midmean - Weighted Average at Xnp24504.5471698113
Midmean - Weighted Average at X(n+1)p24595.3076923077
Midmean - Empirical Distribution Function24504.5471698113
Midmean - Empirical Distribution Function - Averaging24595.3076923077
Midmean - Empirical Distribution Function - Interpolation24595.3076923077
Midmean - Closest Observation24504.5471698113
Midmean - True Basic - Statistics Graphics Toolkit24595.3076923077
Midmean - MS Excel (old versions)24601.5555555556
Number of observations104
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229082079pdcqxiz17nrmmpr/1uow31229082016.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229082079pdcqxiz17nrmmpr/1uow31229082016.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229082079pdcqxiz17nrmmpr/283ye1229082016.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/12/t1229082079pdcqxiz17nrmmpr/283ye1229082016.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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