Home » date » 2009 » Jun » 01 »

Nick Vermeulen Centrummaten 2

*Unverified author*
R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Mon, 01 Jun 2009 13:47:50 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/01/t12438858094iaa4nflma0kgye.htm/, Retrieved Mon, 01 Jun 2009 21:50:11 +0200
 
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/Jun/01/t12438858094iaa4nflma0kgye.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:
Maandelijkse verkoop auto's
 
Dataseries X:
» Textbox « » Textfile « » CSV «
14620 16005 16683 15487 15684 15962 12000 13769 14031 16078 15827 13149 15969 16628 16670 16487 16883 16201 12168 14010 16556 17404 16435 13123 16744 17410 16484 17103 17301 17301 12843 13748 16904 17342 15476 15424 15988 19244 18715 17780 17160 17349 11171 13438 16713 18369 17067 14055 15500 18475 19423 18686 19646 19733 12605 16616 19156 21348 20049 18020 20262 21789 20603 21928 21025 19346 11786 19082 20127 20217 20385 16653 13065 20275 21776 20260 22523 23033 14133 20110 19682 22197 17212 11784 15467 17002 15952 18767 20605 19809 14233 19311 20827 23388 20181 14344
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17264.1041666667291.12193460272859.3019697750556
Geometric Mean17023.8808492476
Harmonic Mean16776.7428262430
Quadratic Mean17495.7346474553
Winsorized Mean ( 1 / 32 )17266.7916666667288.98283766372959.750232249982
Winsorized Mean ( 2 / 32 )17256.2083333333286.8315229702760.1614779109266
Winsorized Mean ( 3 / 32 )17252.7083333333283.5885775932760.8371059220784
Winsorized Mean ( 4 / 32 )17248.5280.22428243268361.5524816417132
Winsorized Mean ( 5 / 32 )17264.0208333333274.75586211646462.8340400104565
Winsorized Mean ( 6 / 32 )17278.0833333333272.01042076701463.5199316431064
Winsorized Mean ( 7 / 32 )17263.0625264.00583991933465.3889417949037
Winsorized Mean ( 8 / 32 )17240.9791666667258.93328959472166.5846372772386
Winsorized Mean ( 9 / 32 )17224.8541666667255.72053858671767.3581178182354
Winsorized Mean ( 10 / 32 )17231.8333333333247.38888905304769.6548393878691
Winsorized Mean ( 11 / 32 )17267.125241.76587342887071.4208533864071
Winsorized Mean ( 12 / 32 )17242.5237.48526177723972.6045055215826
Winsorized Mean ( 13 / 32 )17260.2395833333230.48642249122974.8861446881548
Winsorized Mean ( 14 / 32 )17261.40625229.77169569885275.1241626933176
Winsorized Mean ( 15 / 32 )17264.84375229.17479985318375.3348263467903
Winsorized Mean ( 16 / 32 )17270.6770833333226.28359181411476.3231524869941
Winsorized Mean ( 17 / 32 )17282.0104166667222.8425283312677.5525683812769
Winsorized Mean ( 18 / 32 )17292.6979166667218.48060008611679.1498096849358
Winsorized Mean ( 19 / 32 )17343.9583333333210.41304560893382.4281511782699
Winsorized Mean ( 20 / 32 )17498.75187.35420647589093.3992907293054
Winsorized Mean ( 21 / 32 )17455.65625178.85577218253297.596270095133
Winsorized Mean ( 22 / 32 )17440.3020833333176.21518700592598.971617484632
Winsorized Mean ( 23 / 32 )17430.71875174.238168632995100.039611795479
Winsorized Mean ( 24 / 32 )17424.96875172.635155197010100.935227996376
Winsorized Mean ( 25 / 32 )17414.8125159.291169258118109.326917374690
Winsorized Mean ( 26 / 32 )17432.6875152.159881225294114.568224946157
Winsorized Mean ( 27 / 32 )17458147.006261801231118.756846042417
Winsorized Mean ( 28 / 32 )17441.375144.108349108907121.029594106438
Winsorized Mean ( 29 / 32 )17416.90625140.39586426011124.055693105973
Winsorized Mean ( 30 / 32 )17399.71875136.745886354566127.241259052463
Winsorized Mean ( 31 / 32 )17303.4895833333123.185040347944140.467458828268
Winsorized Mean ( 32 / 32 )17310.4895833333118.334188897443146.284769808461
Trimmed Mean ( 1 / 32 )17263.7765957447282.63031390608861.0825369619802
Trimmed Mean ( 2 / 32 )17260.6304347826275.40467454797262.6737017558358
Trimmed Mean ( 3 / 32 )17262.9888888889268.47063577004664.3012180433588
Trimmed Mean ( 4 / 32 )17266.7272727273261.93752880938165.9192569740274
Trimmed Mean ( 5 / 32 )17271.8139534884255.59703638739967.5743905234884
Trimmed Mean ( 6 / 32 )17273.5952380952249.89291402390769.1239897920543
Trimmed Mean ( 7 / 32 )17272.7195121951244.01134721838470.7865421387
Trimmed Mean ( 8 / 32 )17274.375239.05201050454772.2619942143154
Trimmed Mean ( 9 / 32 )17279.5128205128234.35342552039573.732708545406
Trimmed Mean ( 10 / 32 )17287.1842105263229.49541272067775.326927042184
Trimmed Mean ( 11 / 32 )17294.3648648649225.37166931044576.737084646794
Trimmed Mean ( 12 / 32 )17297.6666666667221.52194965376278.0855653071981
Trimmed Mean ( 13 / 32 )17303.9714285714217.68118934627479.4922679379765
Trimmed Mean ( 14 / 32 )17308.7205882353214.27913827097480.7765082868075
Trimmed Mean ( 15 / 32 )17313.6363636364210.29690149134382.3294886460755
Trimmed Mean ( 16 / 32 )17318.515625205.590903348884.2377524632882
Trimmed Mean ( 17 / 32 )17323.1451612903200.39159949974486.4464638464672
Trimmed Mean ( 18 / 32 )17327.0166666667194.67179462472489.0063026339724
Trimmed Mean ( 19 / 32 )17330.1724137931188.45768794065991.9578957121131
Trimmed Mean ( 20 / 32 )17328.9285714286182.28734783292895.063803261382
Trimmed Mean ( 21 / 32 )17313.8333333333178.61224442193996.9353102827182
Trimmed Mean ( 22 / 32 )17301.3653846154175.47580872759198.5968693352718
Trimmed Mean ( 23 / 32 )17289.24171.913111798266100.569641367950
Trimmed Mean ( 24 / 32 )17276.9375167.674640105828103.038464785705
Trimmed Mean ( 25 / 32 )17264.0652173913162.482802961234106.251645729612
Trimmed Mean ( 26 / 32 )17250.9090909091158.421367301032108.892565345235
Trimmed Mean ( 27 / 32 )17234.9285714286154.409629847408111.618223477776
Trimmed Mean ( 28 / 32 )17215.1149.967504172378114.79220178401
Trimmed Mean ( 29 / 32 )17194.6842105263144.560599278699118.944472396497
Trimmed Mean ( 30 / 32 )17174.25138.065336356287124.392193241616
Trimmed Mean ( 31 / 32 )17153.0294117647129.980654568369131.966018087271
Trimmed Mean ( 32 / 32 )17138.46875123.075917303552139.251196541806
Median17034.5
Midrange17279.5
Midmean - Weighted Average at Xnp17240.4081632653
Midmean - Weighted Average at X(n+1)p17276.9375
Midmean - Empirical Distribution Function17240.4081632653
Midmean - Empirical Distribution Function - Averaging17276.9375
Midmean - Empirical Distribution Function - Interpolation17276.9375
Midmean - Closest Observation17240.4081632653
Midmean - True Basic - Statistics Graphics Toolkit17276.9375
Midmean - MS Excel (old versions)17289.24
Number of observations96
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438858094iaa4nflma0kgye/13u351243885668.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438858094iaa4nflma0kgye/13u351243885668.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438858094iaa4nflma0kgye/20glc1243885668.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t12438858094iaa4nflma0kgye/20glc1243885668.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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