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Opgave 5 - Oef2 - Kelly Janbroers (Central Tendency)

*Unverified author*
R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Wed, 17 Mar 2010 16:47:04 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/17/t1268866059k2i094blqpcqjq9.htm/, Retrieved Wed, 17 Mar 2010 23:47:42 +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/2010/Mar/17/t1268866059k2i094blqpcqjq9.htm/},
    year = {2010},
}
@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 = {2010},
    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:
KDGP1W52
 
Dataseries X:
» Textbox « » Textfile « » CSV «
18450 21845 26488 22394 28057 25451 24872 33424 24052 28449 33533 37351 19969 21701 26249 24493 24603 26485 30723 34569 26689 26157 32064 38870 21337 19419 23166 28286 24570 24001 33151 24878 26804 28967 33311 40226 20504 23060 23562 27562 23940 24584 34303 25517 23494 29095 32903 34379 16991 21109 23740 25552 21752 20294 29009 25500 24166 26960 31222 38641 14672 17543 25453 32683 22449 22316 27595 25451 25421 25288 32568 35110 16052 22146 21198 19543 22084 23816 29961 26773 26635 26972 30207 38687 16974 21697 24179 23757 25013 24019 30345 24488 25156 25650 30923 37240 17466 19463 24352 26805 25236 24735 29356 31234 22724 28496 32857 37198
 
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'Gwilym Jenkins' @ 72.249.127.135


Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean26415.5462962963520.76543837994150.7244612439584
Geometric Mean25875.054668533
Harmonic Mean25338.811338654
Quadratic Mean26959.2122808801
Winsorized Mean ( 1 / 36 )26415.7685185185515.2423493273951.2686283513036
Winsorized Mean ( 2 / 36 )26429.4537037037511.39949329445451.6806411626344
Winsorized Mean ( 3 / 36 )26428.6481481481511.03213710743951.7162155353682
Winsorized Mean ( 4 / 36 )26398.4629629630497.7849687535653.0318603815298
Winsorized Mean ( 5 / 36 )26396.8888888889496.13559132540453.2049894230945
Winsorized Mean ( 6 / 36 )26444.9444444444487.59107585907854.235907410429
Winsorized Mean ( 7 / 36 )26372.4166666667452.01674636793958.3438929609915
Winsorized Mean ( 8 / 36 )26335.6018518519444.45691868653759.2534410976863
Winsorized Mean ( 9 / 36 )26326.4351851852440.77340267013659.7278216555349
Winsorized Mean ( 10 / 36 )26358.8425925926434.01952502965160.7319281103582
Winsorized Mean ( 11 / 36 )26313.5185185185416.43693573001163.1872830213562
Winsorized Mean ( 12 / 36 )26324.7407407407411.3599694513463.9944153434567
Winsorized Mean ( 13 / 36 )26383.9629629630399.85281947955265.9841863746374
Winsorized Mean ( 14 / 36 )26374.7592592593395.09380912827166.7556885223085
Winsorized Mean ( 15 / 36 )26359.6203703704387.26109926340268.0667911662396
Winsorized Mean ( 16 / 36 )26406.1388888889379.85896926085969.5156387652785
Winsorized Mean ( 17 / 36 )26379.3796296296375.46347399472470.2581781097575
Winsorized Mean ( 18 / 36 )26368.7129629630371.47652379086870.9835245949697
Winsorized Mean ( 19 / 36 )26296.4074074074355.93783683298673.8792134081162
Winsorized Mean ( 20 / 36 )26186.9629629630328.05227886426679.8255785743161
Winsorized Mean ( 21 / 36 )26196.6851851852326.31271822302680.2809198729437
Winsorized Mean ( 22 / 36 )26170.4074074074313.61714738316183.4469914217853
Winsorized Mean ( 23 / 36 )26144.4259259259305.71347845816585.5193760438131
Winsorized Mean ( 24 / 36 )26072.6481481481292.69442548040889.0780482250536
Winsorized Mean ( 25 / 36 )26104.3611111111281.07439664930592.873493360839
Winsorized Mean ( 26 / 36 )26126.0277777778264.07619186277698.9336736245948
Winsorized Mean ( 27 / 36 )26001.2777777778241.063672410411107.860622539221
Winsorized Mean ( 28 / 36 )26018.6481481481223.125414411691116.609971198265
Winsorized Mean ( 29 / 36 )26013.8148148148218.232398866152119.202350109206
Winsorized Mean ( 30 / 36 )26051.5925925926211.612295466086123.110013693735
Winsorized Mean ( 31 / 36 )25921.2777777778194.007396754311133.609739687421
Winsorized Mean ( 32 / 36 )25924.8333333333190.465539547007136.112986081322
Winsorized Mean ( 33 / 36 )25912.9166666667180.422370460873143.623634921071
Winsorized Mean ( 34 / 36 )25860.0277777778169.66250500251152.420405306377
Winsorized Mean ( 35 / 36 )25716.1388888889151.288762391262169.980496121595
Winsorized Mean ( 36 / 36 )25716.1388888889148.861755787577172.751817636663
Trimmed Mean ( 1 / 36 )26396.0471698113502.04152657751352.5774179473895
Trimmed Mean ( 2 / 36 )26375.5673076923487.19853354020254.1372058656163
Trimmed Mean ( 3 / 36 )26347.0392156863472.76662229250855.7294825254922
Trimmed Mean ( 4 / 36 )26317.66456.58139398947757.6406755650813
Trimmed Mean ( 5 / 36 )26295.3979591837442.77922154992259.3871543184393
Trimmed Mean ( 6 / 36 )26272.5625427.56516221663561.446920426806
Trimmed Mean ( 7 / 36 )26239.5531914894412.37229538562263.6307372854716
Trimmed Mean ( 8 / 36 )26217.2717391304403.24392457891965.0159125559235
Trimmed Mean ( 9 / 36 )26199.5222222222394.39498418781166.4296537040795
Trimmed Mean ( 10 / 36 )26182.2159090909384.98042414129668.0092136307727
Trimmed Mean ( 11 / 36 )26160.0348837209375.38884589422669.6878321501649
Trimmed Mean ( 12 / 36 )26142.0952380952367.43979591209571.1466083122618
Trimmed Mean ( 13 / 36 )26122.0487804878359.08992033054772.7451462754569
Trimmed Mean ( 14 / 36 )26094.85351.21525509492474.2987373738857
Trimmed Mean ( 15 / 36 )26067.1666666667342.79546876451576.0429149212986
Trimmed Mean ( 16 / 36 )26039.4605263158334.1908318378777.917938032928
Trimmed Mean ( 17 / 36 )26006.0135135135325.16832054739579.9770822376992
Trimmed Mean ( 18 / 36 )25973.0694444444315.23148791446282.3936390881492
Trimmed Mean ( 19 / 36 )25939.1571428571304.07615753295485.3048044059357
Trimmed Mean ( 20 / 36 )25909.2941176471293.42236370139888.300338770407
Trimmed Mean ( 21 / 36 )25886.5757575758285.31953956098890.7283665093761
Trimmed Mean ( 22 / 36 )25861.65625275.81888199335293.7631827926246
Trimmed Mean ( 23 / 36 )25837.2096774194266.45364963151696.966994871904
Trimmed Mean ( 24 / 36 )25813.1666666667256.415645281269100.669234275278
Trimmed Mean ( 25 / 36 )25793.0344827586246.495559960352104.638941516461
Trimmed Mean ( 26 / 36 )25769.0178571429236.271358535757109.065347644510
Trimmed Mean ( 27 / 36 )25741.5555555556226.622713809015113.587712029824
Trimmed Mean ( 28 / 36 )25721.5769230769219.06469279089117.415438313602
Trimmed Mean ( 29 / 36 )25698.66212.755860102990120.789434366507
Trimmed Mean ( 30 / 36 )25674.2083333333205.581494423954124.885794829312
Trimmed Mean ( 31 / 36 )25644.6739130435197.475930299566129.862276755153
Trimmed Mean ( 32 / 36 )25622.7727272727190.981635391202134.163542346821
Trimmed Mean ( 33 / 36 )25598.5183.101500287861139.804971339697
Trimmed Mean ( 34 / 36 )25572.775174.921771846805146.195494877541
Trimmed Mean ( 35 / 36 )25548.7631578947166.694362757051153.267109549054
Trimmed Mean ( 36 / 36 )25534.4166666667160.687675839396158.907125473567
Median25451
Midrange27449
Midmean - Weighted Average at Xnp25692.8
Midmean - Weighted Average at X(n+1)p25741.5555555556
Midmean - Empirical Distribution Function25692.8
Midmean - Empirical Distribution Function - Averaging25741.5555555556
Midmean - Empirical Distribution Function - Interpolation25741.5555555556
Midmean - Closest Observation25692.8
Midmean - True Basic - Statistics Graphics Toolkit25741.5555555556
Midmean - MS Excel (old versions)25769.0178571429
Number of observations108
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Mar/17/t1268866059k2i094blqpcqjq9/15ceb1268866022.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Mar/17/t1268866059k2i094blqpcqjq9/15ceb1268866022.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Mar/17/t1268866059k2i094blqpcqjq9/2jxry1268866022.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Mar/17/t1268866059k2i094blqpcqjq9/2jxry1268866022.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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