Home » date » 2009 » Apr » 21 »

Silke van den Berg - Centrummaten - aardolie etc

*Unverified author*
R Software Module: rwasp_centraltendency.wasp (opens new window with default values)
Title produced by software: Central Tendency
Date of computation: Tue, 21 Apr 2009 11:47:32 -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/Apr/21/t12403360996f174b3850la74t.htm/, Retrieved Tue, 21 Apr 2009 19:48:21 +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/Apr/21/t12403360996f174b3850la74t.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:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
493395,00 487190,00 519493,00 519453,00 538588,00 438224,00 542034,00 512027,00 619880,00 533737,00 573789,00 589213,00 532168,00 551102,00 593789,00 527106,00 547327,00 601305,00 610872,00 601325,00 642143,00 614216,00 657979,00 673098,00 602297,00 615381,00 703671,00 733852,00 716596,00 745798,00 742027,10 679181,20 739022,70 645410,60 729382,10 671052,70 744954,80 677639,30 778207,20 763316,20 658531,60 831700,10 664156,30 621402,10 683588,70 600023,80 643273,80 653615,90 620177,50 574128,80 599828,00 599369,40 596617,70 616114,60 510226,90 493960,10 634503,30 588556,20 603239,00 617458,20 646543,50 680125,60 731595,80 759600,30 785031,70 849573,30 762342,00 815346,60 929603,20 784057,50 944667,70 1007258,30 664292,70 873207,40 1146510,00 1417266,80 1089387,90 1373379,70 1009397,60 818175,10 1003458,10 961142,70 1121906,60 1141713,30 1042352,60 992223,60 920525,30 1076093,40 967880,40 1236416,10
 
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 Mean730764.31888888921520.099017252733.9572935190974
Geometric Mean706556.022842448
Harmonic Mean685793.49658731
Quadratic Mean758441.622442718
Winsorized Mean ( 1 / 30 )730820.75111111121273.340375075934.3538315199125
Winsorized Mean ( 2 / 30 )727915.00444444520308.866995565035.8422261863945
Winsorized Mean ( 3 / 30 )724936.97111111119520.078210745737.1380157028284
Winsorized Mean ( 4 / 30 )725446.75333333319375.292610204037.4418476111827
Winsorized Mean ( 5 / 30 )724446.38666666719101.328311098437.9264925908709
Winsorized Mean ( 6 / 30 )722773.5418545.522405242938.9729404330864
Winsorized Mean ( 7 / 30 )721742.63444444418317.912883551139.4009207835325
Winsorized Mean ( 8 / 30 )719420.16333333317598.929531708140.8786319666289
Winsorized Mean ( 9 / 30 )716630.86333333316875.461003208442.4658540111636
Winsorized Mean ( 10 / 30 )716567.49666666716807.838610481742.6329353388604
Winsorized Mean ( 11 / 30 )716695.92777777816645.881062707643.0554516806814
Winsorized Mean ( 12 / 30 )715657.46111111116303.015372792543.8972450645813
Winsorized Mean ( 13 / 30 )712905.76555555615552.303743899645.8392388224282
Winsorized Mean ( 14 / 30 )712444.90111111115290.053855971346.5953166563162
Winsorized Mean ( 15 / 30 )713480.23444444414359.347377101549.6875112571072
Winsorized Mean ( 16 / 30 )710862.5113873.149301339051.2401686566862
Winsorized Mean ( 17 / 30 )711872.97111111113276.565469614253.618759515807
Winsorized Mean ( 18 / 30 )702540.75111111111644.055653441560.3347125795874
Winsorized Mean ( 19 / 30 )698517.37444444410732.245615593765.0858542996367
Winsorized Mean ( 20 / 30 )695174.15222222210045.463296343869.2027964977227
Winsorized Mean ( 21 / 30 )692660.3822222229499.245240448972.9174123511195
Winsorized Mean ( 22 / 30 )692081.0733333339384.522535259973.7470735173813
Winsorized Mean ( 23 / 30 )684383.978275.2096927500882.702915746001
Winsorized Mean ( 24 / 30 )684465.8366666678200.7028069531183.4642899248013
Winsorized Mean ( 25 / 30 )682846.3088888897980.0712544776885.568948836859
Winsorized Mean ( 26 / 30 )678825.2644444447381.7128364635591.960399907626
Winsorized Mean ( 27 / 30 )678815.6044444447311.2905841031892.8448399958801
Winsorized Mean ( 28 / 30 )680337.3422222226929.9907021939398.1729083715563
Winsorized Mean ( 29 / 30 )676967.4455555566246.893461473108.368655513444
Winsorized Mean ( 30 / 30 )677074.7122222226168.38289167199109.765350840388
Trimmed Mean ( 1 / 30 )726287.47613636420286.992730536635.8006475273752
Trimmed Mean ( 2 / 30 )721543.35116279119122.642953800237.7324072256131
Trimmed Mean ( 3 / 30 )718129.9654761918378.640853242339.0741606634912
Trimmed Mean ( 4 / 30 )715639.59756097617868.55740022240.0502167876230
Trimmed Mean ( 5 / 30 )712881.33517322.113230285641.1544091371954
Trimmed Mean ( 6 / 30 )710212.47692307716765.367376017942.3618797604759
Trimmed Mean ( 7 / 30 )707733.31973684216262.762505281443.5186407910097
Trimmed Mean ( 8 / 30 )705299.26891891915726.038966845744.8491365439105
Trimmed Mean ( 9 / 30 )703092.87916666715258.923021745746.0774904077228
Trimmed Mean ( 10 / 30 )701158.88142857114862.735845776847.175626930610
Trimmed Mean ( 11 / 30 )699119.50588235314401.596647763248.5445831446015
Trimmed Mean ( 12 / 30 )696940.6106060613877.888933816050.2194976433221
Trimmed Mean ( 13 / 30 )696940.6106060613314.160198075352.3458183045453
Trimmed Mean ( 14 / 30 )692719.60161290312784.578009947654.184002090167
Trimmed Mean ( 15 / 30 )690606.17666666712187.055928791356.6671869483378
Trimmed Mean ( 16 / 30 )688239.89482758611631.281575006059.1714584836908
Trimmed Mean ( 17 / 30 )685967.53392857111044.348569902562.1102756388849
Trimmed Mean ( 18 / 30 )683427.78518518510421.522738051165.5784958075129
Trimmed Mean ( 19 / 30 )68159010010.705622639868.086109580382
Trimmed Mean ( 20 / 30 )679986.3549682.9777311321870.2249218041414
Trimmed Mean ( 21 / 30 )678562.4979166679407.2420678456672.1319269795364
Trimmed Mean ( 22 / 30 )677249.0304347839163.1706172434573.9099007018729
Trimmed Mean ( 23 / 30 )675870.0181818188864.0251458720476.2486575860595
Trimmed Mean ( 24 / 30 )675076.7928571438720.757460556277.4103391718553
Trimmed Mean ( 25 / 30 )674196.578533.899594061879.0021680673546
Trimmed Mean ( 26 / 30 )674196.578325.559892662180.9791267725089
Trimmed Mean ( 27 / 30 )672853.2611111118179.8006747285882.257904301982
Trimmed Mean ( 28 / 30 )672268.7176470597979.4476421818984.250031805865
Trimmed Mean ( 29 / 30 )671458.2531257778.572233429886.3215295783059
Trimmed Mean ( 30 / 30 )670888.3366666677672.110924387387.4450777991383
Median664224.5
Midrange927745.4
Midmean - Weighted Average at Xnp674180.195555556
Midmean - Weighted Average at X(n+1)p677249.030434783
Midmean - Empirical Distribution Function677249.030434783
Midmean - Empirical Distribution Function - Averaging677249.030434783
Midmean - Empirical Distribution Function - Interpolation675870.018181818
Midmean - Closest Observation677249.030434783
Midmean - True Basic - Statistics Graphics Toolkit677249.030434783
Midmean - MS Excel (old versions)677249.030434783
Number of observations90
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/21/t12403360996f174b3850la74t/1t3ib1240336050.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/21/t12403360996f174b3850la74t/1t3ib1240336050.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/21/t12403360996f174b3850la74t/21l031240336050.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/21/t12403360996f174b3850la74t/21l031240336050.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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