Home » date » 2009 » Apr » 22 »

Werkloosheidcentrummaten-Datareeks-Robin Bosmans

*Unverified author*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 22 Apr 2009 12:09:53 -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/22/t1240423867dyukmrmowraeh3r.htm/, Retrieved Wed, 22 Apr 2009 20:11:09 +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/22/t1240423867dyukmrmowraeh3r.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 «

467 460 448 443 436 431 484 510 513 503 471 471 476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	537.164948453608	5.09623202420979	105.404335183679
Geometric Mean	534.818000949388
Harmonic Mean	532.447746196509
Quadratic Mean	539.48072589134
Winsorized Mean ( 1 / 32 )	537.20618556701	5.08336723576795	105.679200547834
Winsorized Mean ( 2 / 32 )	537.309278350515	5.04673946374647	106.466617151590
Winsorized Mean ( 3 / 32 )	537.309278350515	4.98960174830503	107.685804489915
Winsorized Mean ( 4 / 32 )	537.556701030928	4.93031267245247	109.030955386351
Winsorized Mean ( 5 / 32 )	537.60824742268	4.92136526395044	109.239655784284
Winsorized Mean ( 6 / 32 )	537.422680412371	4.8059830590621	111.823673493608
Winsorized Mean ( 7 / 32 )	537.422680412371	4.7821491849609	112.380994324159
Winsorized Mean ( 8 / 32 )	537.835051546392	4.68859936506559	114.711240963295
Winsorized Mean ( 9 / 32 )	538.020618556701	4.65968072271000	115.462979241161
Winsorized Mean ( 10 / 32 )	536.680412371134	4.42298904914005	121.338851715104
Winsorized Mean ( 11 / 32 )	536.567010309278	4.37333442071753	122.690596851554
Winsorized Mean ( 12 / 32 )	536.567010309278	4.37333442071753	122.690596851554
Winsorized Mean ( 13 / 32 )	536.969072164948	4.27231491629999	125.685742433516
Winsorized Mean ( 14 / 32 )	537.113402061856	4.25060325940569	126.361687808275
Winsorized Mean ( 15 / 32 )	537.268041237113	4.18310799484616	128.437525853758
Winsorized Mean ( 16 / 32 )	537.927835051546	3.99468739295257	134.660808753285
Winsorized Mean ( 17 / 32 )	538.80412371134	3.82647224702191	140.809625401225
Winsorized Mean ( 18 / 32 )	539.175257731959	3.7277118380483	144.639736427227
Winsorized Mean ( 19 / 32 )	540.154639175258	3.55351032238464	152.005929396817
Winsorized Mean ( 20 / 32 )	539.742268041237	3.39012863388992	159.209967033588
Winsorized Mean ( 21 / 32 )	539.092783505155	3.24864769890678	165.943750590921
Winsorized Mean ( 22 / 32 )	539.319587628866	3.22184294951753	167.394747689247
Winsorized Mean ( 23 / 32 )	539.556701030928	3.07760342506305	175.317162905703
Winsorized Mean ( 24 / 32 )	538.814432989691	2.92302926153139	184.334259010258
Winsorized Mean ( 25 / 32 )	538.814432989691	2.86176844284610	188.280234320366
Winsorized Mean ( 26 / 32 )	539.082474226804	2.83190547088442	190.360335035635
Winsorized Mean ( 27 / 32 )	539.082474226804	2.83190547088442	190.360335035635
Winsorized Mean ( 28 / 32 )	538.216494845361	2.65823247948238	202.471566726987
Winsorized Mean ( 29 / 32 )	538.216494845361	2.65823247948238	202.471566726987
Winsorized Mean ( 30 / 32 )	537.59793814433	2.58426127028683	208.027703826039
Winsorized Mean ( 31 / 32 )	537.59793814433	2.51108623496436	214.089795347852
Winsorized Mean ( 32 / 32 )	537.59793814433	2.43606651362580	220.682783141327
Trimmed Mean ( 1 / 32 )	537.315789473684	4.98756040825134	107.731184284958
Trimmed Mean ( 2 / 32 )	537.430107526882	4.87873992790344	110.157564344249
Trimmed Mean ( 3 / 32 )	537.494505494505	4.77693823057189	112.518621667452
Trimmed Mean ( 4 / 32 )	537.561797752809	4.68499427562733	114.741185608136
Trimmed Mean ( 5 / 32 )	537.563218390805	4.59962636783870	116.871061995281
Trimmed Mean ( 6 / 32 )	537.552941176471	4.5040444284603	119.348942870049
Trimmed Mean ( 7 / 32 )	537.552941176471	4.42288283695811	121.539041614355
Trimmed Mean ( 8 / 32 )	537.604938271605	4.33431894105899	124.034466679153
Trimmed Mean ( 9 / 32 )	537.569620253165	4.25118818163023	126.451617121080
Trimmed Mean ( 10 / 32 )	537.506493506493	4.15993582751844	129.210284916134
Trimmed Mean ( 11 / 32 )	537.613333333333	4.09728072132107	131.212228280027
Trimmed Mean ( 12 / 32 )	537.739726027397	4.03183806565866	133.373344184534
Trimmed Mean ( 13 / 32 )	537.87323943662	3.95410947260111	136.028919574347
Trimmed Mean ( 14 / 32 )	537.87323943662	3.87908523014337	138.659814756568
Trimmed Mean ( 15 / 32 )	538.059701492537	3.79309285588876	141.852499249314
Trimmed Mean ( 16 / 32 )	538.138461538462	3.70147299961298	145.384948531228
Trimmed Mean ( 17 / 32 )	538.15873015873	3.6229912667573	148.539891635014
Trimmed Mean ( 18 / 32 )	538.098360655738	3.55531656979984	151.350336908545
Trimmed Mean ( 19 / 32 )	538	3.48822851384709	154.233014799438
Trimmed Mean ( 20 / 32 )	537.80701754386	3.43279906145084	156.667200123435
Trimmed Mean ( 21 / 32 )	537.636363636364	3.38966180651322	158.610620859963
Trimmed Mean ( 22 / 32 )	537.509433962264	3.35703479481182	160.114346980545
Trimmed Mean ( 23 / 32 )	537.352941176471	3.31731329151294	161.984381321849
Trimmed Mean ( 24 / 32 )	537.163265306122	3.28782889236794	163.379325047311
Trimmed Mean ( 25 / 32 )	537.163265306122	3.27275204950250	164.131977363754
Trimmed Mean ( 26 / 32 )	536.866666666667	3.25818317099539	164.774857179884
Trimmed Mean ( 27 / 32 )	536.674418604651	3.23801494538329	165.741797878306
Trimmed Mean ( 28 / 32 )	536.674418604651	3.20519729634649	167.438809216640
Trimmed Mean ( 29 / 32 )	536.307692307692	3.19077487873922	168.080705373863
Trimmed Mean ( 30 / 32 )	536.135135135135	3.16302829440941	169.500581478434
Trimmed Mean ( 31 / 32 )	536.135135135135	3.13425101288405	171.056859495691
Trimmed Mean ( 32 / 32 )	535.848484848485	3.10245540957665	172.717545978076
Median	532
Midrange	530
Midmean - Weighted Average at Xnp	536.395833333333
Midmean - Weighted Average at X(n+1)p	537.163265306122
Midmean - Empirical Distribution Function	537.163265306122
Midmean - Empirical Distribution Function - Averaging	537.163265306122
Midmean - Empirical Distribution Function - Interpolation	537.163265306122
Midmean - Closest Observation	536.54
Midmean - True Basic - Statistics Graphics Toolkit	537.163265306122
Midmean - MS Excel (old versions)	537.163265306122
Number of observations	97

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240423867dyukmrmowraeh3r/12ql71240423789.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240423867dyukmrmowraeh3r/12ql71240423789.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240423867dyukmrmowraeh3r/2n4491240423789.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Apr/22/t1240423867dyukmrmowraeh3r/2n4491240423789.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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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