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Werkloosheid

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 12 Mar 2010 05:41:07 -0700

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/12/t12683977341hmhssx7fzaeha3.htm/, Retrieved Fri, 12 Mar 2010 13:42:16 +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/12/t12683977341hmhssx7fzaeha3.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 «

43657 42811 45419 50846 54500 51035 38675 36214 38763 39486 40540 40719 40471 39947 42683 47090 51520 48823 36122 33812 36928 37737 40123 41713 42025 42169 46352 50939 56139 52713 38532 37860 40880 41988 44576 46728 46913 49357 54709 60819 63695 60109 45544 43596 44431 45575 47980 49211 51374 52954 57529 62960 64530 61008 44964 43480 45429 47616 49364 51010 53188 55317 60106 65845 67028 63617 47605 45844 47925 50156 52258 53476 54327 55214 59347 64718 66208 62744 45587 43684 45676 47088 48907 50964 51798

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	48980.2235294118	887.549015709852	55.1859363961301
Geometric Mean	48323.3908026116
Harmonic Mean	47686.5791949674
Quadratic Mean	49651.1100624678
Winsorized Mean ( 1 / 28 )	48997.7529411765	880.125538363113	55.6713227891377
Winsorized Mean ( 2 / 28 )	48991.3764705882	877.77915045198	55.8128732556042
Winsorized Mean ( 3 / 28 )	48976.8	864.64661938538	56.6437188348858
Winsorized Mean ( 4 / 28 )	49006.0235294118	856.593676981327	57.2103493713742
Winsorized Mean ( 5 / 28 )	48964.1411764706	845.064849276443	57.9412825162405
Winsorized Mean ( 6 / 28 )	49006.0705882353	836.675572193875	58.572369287339
Winsorized Mean ( 7 / 28 )	48963.7411764706	823.825681527495	59.4345894700497
Winsorized Mean ( 8 / 28 )	48951.6941176471	818.501307392156	59.8064947185155
Winsorized Mean ( 9 / 28 )	48844.4352941176	771.57803783711	63.3045951269407
Winsorized Mean ( 10 / 28 )	48876.4352941176	759.699887753682	64.336504561871
Winsorized Mean ( 11 / 28 )	48807.3294117647	739.555648515787	65.9954791903977
Winsorized Mean ( 12 / 28 )	48856.0352941176	732.697362336652	66.6796931523138
Winsorized Mean ( 13 / 28 )	48750.5058823529	710.33103925474	68.630685114789
Winsorized Mean ( 14 / 28 )	48480.5529411765	654.931957144437	74.023801117533
Winsorized Mean ( 15 / 28 )	48263.6705882353	611.876578835795	78.8781140799106
Winsorized Mean ( 16 / 28 )	48265.7411764706	566.465608874218	85.2050687991332
Winsorized Mean ( 17 / 28 )	48300.1411764706	555.909230281121	86.884941903277
Winsorized Mean ( 18 / 28 )	48201.0352941176	539.242766469475	89.3865217881345
Winsorized Mean ( 19 / 28 )	48186.5058823529	528.185066089722	91.2303451498334
Winsorized Mean ( 20 / 28 )	48266.7411764706	506.241072585238	95.34339228934
Winsorized Mean ( 21 / 28 )	48088.1176470588	472.797214160131	101.709815977833
Winsorized Mean ( 22 / 28 )	48186.7294117647	440.156534858654	109.476346698428
Winsorized Mean ( 23 / 28 )	48154.8	427.654201651844	112.602190774693
Winsorized Mean ( 24 / 28 )	48103.9764705882	416.437392598447	115.513105512532
Winsorized Mean ( 25 / 28 )	47978.0941176471	398.035746682183	120.537149031380
Winsorized Mean ( 26 / 28 )	48065.8823529412	351.345423419627	136.805204078420
Winsorized Mean ( 27 / 28 )	48023.6352941176	334.605898394025	143.522978897300
Winsorized Mean ( 28 / 28 )	48103.3529411765	313.151890686138	153.610290634933
Trimmed Mean ( 1 / 28 )	48945.5301204819	862.973770842269	56.717285941044
Trimmed Mean ( 2 / 28 )	48890.7283950617	843.082843053234	57.9904202747187
Trimmed Mean ( 3 / 28 )	48836.582278481	821.404291007276	59.4549880164291
Trimmed Mean ( 4 / 28 )	48784.987012987	801.921556645121	60.8351111261822
Trimmed Mean ( 5 / 28 )	48722.36	781.89374122893	62.313275360692
Trimmed Mean ( 6 / 28 )	48666.0547945205	761.84628036437	63.8791000872839
Trimmed Mean ( 7 / 28 )	48598.2112676056	740.340485026187	65.6430551219776
Trimmed Mean ( 8 / 28 )	48533.884057971	718.032921559594	67.5928395491304
Trimmed Mean ( 9 / 28 )	48467.6268656716	692.6258753993	69.9766332549011
Trimmed Mean ( 10 / 28 )	48412.8769230769	672.831864608495	71.9539003273087
Trimmed Mean ( 11 / 28 )	48350.3333333333	651.402423433859	74.2249822750969
Trimmed Mean ( 12 / 28 )	48292.4426229508	629.696392505745	76.6916298039777
Trimmed Mean ( 13 / 28 )	48224.779661017	604.447040252313	79.7833001893541
Trimmed Mean ( 14 / 28 )	48164.4736842105	578.240048184229	83.2949461654464
Trimmed Mean ( 15 / 28 )	48129.5818181818	557.799213051991	86.2847789885566
Trimmed Mean ( 16 / 28 )	48115.2452830189	541.24767764188	88.8969085145056
Trimmed Mean ( 17 / 28 )	48099.568627451	529.335887474627	90.8677642412004
Trimmed Mean ( 18 / 28 )	48079.1020408163	516.115337763676	93.155731912837
Trimmed Mean ( 19 / 28 )	48066.8510638298	502.491178837181	95.6571042203401
Trimmed Mean ( 20 / 28 )	48054.9555555556	487.066526221221	98.6619957819262
Trimmed Mean ( 21 / 28 )	48034.023255814	471.50687785813	101.873430720700
Trimmed Mean ( 22 / 28 )	48028.6829268293	458.398181953553	104.775029259815
Trimmed Mean ( 23 / 28 )	48013.0256410256	447.886591413634	107.199069053363
Trimmed Mean ( 24 / 28 )	47998.8648648649	436.132670123659	110.055650844170
Trimmed Mean ( 25 / 28 )	47988.2285714286	422.361480620718	113.618856769096
Trimmed Mean ( 26 / 28 )	47989.2727272727	407.697949394857	117.707908019903
Trimmed Mean ( 27 / 28 )	47981.1935483871	399.402878014611	120.132317991539
Trimmed Mean ( 28 / 28 )	47976.5862068966	391.153660347257	122.65406429868
Median	47616
Midrange	50420
Midmean - Weighted Average at Xnp	47904.4523809524
Midmean - Weighted Average at X(n+1)p	48034.023255814
Midmean - Empirical Distribution Function	48034.023255814
Midmean - Empirical Distribution Function - Averaging	48034.023255814
Midmean - Empirical Distribution Function - Interpolation	48034.023255814
Midmean - Closest Observation	47912.4090909091
Midmean - True Basic - Statistics Graphics Toolkit	48034.023255814
Midmean - MS Excel (old versions)	48034.023255814
Number of observations	85

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/12/t12683977341hmhssx7fzaeha3/10grc1268397666.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/12/t12683977341hmhssx7fzaeha3/10grc1268397666.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/12/t12683977341hmhssx7fzaeha3/26lov1268397666.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Mar/12/t12683977341hmhssx7fzaeha3/26lov1268397666.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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