Berekening Centrummaten (eigen reeks) - Yesse De Ley

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 29 Mar 2011 16:52:51 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Mar/29/t1301417548xi9t6acik9ydxdf.htm/, Retrieved Tue, 29 Mar 2011 18:52:29 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

15,57 12,73 13,56 15,54 17,22 12,14 11,07 12,02 11,55 6,92 10,33 8,38 12,11 11,46 12,75 13,32 13 11,9 11,79 12,55 11,84 11,25 11,15 10,99 11,7 14,01 17,51 17,27 16,9 15,79 15,45 16,24 16,71 16,77 16,64 17,8 16,87 16,13 15,76 15,66 15,54 15,3 15,05 14,69 14,39 14,18 13,7 13,66 13,27 13,56 13,14 14,19 22,57 23,09 23,31 22,91 22,36 43,06 64,67 64,68 56,9 48,79 45,21 41,4 22,17 25,52 20,28 22,87 27,63 22,95 21,35 18,38 17,15 18,27 19,4 20,52

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 2 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 19.1376315789474 1.33745534594645 14.3089873145668 Geometric Mean 17.0553994410916 Harmonic Mean 15.7511002790208 Quadratic Mean 22.3698000132227 Winsorized Mean ( 1 / 25 ) 19.1567105263158 1.3351918501764 14.3475340444783 Winsorized Mean ( 2 / 25 ) 19.0035526315789 1.2417841678153 15.3034264118637 Winsorized Mean ( 3 / 25 ) 18.7094736842105 1.11632394680097 16.7598963883431 Winsorized Mean ( 4 / 25 ) 18.5252631578947 1.05010331110273 17.6413720079037 Winsorized Mean ( 5 / 25 ) 18.3890789473684 1.0024124965553 18.344822127179 Winsorized Mean ( 6 / 25 ) 18.2659210526316 0.959060654789894 19.0456369588357 Winsorized Mean ( 7 / 25 ) 17.0169736842105 0.588110146615555 28.9350112085967 Winsorized Mean ( 8 / 25 ) 16.8043421052632 0.535973760012536 31.3529194132006 Winsorized Mean ( 9 / 25 ) 16.5603947368421 0.480527467524224 34.4629513525307 Winsorized Mean ( 10 / 25 ) 16.5432894736842 0.47355758419584 34.9340608740895 Winsorized Mean ( 11 / 25 ) 16.5302631578947 0.468873490350896 35.255273539828 Winsorized Mean ( 12 / 25 ) 16.5334210526316 0.466462256709416 35.4442847514909 Winsorized Mean ( 13 / 25 ) 16.5471052631579 0.46251637489417 35.7762582285742 Winsorized Mean ( 14 / 25 ) 16.5084210526316 0.450358728463058 36.6561587669678 Winsorized Mean ( 15 / 25 ) 16.4728947368421 0.442188251400717 37.2531262073586 Winsorized Mean ( 16 / 25 ) 16.5192105263158 0.424054480245247 38.9553967611947 Winsorized Mean ( 17 / 25 ) 16.3760526315789 0.386975454996933 42.3180654486439 Winsorized Mean ( 18 / 25 ) 16.1842105263158 0.353414088578172 45.7939030994119 Winsorized Mean ( 19 / 25 ) 16.1867105263158 0.335620053985335 48.2292709690794 Winsorized Mean ( 20 / 25 ) 15.9919736842105 0.294130059532498 54.3704159637026 Winsorized Mean ( 21 / 25 ) 15.7460526315789 0.247498579045885 63.620779934497 Winsorized Mean ( 22 / 25 ) 15.7286842105263 0.241071900325402 65.2447846028324 Winsorized Mean ( 23 / 25 ) 15.6590789473684 0.211826408375629 73.9241111032786 Winsorized Mean ( 24 / 25 ) 15.5675 0.199710678891135 77.950263283047 Winsorized Mean ( 25 / 25 ) 15.5214473684211 0.185208342045021 83.8053361799872 Trimmed Mean ( 1 / 25 ) 18.6872972972973 1.21371433688891 15.3967838471762 Trimmed Mean ( 2 / 25 ) 18.1918055555556 1.05773970128776 17.1987546022974 Trimmed Mean ( 3 / 25 ) 17.7511428571429 0.926451444603189 19.1603596287185 Trimmed Mean ( 4 / 25 ) 17.3941176470588 0.828574524969352 20.9928221576716 Trimmed Mean ( 5 / 25 ) 17.0684848484849 0.733345091315706 23.274833431914 Trimmed Mean ( 6 / 25 ) 16.75484375 0.628020004933443 26.6788376459053 Trimmed Mean ( 7 / 25 ) 16.4461290322581 0.500307063556431 32.8720704348062 Trimmed Mean ( 8 / 25 ) 16.3428333333333 0.474216874011234 34.4627832305819 Trimmed Mean ( 9 / 25 ) 16.2672413793103 0.456371827123301 35.6447098889724 Trimmed Mean ( 10 / 25 ) 16.2230357142857 0.447934793466179 36.2174047448954 Trimmed Mean ( 11 / 25 ) 16.177962962963 0.438802638312387 36.868426828933 Trimmed Mean ( 12 / 25 ) 16.1311538461538 0.42820934937994 37.6711855299569 Trimmed Mean ( 13 / 25 ) 16.0802 0.415168565716606 38.7317377274086 Trimmed Mean ( 14 / 25 ) 16.0233333333333 0.399219243935124 40.136675715806 Trimmed Mean ( 15 / 25 ) 15.9660869565217 0.381472164636366 41.8538714921474 Trimmed Mean ( 16 / 25 ) 15.9077272727273 0.360260045794437 44.1562350819334 Trimmed Mean ( 17 / 25 ) 15.8385714285714 0.336396765944688 47.0830074245591 Trimmed Mean ( 18 / 25 ) 15.7785 0.314889999108358 50.107974355103 Trimmed Mean ( 19 / 25 ) 15.7334210526316 0.295716281195066 53.2044464682457 Trimmed Mean ( 20 / 25 ) 15.6830555555556 0.274176637376792 57.2005540136624 Trimmed Mean ( 21 / 25 ) 15.6485294117647 0.257497947434126 60.7714724241363 Trimmed Mean ( 22 / 25 ) 15.6375 0.248528329663162 62.9203922997188 Trimmed Mean ( 23 / 25 ) 15.627 0.237244793312778 65.8686742153186 Trimmed Mean ( 24 / 25 ) 15.6232142857143 0.229944813698719 67.9433209838961 Trimmed Mean ( 25 / 25 ) 15.63 0.222417486860945 70.2732515351721 Median 15.615 Midrange 35.8 Midmean - Weighted Average at Xnp 15.6569230769231 Midmean - Weighted Average at X(n+1)p 15.7334210526316 Midmean - Empirical Distribution Function 15.6569230769231 Midmean - Empirical Distribution Function - Averaging 15.7334210526316 Midmean - Empirical Distribution Function - Interpolation 15.7334210526316 Midmean - Closest Observation 15.6569230769231 Midmean - True Basic - Statistics Graphics Toolkit 15.7334210526316 Midmean - MS Excel (old versions) 15.7785 Number of observations 76

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Mar/29/t1301417548xi9t6acik9ydxdf/1fj0o1301417566.png (open in new window) http://www.freestatistics.org/blog/date/2011/Mar/29/t1301417548xi9t6acik9ydxdf/1fj0o1301417566.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Mar/29/t1301417548xi9t6acik9ydxdf/2snj21301417566.png (open in new window) http://www.freestatistics.org/blog/date/2011/Mar/29/t1301417548xi9t6acik9ydxdf/2snj21301417566.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')

Copyright

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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