stephanie De Coninck - opgave 5

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

Title produced by software: Central Tendency

Date of computation: Mon, 21 Apr 2008 14:34:55 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/21/t1208810191ed6yh3l0x34fhun.htm/, Retrieved Mon, 21 Apr 2008 22:36:33 +0200

User-defined keywords:

robuustheid eigen reeks

Dataseries X:

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68,64 68,61 68,61 68,61 68,58 68,75 68,54 68,5 68,47 68,47 68,47 68,59 68,32 67,86 67,91 67,91 68,05 68,15 68,25 68,25 68,31 68,31 69,65 69,65 70,18 70,08 70,08 70,09 70,04 70,14 70,26 70,23 70,54 70,54 70,57 70,61 70,63 70,45 70,4 70,4 70,33 70,51 70,45 70,39 70,59 70,59 70,32 70,94 70,44 70,57 70,61 70,61 70,68 69,96 70,11 70,22 70,49 70,49 70,58 70,85 70,69 70,7 70,7 70,7 70,67 70,64 70,98 70,75 70,88 70,88 70,92 70,89 71,02 71,01 71,02

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 69.8784 0.118318556113235 590.595442469091 Geometric Mean 69.8709319864616 Harmonic Mean 69.8634089121463 Quadratic Mean 69.8858121032684 Winsorized Mean ( 1 / 25 ) 69.8790666666667 0.118166651799895 591.360300070115 Winsorized Mean ( 2 / 25 ) 69.8788 0.118132001294017 591.531500647986 Winsorized Mean ( 3 / 25 ) 69.8832 0.116753248696047 598.554650774063 Winsorized Mean ( 4 / 25 ) 69.8864 0.115377896926140 605.717402222525 Winsorized Mean ( 5 / 25 ) 69.8917333333333 0.113886837042968 613.69456864417 Winsorized Mean ( 6 / 25 ) 69.8893333333333 0.113597572194164 615.23615323289 Winsorized Mean ( 7 / 25 ) 69.894 0.112407399326839 621.791807466111 Winsorized Mean ( 8 / 25 ) 69.894 0.112407399326839 621.791807466111 Winsorized Mean ( 9 / 25 ) 69.8916 0.111757143391817 625.388211248048 Winsorized Mean ( 10 / 25 ) 69.8982666666667 0.10654921010582 656.018628361926 Winsorized Mean ( 11 / 25 ) 69.8909333333333 0.105774053483784 660.756877810759 Winsorized Mean ( 12 / 25 ) 69.8909333333333 0.105774053483784 660.756877810759 Winsorized Mean ( 13 / 25 ) 69.8961333333334 0.1048341278132 666.730718243573 Winsorized Mean ( 14 / 25 ) 69.9017333333333 0.103304216763892 676.659051518662 Winsorized Mean ( 15 / 25 ) 69.9077333333333 0.101680044607934 687.52658009631 Winsorized Mean ( 16 / 25 ) 69.9077333333333 0.101085740670813 691.568690790806 Winsorized Mean ( 17 / 25 ) 69.9054666666667 0.0996026869881293 701.843180947498 Winsorized Mean ( 18 / 25 ) 69.9030666666667 0.099364462139823 703.50168622964 Winsorized Mean ( 19 / 25 ) 69.898 0.0988674606469428 706.986904919171 Winsorized Mean ( 20 / 25 ) 69.906 0.0974611033523972 717.270763365317 Winsorized Mean ( 21 / 25 ) 69.9368 0.0920748148601534 759.56492669817 Winsorized Mean ( 22 / 25 ) 70.1949333333333 0.0470638337202191 1491.48354021948 Winsorized Mean ( 23 / 25 ) 70.1949333333333 0.0470638337202191 1491.48354021948 Winsorized Mean ( 24 / 25 ) 70.2909333333333 0.0318007158020938 2210.35695456595 Winsorized Mean ( 25 / 25 ) 70.3142666666667 0.0277246261452677 2536.16644993673 Trimmed Mean ( 1 / 25 ) 69.8904109589041 0.117291451370260 595.869606372911 Trimmed Mean ( 2 / 25 ) 69.9023943661972 0.116193910081334 601.601188197095 Trimmed Mean ( 3 / 25 ) 69.9152173913044 0.114852217713506 608.740682445547 Trimmed Mean ( 4 / 25 ) 69.9271641791045 0.113803095514258 614.45748784877 Trimmed Mean ( 5 / 25 ) 69.9389230769231 0.112955088734443 619.174610551182 Trimmed Mean ( 6 / 25 ) 69.9501587301587 0.112293388145394 622.923218236049 Trimmed Mean ( 7 / 25 ) 69.9626229508197 0.111461454446309 627.684460949869 Trimmed Mean ( 8 / 25 ) 69.9750847457627 0.110639016563111 632.463003734739 Trimmed Mean ( 9 / 25 ) 69.9884210526316 0.109520425726133 639.044457584971 Trimmed Mean ( 10 / 25 ) 70.0030909090909 0.108167121204092 647.175316582641 Trimmed Mean ( 11 / 25 ) 70.0179245283019 0.107466995807990 651.529560325682 Trimmed Mean ( 12 / 25 ) 70.0349019607843 0.106556575251529 657.255563961822 Trimmed Mean ( 13 / 25 ) 70.0532653061225 0.105232326288941 665.701004402147 Trimmed Mean ( 14 / 25 ) 70.0725531914894 0.103583555713967 676.483373335689 Trimmed Mean ( 15 / 25 ) 70.0928888888889 0.101624990077762 689.720991217363 Trimmed Mean ( 16 / 25 ) 70.1144186046512 0.099264349644032 706.340381577935 Trimmed Mean ( 17 / 25 ) 70.1380487804878 0.0960812787989083 729.986628584347 Trimmed Mean ( 18 / 25 ) 70.164358974359 0.0919351080124588 763.19439321103 Trimmed Mean ( 19 / 25 ) 70.1937837837838 0.0860418846179656 815.809464140064 Trimmed Mean ( 20 / 25 ) 70.2271428571429 0.0774624565377909 906.595865868026 Trimmed Mean ( 21 / 25 ) 70.2636363636364 0.0647764485906028 1084.70961116923 Trimmed Mean ( 22 / 25 ) 70.3012903225806 0.0460942044627118 1525.16549839690 Trimmed Mean ( 23 / 25 ) 70.3137931034483 0.0424595251868118 1656.01929823954 Trimmed Mean ( 24 / 25 ) 70.3281481481481 0.0366201610166864 1920.47621298285 Trimmed Mean ( 25 / 25 ) 70.3328 0.0351639967390889 2000.13668872335 Median 70.39 Midrange 69.44 Midmean - Weighted Average at Xnp 70.1125641025641 Midmean - Weighted Average at X(n+1)p 70.1255 Midmean - Empirical Distribution Function 70.1255 Midmean - Empirical Distribution Function - Averaging 70.1255 Midmean - Empirical Distribution Function - Interpolation 70.1125641025641 Midmean - Closest Observation 70.1125641025641 Midmean - True Basic - Statistics Graphics Toolkit 70.1255 Midmean - MS Excel (old versions) 70.1255 Number of observations 75

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208810191ed6yh3l0x34fhun/1mf0t1208810092.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208810191ed6yh3l0x34fhun/1mf0t1208810092.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208810191ed6yh3l0x34fhun/2xwlm1208810092.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t1208810191ed6yh3l0x34fhun/2xwlm1208810092.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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