opgave 5, oef 2, stap 1

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

Title produced by software: Central Tendency

Date of computation: Sun, 01 Jun 2008 07:52:40 -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/Jun/01/t1212328603xz8pvlve2mr7ar9.htm/, Retrieved Sun, 01 Jun 2008 13:56:44 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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-22 -31 -22 -26 -19 -20 -24 -29 -28 -31 -30 -32 -38 -43 -51 -43 -43 -42 -47 -45 -38 -46 -38 -32 -27 -26 -21 -23 -24 -17 -23 -16 -22 -26 -25 -21 -21 -18 -12 -19 -31 -38 -38 -32 -43 -33 -28 -25 -19 -20 -21 -19 -17 -16 -10 -16 -10 -8 -7 -15 -7 -6 -6 2 -4 -4 -8 -10 -16 -14 -30 -33

Text written by user:

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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean -24.2083333333333 1.41807269359481 -17.071292214199 Geometric Mean NaN Harmonic Mean -19.9406089767443 Quadratic Mean 26.9966561715418 Winsorized Mean ( 1 / 24 ) -24.2361111111111 1.38478952932014 -17.5016568207371 Winsorized Mean ( 2 / 24 ) -24.2083333333333 1.37848115312284 -17.5615990675617 Winsorized Mean ( 3 / 24 ) -24.25 1.35281396866044 -17.9255984649629 Winsorized Mean ( 4 / 24 ) -24.1388888888889 1.3297053863682 -18.1535617862082 Winsorized Mean ( 5 / 24 ) -24.2083333333333 1.31664103796297 -18.3864338383278 Winsorized Mean ( 6 / 24 ) -24.2083333333333 1.31664103796297 -18.3864338383278 Winsorized Mean ( 7 / 24 ) -24.3055555555556 1.29909666593854 -18.7095819678638 Winsorized Mean ( 8 / 24 ) -24.1944444444444 1.27692272541064 -18.9474617085100 Winsorized Mean ( 9 / 24 ) -23.9444444444444 1.14019067552783 -21.0003861269607 Winsorized Mean ( 10 / 24 ) -23.9444444444444 1.14019067552783 -21.0003861269607 Winsorized Mean ( 11 / 24 ) -23.9444444444444 1.14019067552783 -21.0003861269607 Winsorized Mean ( 12 / 24 ) -24.2777777777778 1.08486208895100 -22.3786765387415 Winsorized Mean ( 13 / 24 ) -24.6388888888889 1.02974265506648 -23.9272295535803 Winsorized Mean ( 14 / 24 ) -23.8611111111111 0.835983007151176 -28.5425791038790 Winsorized Mean ( 15 / 24 ) -24.0694444444444 0.805722488234812 -29.8731198345675 Winsorized Mean ( 16 / 24 ) -23.8472222222222 0.771828845099501 -30.8970341982333 Winsorized Mean ( 17 / 24 ) -23.8472222222222 0.771828845099501 -30.8970341982333 Winsorized Mean ( 18 / 24 ) -23.8472222222222 0.771828845099501 -30.8970341982333 Winsorized Mean ( 19 / 24 ) -23.8472222222222 0.69585732640376 -34.2702754104298 Winsorized Mean ( 20 / 24 ) -23.8472222222222 0.69585732640376 -34.2702754104298 Winsorized Mean ( 21 / 24 ) -24.1388888888889 0.656407433029194 -36.7742467166963 Winsorized Mean ( 22 / 24 ) -24.1388888888889 0.572349834593713 -42.1750604785691 Winsorized Mean ( 23 / 24 ) -24.1388888888889 0.572349834593713 -42.1750604785691 Winsorized Mean ( 24 / 24 ) -23.8055555555556 0.525052679706238 -45.3393658877706 Trimmed Mean ( 1 / 24 ) -24.2 1.35554989873125 -17.8525335162139 Trimmed Mean ( 2 / 24 ) -24.1617647058824 1.32073527126675 -18.2941769115533 Trimmed Mean ( 3 / 24 ) -24.1363636363636 1.28318629563066 -18.8097111998076 Trimmed Mean ( 4 / 24 ) -24.09375 1.2499441951829 -19.2758605486979 Trimmed Mean ( 5 / 24 ) -24.0806451612903 1.21842422076795 -19.7637610536934 Trimmed Mean ( 6 / 24 ) -24.05 1.18427192823270 -20.3078359172880 Trimmed Mean ( 7 / 24 ) -24.0172413793103 1.14245238266141 -21.0225316554208 Trimmed Mean ( 8 / 24 ) -23.9642857142857 1.09573087916456 -21.8705944771378 Trimmed Mean ( 9 / 24 ) -23.9259259259259 1.04371663338185 -22.9237756309404 Trimmed Mean ( 10 / 24 ) -23.9230769230769 1.01379852354375 -23.5974667229278 Trimmed Mean ( 11 / 24 ) -23.92 0.975972565690036 -24.5088856397188 Trimmed Mean ( 12 / 24 ) -23.9166666666667 0.927721859556928 -25.7799969034782 Trimmed Mean ( 13 / 24 ) -23.8695652173913 0.87950836928628 -27.1396680815686 Trimmed Mean ( 14 / 24 ) -23.7727272727273 0.83010457857914 -28.6382317194518 Trimmed Mean ( 15 / 24 ) -23.7619047619048 0.814224243932292 -29.1834896086449 Trimmed Mean ( 16 / 24 ) -23.725 0.799027854846446 -29.6923315702922 Trimmed Mean ( 17 / 24 ) -23.7105263157895 0.785635525455365 -30.1800587518576 Trimmed Mean ( 18 / 24 ) -23.6944444444444 0.766169035645306 -30.9258705874061 Trimmed Mean ( 19 / 24 ) -23.6764705882353 0.738211680527952 -32.0727390432273 Trimmed Mean ( 20 / 24 ) -23.65625 0.719275754413491 -32.8889856982454 Trimmed Mean ( 21 / 24 ) -23.6333333333333 0.690632449336569 -34.2198420535204 Trimmed Mean ( 22 / 24 ) -23.5714285714286 0.659542432835452 -35.7390630199367 Trimmed Mean ( 23 / 24 ) -23.5 0.640312423743285 -36.7008340438224 Trimmed Mean ( 24 / 24 ) -23.4166666666667 0.607670375305687 -38.5351460565886 Median -23 Midrange -24.5 Midmean - Weighted Average at Xnp -23.5365853658537 Midmean - Weighted Average at X(n+1)p -23.5365853658537 Midmean - Empirical Distribution Function -23.5365853658537 Midmean - Empirical Distribution Function - Averaging -23.5365853658537 Midmean - Empirical Distribution Function - Interpolation -23.5365853658537 Midmean - Closest Observation -23.5365853658537 Midmean - True Basic - Statistics Graphics Toolkit -23.5365853658537 Midmean - MS Excel (old versions) -23.5365853658537 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212328603xz8pvlve2mr7ar9/1zorw1212328353.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212328603xz8pvlve2mr7ar9/1zorw1212328353.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212328603xz8pvlve2mr7ar9/2wv8j1212328353.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212328603xz8pvlve2mr7ar9/2wv8j1212328353.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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