IKO opdracht 5 werknemers Marin Peeters MAR 201B

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 18 May 2011 14:52:50 +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/May/18/t1305730182vkmvwsi9np0wy9b.htm/, Retrieved Wed, 18 May 2011 16:49:44 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

3893,9 3799,2 3769,6 3768,6 3854,9 3778,5 3779,7 3803,2 3900,3 3792,6 3767,4 3752,6 3829,6 3722,6 3692,9 3681 3762,9 3661,7 3633,1 3621,5 3710 3619,4 3595,2 3573,2 3650,1 3554,2 3537 3528,6 3597,1 3521,9 3516,5 3515,7 3600,2 3517,1 3513,7 3528,2 3608,3 3502,5 3502,5 3495,3 3543,8 3425,3 3418,4 3406,4 3446,1 3341,1 3347 3354,9 3399 3288,9 3279 3275,2 3314 3227,1 3225,3 3228,6 3287,1 3210,1 3213,1 3228 3287 3211 3199,8 3166,3 3164 3156,7 3156 3165,5 3179,2 3182,5 3179,5 3193,5 3219,6 3221,9 3210,1

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 'Gwilym Jenkins' @ www.wessa.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 3477.38 26.2389289223282 132.527513234006 Geometric Mean 3470.07040612634 Harmonic Mean 3462.78930305835 Quadratic Mean 3484.69787604798 Winsorized Mean ( 1 / 25 ) 3477.304 26.2189307469529 132.62569833837 Winsorized Mean ( 2 / 25 ) 3476.45866666667 25.9729374121183 133.849268240436 Winsorized Mean ( 3 / 25 ) 3475.50666666667 25.7695725550439 134.868619153188 Winsorized Mean ( 4 / 25 ) 3474.14133333333 25.5091411344525 136.192015051466 Winsorized Mean ( 5 / 25 ) 3474.73466666667 25.3248698399105 137.206417589981 Winsorized Mean ( 6 / 25 ) 3474.23066666667 25.2303563745498 137.700419886703 Winsorized Mean ( 7 / 25 ) 3473.30666666667 24.9838003249842 139.022351343135 Winsorized Mean ( 8 / 25 ) 3474.352 24.7804372391967 140.205435701692 Winsorized Mean ( 9 / 25 ) 3474.04 24.4896689378334 141.857368869248 Winsorized Mean ( 10 / 25 ) 3475.28 24.2625633843991 143.236307925923 Winsorized Mean ( 11 / 25 ) 3475.104 24.2338433920323 143.398797449626 Winsorized Mean ( 12 / 25 ) 3474.528 24.095662019213 144.197241695602 Winsorized Mean ( 13 / 25 ) 3473.10666666667 23.7555322590952 146.202014283933 Winsorized Mean ( 14 / 25 ) 3468.72 22.7071372674515 152.759018415416 Winsorized Mean ( 15 / 25 ) 3466.66 22.2623372820839 155.718600256312 Winsorized Mean ( 16 / 25 ) 3463.73733333333 21.6236526131996 160.182805157487 Winsorized Mean ( 17 / 25 ) 3461.448 21.1806466447153 163.42503881314 Winsorized Mean ( 18 / 25 ) 3457.032 20.5112979774738 168.542819854532 Winsorized Mean ( 19 / 25 ) 3454.24533333333 20.0966159397105 171.881939909485 Winsorized Mean ( 20 / 25 ) 3462.13866666667 17.666861215315 195.967955171653 Winsorized Mean ( 21 / 25 ) 3459.95466666667 17.0948509494814 202.397474940934 Winsorized Mean ( 22 / 25 ) 3461.68533333333 16.6822765846886 207.50677017971 Winsorized Mean ( 23 / 25 ) 3458.312 16.2480978745372 212.844114228263 Winsorized Mean ( 24 / 25 ) 3456.296 15.8452159989712 218.128676833715 Winsorized Mean ( 25 / 25 ) 3463.62933333333 14.538011038273 238.246437164955 Trimmed Mean ( 1 / 25 ) 3475.98904109589 25.9477289341543 133.96120523367 Trimmed Mean ( 2 / 25 ) 3474.6 25.6192991891986 135.624318773908 Trimmed Mean ( 3 / 25 ) 3473.58985507246 25.3739346716284 136.895987950833 Trimmed Mean ( 4 / 25 ) 3472.87462686567 25.1597532004863 138.032936936701 Trimmed Mean ( 5 / 25 ) 3472.50923076923 24.9811118766102 139.005391270055 Trimmed Mean ( 6 / 25 ) 3471.97936507936 24.8049116379346 139.971446613404 Trimmed Mean ( 7 / 25 ) 3471.51803278689 24.6003195932188 141.116785886953 Trimmed Mean ( 8 / 25 ) 3471.19322033898 24.3946546425244 142.293189684598 Trimmed Mean ( 9 / 25 ) 3470.67368421053 24.1708557245211 143.589193687072 Trimmed Mean ( 10 / 25 ) 3470.16363636364 23.9395929412519 144.954997559042 Trimmed Mean ( 11 / 25 ) 3469.43962264151 23.6799081577633 146.51406582859 Trimmed Mean ( 12 / 25 ) 3468.68235294118 23.3416852905483 148.604623435041 Trimmed Mean ( 13 / 25 ) 3467.93673469388 22.927124396906 151.259123240151 Trimmed Mean ( 14 / 25 ) 3467.30212765957 22.4570931189668 154.396747134257 Trimmed Mean ( 15 / 25 ) 3467.13333333333 22.0628972336689 157.147689925435 Trimmed Mean ( 16 / 25 ) 3467.18837209302 21.6265968714529 160.320571595326 Trimmed Mean ( 17 / 25 ) 3467.58292682927 21.173234341233 163.771999636185 Trimmed Mean ( 18 / 25 ) 3468.27692307692 20.647807051916 167.973137019173 Trimmed Mean ( 19 / 25 ) 3469.54324324324 20.0715520154376 172.858742591242 Trimmed Mean ( 20 / 25 ) 3471.26857142857 19.356464523449 179.333812082438 Trimmed Mean ( 21 / 25 ) 3472.30606060606 18.9994198173947 182.758531259308 Trimmed Mean ( 22 / 25 ) 3473.72903225806 18.5930928286965 186.829004956977 Trimmed Mean ( 23 / 25 ) 3475.14482758621 18.0774875552582 192.236051440422 Trimmed Mean ( 24 / 25 ) 3477.17777777778 17.3843450003766 200.017761825508 Trimmed Mean ( 25 / 25 ) 3479.788 16.4013173454655 212.165152755981 Median 3513.7 Midrange 3528.15 Midmean - Weighted Average at Xnp 3463.18684210526 Midmean - Weighted Average at X(n+1)p 3468.27692307692 Midmean - Empirical Distribution Function 3468.27692307692 Midmean - Empirical Distribution Function - Averaging 3468.27692307692 Midmean - Empirical Distribution Function - Interpolation 3469.54324324324 Midmean - Closest Observation 3463.18684210526 Midmean - True Basic - Statistics Graphics Toolkit 3468.27692307692 Midmean - MS Excel (old versions) 3468.27692307692 Number of observations 75

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305730182vkmvwsi9np0wy9b/1vyj51305730367.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305730182vkmvwsi9np0wy9b/1vyj51305730367.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305730182vkmvwsi9np0wy9b/2pdt81305730367.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305730182vkmvwsi9np0wy9b/2pdt81305730367.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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