opgave 5(oefening2)

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

Title produced by software: Central Tendency

Date of computation: Tue, 15 Apr 2008 07:54:15 -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/15/t1208267710jqghuhhmwixqmps.htm/, Retrieved Tue, 15 Apr 2008 15:55:10 +0200

User-defined keywords:

Inleiding tot kwanitatief onderzoek

Dataseries X:

» Textbox « » Textfile « » CSV «

107,5 107,5 113,3 107,8 104,5 105,1 104,2 106,6 103,8 107,7 106,4 110 113,2 113,9 112 113,9 113,1 111,7 110,7 113,5 114 112,7 112,2 115,8 118,4 118,8 123,9 118 120,2 118,7 119,8 124,8 121,3 120,2 118,3 129,6 130,2 127,19 133,1 129,12 123,28 123,36 124,13 126,96 127,14 123,7 123,67 130,19 134,01 124,96 129,96 128,32 132,38 126,25 128,91 131,42 129,44 126,86 126,71 131,63 132,78 126,61 132,84 123,14 128,13 125,49 126,48 130,86 127,32 126,56 126,64 129,26 126,47 135,38 135,5 132,22 122,62 125,16 128,5 133,86 128,87 125,07 125,25 132,16 130,24

Text written by user:

Kara Van den Acker

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 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 122.157647058824 0.950153100549296 128.566277359094 Geometric Mean 121.837576670426 Harmonic Mean 121.50806797471 Quadratic Mean 122.46764949065 Winsorized Mean ( 1 / 28 ) 122.160941176471 0.948846588969251 128.746778032027 Winsorized Mean ( 2 / 28 ) 122.135764705882 0.942172431191454 129.632072285783 Winsorized Mean ( 3 / 28 ) 122.151647058824 0.936727210485738 130.402582194107 Winsorized Mean ( 4 / 28 ) 122.177058823529 0.91864752346467 132.996667059788 Winsorized Mean ( 5 / 28 ) 122.173529411765 0.914106989580578 133.653424385062 Winsorized Mean ( 6 / 28 ) 122.232823529412 0.900889128371554 135.680207119781 Winsorized Mean ( 7 / 28 ) 122.199882352941 0.896366482519113 136.328036284350 Winsorized Mean ( 8 / 28 ) 122.203647058824 0.89067839702129 137.202886549748 Winsorized Mean ( 9 / 28 ) 122.207882352941 0.887780083143176 137.655580107481 Winsorized Mean ( 10 / 28 ) 122.404352941176 0.831446420268653 147.218569900903 Winsorized Mean ( 11 / 28 ) 122.467764705882 0.812006219299611 150.821215152164 Winsorized Mean ( 12 / 28 ) 122.529882352941 0.777887599516979 157.516178981417 Winsorized Mean ( 13 / 28 ) 122.480941176471 0.758489591255438 161.480055347553 Winsorized Mean ( 14 / 28 ) 122.507294117647 0.752291371606577 162.845539296859 Winsorized Mean ( 15 / 28 ) 122.593764705882 0.737835694410317 166.153204073246 Winsorized Mean ( 16 / 28 ) 122.625764705882 0.720624308706622 170.166011920929 Winsorized Mean ( 17 / 28 ) 122.573764705882 0.708865665379413 172.915364211181 Winsorized Mean ( 18 / 28 ) 122.561058823529 0.701558170222046 174.698355782441 Winsorized Mean ( 19 / 28 ) 122.565529411765 0.689875836388374 177.663172047622 Winsorized Mean ( 20 / 28 ) 122.626705882353 0.671432587501092 182.634426992499 Winsorized Mean ( 21 / 28 ) 122.574823529412 0.665506012317232 184.182894310177 Winsorized Mean ( 22 / 28 ) 122.590352941176 0.660320893195455 185.652694325530 Winsorized Mean ( 23 / 28 ) 122.977294117647 0.574918150019877 213.904003749743 Winsorized Mean ( 24 / 28 ) 123.547647058824 0.47979321663602 257.501862833857 Winsorized Mean ( 25 / 28 ) 123.58 0.461113984219278 268.003149393172 Winsorized Mean ( 26 / 28 ) 123.362823529412 0.428723256403993 287.744650393225 Winsorized Mean ( 27 / 28 ) 123.416823529412 0.411123221006247 300.194241588549 Winsorized Mean ( 28 / 28 ) 123.433294117647 0.40483199780794 304.900044428321 Trimmed Mean ( 1 / 28 ) 122.218072289157 0.933476599488952 130.927837244198 Trimmed Mean ( 2 / 28 ) 122.278024691358 0.915607475937358 133.548521506091 Trimmed Mean ( 3 / 28 ) 122.354556962025 0.898831146169216 136.126298563969 Trimmed Mean ( 4 / 28 ) 122.429220779221 0.881547348020654 138.879915020007 Trimmed Mean ( 5 / 28 ) 122.500666666667 0.867486320650946 141.213369883164 Trimmed Mean ( 6 / 28 ) 122.576849315068 0.852116933148979 143.849798714935 Trimmed Mean ( 7 / 28 ) 122.645492957746 0.837338958089075 146.470544303397 Trimmed Mean ( 8 / 28 ) 122.723913043478 0.820672488922743 149.540669024463 Trimmed Mean ( 9 / 28 ) 122.806417910448 0.801926662949642 153.139212828692 Trimmed Mean ( 10 / 28 ) 122.893384615385 0.779939940886818 157.567753839675 Trimmed Mean ( 11 / 28 ) 122.959365079365 0.765305037859855 160.667131400593 Trimmed Mean ( 12 / 28 ) 123.021639344262 0.751246911755574 163.756599087743 Trimmed Mean ( 13 / 28 ) 123.080677966102 0.740372884727625 166.241471702981 Trimmed Mean ( 14 / 28 ) 123.149473684211 0.730097043582845 168.675486042064 Trimmed Mean ( 15 / 28 ) 123.220363636364 0.718113829625043 171.588902139236 Trimmed Mean ( 16 / 28 ) 123.287358490566 0.705591402448503 174.729111016293 Trimmed Mean ( 17 / 28 ) 123.356274509804 0.692693348716178 178.08208313019 Trimmed Mean ( 18 / 28 ) 123.436122448980 0.677977485449233 182.065223548227 Trimmed Mean ( 19 / 28 ) 123.524042553191 0.660065498640343 187.139068482804 Trimmed Mean ( 20 / 28 ) 123.619333333333 0.638876412702074 193.494908992642 Trimmed Mean ( 21 / 28 ) 123.717441860465 0.614978332278472 201.173659894807 Trimmed Mean ( 22 / 28 ) 123.830243902439 0.58391012587397 212.070725297143 Trimmed Mean ( 23 / 28 ) 123.953076923077 0.542734138090284 228.386364932248 Trimmed Mean ( 24 / 28 ) 124.050540540541 0.511900267411209 242.333416170871 Trimmed Mean ( 25 / 28 ) 124.101428571429 0.497144644061311 249.628413086401 Trimmed Mean ( 26 / 28 ) 124.155151515152 0.480816288471877 258.217440822855 Trimmed Mean ( 27 / 28 ) 124.238709677419 0.464637849942327 267.388267427719 Trimmed Mean ( 28 / 28 ) 124.327931034483 0.445500045421466 279.075013150363 Median 124.96 Midrange 119.65 Midmean - Weighted Average at Xnp 123.368372093023 Midmean - Weighted Average at X(n+1)p 123.494318181818 Midmean - Empirical Distribution Function 123.494318181818 Midmean - Empirical Distribution Function - Averaging 123.494318181818 Midmean - Empirical Distribution Function - Interpolation 123.494318181818 Midmean - Closest Observation 123.494318181818 Midmean - True Basic - Statistics Graphics Toolkit 123.494318181818 Midmean - MS Excel (old versions) 123.494318181818 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208267710jqghuhhmwixqmps/1rylb1208267649.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208267710jqghuhhmwixqmps/1rylb1208267649.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208267710jqghuhhmwixqmps/2p8hc1208267649.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/15/t1208267710jqghuhhmwixqmps/2p8hc1208267649.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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