Opgave 5 oef 2

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Tue, 19 Oct 2010 17:46:38 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Oct/19/t1287510381jl0om660lwdwktc.htm/, Retrieved Tue, 19 Oct 2010 19:46:21 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Oct/19/t1287510381jl0om660lwdwktc.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

6715 7703 9856 8326 9269 7035 10342 11682 10304 11385 9777 8882 7897 6930 9545 9110 7459 7320 10017 12307 11072 10749 9589 9080 7384 8062 8511 8684 8306 7643 10577 13747 11783 11611 9946 8693 7303 7609 9423 8584 7586 6843 11811 13414 12103 11501 8213 7982 7687 7180 7862 8043 8340 6692 10065 12684 11587 9843 8110 7940 6475 6121 9669 7778 7826 7403 10741 14023 11519 10236 8075 8157

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 9218.41666666667 223.34937468667 41.2735279854663 Geometric Mean 9035.89592401272 Harmonic Mean 8863.7890559486 Quadratic Mean 9408.5618882779 Winsorized Mean ( 1 / 24 ) 9219.5 221.306467202531 41.6594242208144 Winsorized Mean ( 2 / 24 ) 9216.27777777778 217.698198348654 42.3351127739582 Winsorized Mean ( 3 / 24 ) 9186.81944444445 209.829799429524 43.7822438443976 Winsorized Mean ( 4 / 24 ) 9172.98611111111 203.939849570846 44.9788804415319 Winsorized Mean ( 5 / 24 ) 9164.86111111111 199.978603418803 45.8292084974597 Winsorized Mean ( 6 / 24 ) 9149.27777777778 193.742755149743 47.22384468367 Winsorized Mean ( 7 / 24 ) 9160.65277777778 191.103635330443 47.9355233715874 Winsorized Mean ( 8 / 24 ) 9163.09722222222 186.999136097736 49.0007462784912 Winsorized Mean ( 9 / 24 ) 9156.34722222222 185.030671610171 49.4855644339503 Winsorized Mean ( 10 / 24 ) 9161.90277777778 183.179597470539 50.0159564945615 Winsorized Mean ( 11 / 24 ) 9154.41666666667 180.858049575473 50.6165840456357 Winsorized Mean ( 12 / 24 ) 9160.75 179.044410466804 51.1646801825096 Winsorized Mean ( 13 / 24 ) 9162.73611111111 172.19801648986 53.2104625702856 Winsorized Mean ( 14 / 24 ) 9106.34722222222 160.837328953411 56.6183688915898 Winsorized Mean ( 15 / 24 ) 9046.13888888889 148.668663149971 60.8476507235658 Winsorized Mean ( 16 / 24 ) 9054.13888888889 147.091761925248 61.5543574322689 Winsorized Mean ( 17 / 24 ) 9019.19444444445 140.440819851742 64.220605191323 Winsorized Mean ( 18 / 24 ) 8979.19444444445 129.004331791024 69.603821203384 Winsorized Mean ( 19 / 24 ) 8981.83333333333 125.866593869339 71.3599459333688 Winsorized Mean ( 20 / 24 ) 8972.94444444445 121.80049538653 73.669194989471 Winsorized Mean ( 21 / 24 ) 8933.27777777778 113.333081714410 78.8232142163832 Winsorized Mean ( 22 / 24 ) 8931.75 109.595278629187 81.4975801121906 Winsorized Mean ( 23 / 24 ) 8922.48611111111 104.749048036609 85.1796391313533 Winsorized Mean ( 24 / 24 ) 8912.81944444445 98.0964887137212 90.8576806500697 Trimmed Mean ( 1 / 24 ) 9194.02857142857 214.530246094122 42.8565609690059 Trimmed Mean ( 2 / 24 ) 9167.05882352941 206.415995411451 44.4106029925473 Trimmed Mean ( 3 / 24 ) 9140.21212121212 199.012751597577 45.9277711997797 Trimmed Mean ( 4 / 24 ) 9122.734375 193.809467630321 47.0706332695831 Trimmed Mean ( 5 / 24 ) 9108.14516129032 189.700767522741 48.0132225094895 Trimmed Mean ( 6 / 24 ) 9094.53333333333 185.928654785735 48.914102798269 Trimmed Mean ( 7 / 24 ) 9083.20689655172 183.027238986173 49.6276234448246 Trimmed Mean ( 8 / 24 ) 9068.98214285714 180.029926247976 50.3748589574236 Trimmed Mean ( 9 / 24 ) 9053.2962962963 177.1990152513 51.0911208138324 Trimmed Mean ( 10 / 24 ) 9037.4423076923 174.015338892959 51.934745322948 Trimmed Mean ( 11 / 24 ) 9019.52 170.300973045982 52.9622340887313 Trimmed Mean ( 12 / 24 ) 9001.125 166.017111784123 54.2180556164864 Trimmed Mean ( 13 / 24 ) 8980.30434782609 160.812682070028 55.8432595752337 Trimmed Mean ( 14 / 24 ) 8957.34090909091 155.555744966063 57.5828357290505 Trimmed Mean ( 15 / 24 ) 8939.09523809524 151.412343632628 59.0380878046785 Trimmed Mean ( 16 / 24 ) 8926.25 148.746543808156 60.0097976831818 Trimmed Mean ( 17 / 24 ) 8911.1052631579 145.2864428737 61.33473355738 Trimmed Mean ( 18 / 24 ) 8898.38888888889 142.086254139942 62.62666957301 Trimmed Mean ( 19 / 24 ) 8888.88235294118 140.330516173529 63.3424760010816 Trimmed Mean ( 20 / 24 ) 8877.875 138.245790856417 64.2180492078825 Trimmed Mean ( 21 / 24 ) 8866.46666666667 135.945363715387 65.220809480707 Trimmed Mean ( 22 / 24 ) 8858.28571428571 134.618664408975 65.8028049318185 Trimmed Mean ( 23 / 24 ) 8849.03846153846 133.083438035279 66.4924095152447 Trimmed Mean ( 24 / 24 ) 8839.45833333333 131.566632966053 67.1861712506855 Median 8688.5 Midrange 10072 Midmean - Weighted Average at Xnp 8866.08108108108 Midmean - Weighted Average at X(n+1)p 8898.38888888889 Midmean - Empirical Distribution Function 8866.08108108108 Midmean - Empirical Distribution Function - Averaging 8898.38888888889 Midmean - Empirical Distribution Function - Interpolation 8898.38888888889 Midmean - Closest Observation 8866.08108108108 Midmean - True Basic - Statistics Graphics Toolkit 8898.38888888889 Midmean - MS Excel (old versions) 8911.1052631579 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Oct/19/t1287510381jl0om660lwdwktc/11wj41287510395.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/19/t1287510381jl0om660lwdwktc/11wj41287510395.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/19/t1287510381jl0om660lwdwktc/2b6io1287510395.png (open in new window) http://www.freestatistics.org/blog/date/2010/Oct/19/t1287510381jl0om660lwdwktc/2b6io1287510395.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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