WS 3 - Vraag 2 (1)

*The author of this computation has been verified*

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

Title produced by software: Central Tendency

Date of computation: Wed, 21 Oct 2009 09:49:21 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/21/t12561402082tyaayy4cvjbjly.htm/, Retrieved Wed, 21 Oct 2009 17:50:10 +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/2009/Oct/21/t12561402082tyaayy4cvjbjly.htm/}, year = {2009}, } @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 = {2009}, 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:

SHW WS 3 - Vraag 2 (1)

Dataseries X:

» Textbox « » Textfile « » CSV «

14.2 13.5 11.9 14.6 15.6 14.1 14.9 14.2 14.6 17.2 15.4 14.3 17.5 14.5 14.4 16.6 16.7 16.6 16.9 15.7 16.4 18.4 16.9 16.5 18.3 15.1 15.7 18.1 16.8 18.9 19 18.1 17.8 21.5 17.1 18.7 19 16.4 16.9 18.6 19.3 19.4 17.6 18.6 18.1 20.4 18.1 19.6 19.9 19.2 17.8 19.2 22 21.1 19.5 22.2 20.9 22.2 23.5 21.5 24.3 22.8 20.3 23.7 23.3 19.6 18 17.3 16.8 18.2 16.5 16 18.4

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 17.9849315068493 0.312497617847095 57.552219536116 Geometric Mean 17.7909972690593 Harmonic Mean 17.5980950099908 Quadratic Mean 18.1793537869086 Winsorized Mean ( 1 / 24 ) 17.9986301369863 0.305059399552399 59.0004116031008 Winsorized Mean ( 2 / 24 ) 18.0095890410959 0.300482643111241 59.9355385543138 Winsorized Mean ( 3 / 24 ) 18.0054794520548 0.297688267245627 60.4843436345384 Winsorized Mean ( 4 / 24 ) 17.9780821917808 0.291150858808654 61.7483398996123 Winsorized Mean ( 5 / 24 ) 17.9438356164384 0.280858018246101 63.8893478224115 Winsorized Mean ( 6 / 24 ) 17.9520547945205 0.279391799693687 64.2540504560349 Winsorized Mean ( 7 / 24 ) 17.9424657534247 0.27370782486997 65.5533533319647 Winsorized Mean ( 8 / 24 ) 17.8986301369863 0.260885486862090 68.6072282221199 Winsorized Mean ( 9 / 24 ) 17.8986301369863 0.260885486862090 68.6072282221199 Winsorized Mean ( 10 / 24 ) 17.8849315068493 0.24348959166961 73.4525504117535 Winsorized Mean ( 11 / 24 ) 17.8849315068493 0.232947097430307 76.7767948351453 Winsorized Mean ( 12 / 24 ) 17.8520547945205 0.210539547410334 84.7919310842229 Winsorized Mean ( 13 / 24 ) 17.8698630136986 0.201890653862047 88.5125817954366 Winsorized Mean ( 14 / 24 ) 17.8123287671233 0.186491531563906 95.512802204745 Winsorized Mean ( 15 / 24 ) 17.7506849315069 0.177224106416842 100.159539751077 Winsorized Mean ( 16 / 24 ) 17.8164383561644 0.166963362611241 106.708669959220 Winsorized Mean ( 17 / 24 ) 17.886301369863 0.150016679292016 119.228751458005 Winsorized Mean ( 18 / 24 ) 17.8616438356164 0.146374633204535 122.026907562991 Winsorized Mean ( 19 / 24 ) 17.8616438356164 0.139028348906961 128.474832478731 Winsorized Mean ( 20 / 24 ) 17.8342465753425 0.135136482929583 131.972108410099 Winsorized Mean ( 21 / 24 ) 17.8630136986301 0.131240812526378 136.108679569778 Winsorized Mean ( 22 / 24 ) 17.8027397260274 0.12289278040087 144.863999886370 Winsorized Mean ( 23 / 24 ) 17.8342465753425 0.118659098478620 150.298180282871 Winsorized Mean ( 24 / 24 ) 17.8342465753425 0.109867416605959 162.325165424661 Trimmed Mean ( 1 / 24 ) 17.9816901408451 0.296310714748333 60.6852511429348 Trimmed Mean ( 2 / 24 ) 17.9637681159420 0.285915253232642 62.8289953503297 Trimmed Mean ( 3 / 24 ) 17.9388059701493 0.276445710353526 64.890882000696 Trimmed Mean ( 4 / 24 ) 17.9138461538462 0.266375935574621 67.250242088133 Trimmed Mean ( 5 / 24 ) 17.8952380952381 0.256751423070023 69.6986909800206 Trimmed Mean ( 6 / 24 ) 17.8836065573770 0.248505701662650 71.964572393008 Trimmed Mean ( 7 / 24 ) 17.8694915254237 0.238863643273025 74.8104285799518 Trimmed Mean ( 8 / 24 ) 17.8561403508772 0.228608868344685 78.1078200516466 Trimmed Mean ( 9 / 24 ) 17.8490909090909 0.219378871071358 81.3619416579323 Trimmed Mean ( 10 / 24 ) 17.8415094339623 0.207836913467952 85.8437951962435 Trimmed Mean ( 11 / 24 ) 17.8352941176471 0.197808057676276 90.164649141015 Trimmed Mean ( 12 / 24 ) 17.8285714285714 0.187740775111471 94.9637680891951 Trimmed Mean ( 13 / 24 ) 17.8255319148936 0.180437029462786 98.790874400701 Trimmed Mean ( 14 / 24 ) 17.82 0.173076733143296 102.960112987840 Trimmed Mean ( 15 / 24 ) 17.8209302325581 0.167204827920425 106.581433408366 Trimmed Mean ( 16 / 24 ) 17.8292682926829 0.161594339373473 110.333495355158 Trimmed Mean ( 17 / 24 ) 17.8307692307692 0.156598192439187 113.863186752258 Trimmed Mean ( 18 / 24 ) 17.8243243243243 0.153800961690420 115.892151313086 Trimmed Mean ( 19 / 24 ) 17.82 0.150617775463968 118.312728661054 Trimmed Mean ( 20 / 24 ) 17.8151515151515 0.147781652772714 120.550495822042 Trimmed Mean ( 21 / 24 ) 17.8129032258065 0.144485883931847 123.284730252325 Trimmed Mean ( 22 / 24 ) 17.8068965517241 0.140454139780032 126.780859429362 Trimmed Mean ( 23 / 24 ) 17.8074074074074 0.136805841781219 130.16554830959 Trimmed Mean ( 24 / 24 ) 17.804 0.132222035480727 134.652291013892 Median 18 Midrange 18.1 Midmean - Weighted Average at Xnp 17.7432432432432 Midmean - Weighted Average at X(n+1)p 17.7868421052632 Midmean - Empirical Distribution Function 17.7868421052632 Midmean - Empirical Distribution Function - Averaging 17.7868421052632 Midmean - Empirical Distribution Function - Interpolation 17.7868421052632 Midmean - Closest Observation 17.7868421052632 Midmean - True Basic - Statistics Graphics Toolkit 17.7868421052632 Midmean - MS Excel (old versions) 17.7868421052632 Number of observations 73

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t12561402082tyaayy4cvjbjly/1ln311256140159.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t12561402082tyaayy4cvjbjly/1ln311256140159.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t12561402082tyaayy4cvjbjly/2luch1256140159.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t12561402082tyaayy4cvjbjly/2luch1256140159.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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