OPGAVE5- o2

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 14 Mar 2010 13:59:47 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/14/t1268596997wbhz2swmzfvilzy.htm/, Retrieved Sun, 14 Mar 2010 21:03:19 +0100

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/Mar/14/t1268596997wbhz2swmzfvilzy.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

278,1 283,3 287 287,9 279,7 273,2 272,6 274,8 277,2 277,5 278,7 279 280,1 280,8 280,1 270,5 260 258,2 260,1 262,2 263,4 264,7 267,4 266,8 265,2 262,5 255 252,8 249,6 254,2 259,4 260,8 261,6 257,2 249,8 235,2 227,4 223,1 221,6 218,5 220,1 222,1 222,9 222,8 222,1 209 201,7 204,5 208,7 213 218,6 221,9 224,6 226,8 229,6 231,4 229,1 232,7 236,6 242,2 251,5 261,5 266,4 280,9 294,4 308,8 328,8 348,2 365,9 387,5 395,9 395,8

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' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 261.711111111111 4.9350636777795 53.0309491829833 Geometric Mean 258.748664300609 Harmonic Mean 256.065971032172 Quadratic Mean 264.994151402965 Winsorized Mean ( 1 / 24 ) 261.748611111111 4.9280198327572 53.114358300921 Winsorized Mean ( 2 / 24 ) 261.634722222222 4.82289432826116 54.2484874049794 Winsorized Mean ( 3 / 24 ) 260.747222222222 4.50704802442276 57.8532158542103 Winsorized Mean ( 4 / 24 ) 259.986111111111 4.16249617836232 62.4591831369319 Winsorized Mean ( 5 / 24 ) 259.020833333333 3.72259571372034 69.580704769702 Winsorized Mean ( 6 / 24 ) 257.3625 3.31706973598862 77.5873046043441 Winsorized Mean ( 7 / 24 ) 256.108333333333 3.01331470843677 84.992228862214 Winsorized Mean ( 8 / 24 ) 255.552777777778 2.86309074667877 89.2576590784706 Winsorized Mean ( 9 / 24 ) 255.477777777778 2.83908779227804 89.9858674580775 Winsorized Mean ( 10 / 24 ) 254.991666666667 2.75705791542049 92.486873503989 Winsorized Mean ( 11 / 24 ) 254.625 2.70545422988162 94.115434365024 Winsorized Mean ( 12 / 24 ) 254.725 2.68352195849437 94.921898885045 Winsorized Mean ( 13 / 24 ) 254.616666666667 2.66332977841784 95.6008785430706 Winsorized Mean ( 14 / 24 ) 254.655555555556 2.65681564318078 95.849915747514 Winsorized Mean ( 15 / 24 ) 254.884722222222 2.59374145904073 98.2691321580252 Winsorized Mean ( 16 / 24 ) 255.218055555556 2.49335292100595 102.359378572283 Winsorized Mean ( 17 / 24 ) 255.288888888889 2.46117390241260 103.726473224276 Winsorized Mean ( 18 / 24 ) 255.563888888889 2.37380585707582 107.659979069942 Winsorized Mean ( 19 / 24 ) 255.5375 2.33202464767319 109.577529660746 Winsorized Mean ( 20 / 24 ) 255.954166666667 2.24322309049380 114.101075256997 Winsorized Mean ( 21 / 24 ) 255.633333333333 2.09284869244106 122.14611321718 Winsorized Mean ( 22 / 24 ) 255.908333333333 1.91296412126952 133.775814448366 Winsorized Mean ( 23 / 24 ) 256.163888888889 1.82063496631733 140.700301613476 Winsorized Mean ( 24 / 24 ) 257.330555555556 1.45281503077639 177.125477162800 Trimmed Mean ( 1 / 24 ) 260.651428571429 4.61376585601715 56.4942905005667 Trimmed Mean ( 2 / 24 ) 259.489705882353 4.2244304621066 61.4259622001099 Trimmed Mean ( 3 / 24 ) 258.319696969697 3.80923134614724 67.8141266560164 Trimmed Mean ( 4 / 24 ) 257.409375 3.45714818960812 74.4571423850877 Trimmed Mean ( 5 / 24 ) 256.661290322581 3.16729582601480 81.0348336314137 Trimmed Mean ( 6 / 24 ) 256.095 2.9716460703172 86.179509248443 Trimmed Mean ( 7 / 24 ) 255.832758620690 2.86164783999348 89.4005038094668 Trimmed Mean ( 8 / 24 ) 255.782142857143 2.80933752317329 91.0471386037743 Trimmed Mean ( 9 / 24 ) 255.820370370370 2.77935809926549 92.0429686401247 Trimmed Mean ( 10 / 24 ) 255.873076923077 2.74518379214841 93.2079949090869 Trimmed Mean ( 11 / 24 ) 256 2.71743426407923 94.2065106722066 Trimmed Mean ( 12 / 24 ) 256.1875 2.68969933099125 95.2476349486938 Trimmed Mean ( 13 / 24 ) 256.378260869565 2.65566737528433 96.54004987809 Trimmed Mean ( 14 / 24 ) 256.6 2.61249437317945 98.2203072413562 Trimmed Mean ( 15 / 24 ) 256.838095238095 2.55443171726174 100.546079780679 Trimmed Mean ( 16 / 24 ) 257.0725 2.48999275948901 103.242268083043 Trimmed Mean ( 17 / 24 ) 257.292105263158 2.42571390139516 106.068611436483 Trimmed Mean ( 18 / 24 ) 257.527777777778 2.34337841557634 109.895941716456 Trimmed Mean ( 19 / 24 ) 257.758823529412 2.25116772093745 114.500053075598 Trimmed Mean ( 20 / 24 ) 258.021875 2.13013485098173 121.129361777769 Trimmed Mean ( 21 / 24 ) 258.27 1.98349598483059 130.209489696577 Trimmed Mean ( 22 / 24 ) 258.592857142857 1.81586867992600 142.407245634852 Trimmed Mean ( 23 / 24 ) 258.930769230769 1.63107108962433 158.748917124395 Trimmed Mean ( 24 / 24 ) 259.291666666667 1.37301789503874 188.847987781944 Median 260.45 Midrange 298.8 Midmean - Weighted Average at Xnp 256.713513513513 Midmean - Weighted Average at X(n+1)p 257.527777777778 Midmean - Empirical Distribution Function 256.713513513513 Midmean - Empirical Distribution Function - Averaging 257.527777777778 Midmean - Empirical Distribution Function - Interpolation 257.527777777778 Midmean - Closest Observation 256.713513513513 Midmean - True Basic - Statistics Graphics Toolkit 257.527777777778 Midmean - MS Excel (old versions) 257.292105263158 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/14/t1268596997wbhz2swmzfvilzy/11hrq1268596785.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268596997wbhz2swmzfvilzy/11hrq1268596785.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268596997wbhz2swmzfvilzy/272dt1268596785.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268596997wbhz2swmzfvilzy/272dt1268596785.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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