Centrummaten

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 16 Aug 2010 14:46:23 +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/Aug/16/t1281969945wc6137v3rkb7nhd.htm/, Retrieved Mon, 16 Aug 2010 16:45:46 +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/Aug/16/t1281969945wc6137v3rkb7nhd.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 «

257 256 255 253 251 250 251 253 254 254 255 257 260 251 255 252 245 239 240 247 251 255 259 260 259 266 261 243 232 225 229 238 240 241 239 246 242 251 246 219 203 192 197 203 208 207 208 212 208 215 200 170 162 150 148 152 155 150 146 147 142 146 130 102 98 90 86 104 108 94 88 92 93 95 81 50 49 34 27 45 47 42 32

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 186.084337349398 8.1503504107965 22.8314523879731 Geometric Mean 163.823684646856 Harmonic Mean 131.955614287802 Quadratic Mean 200.186148311774 Winsorized Mean ( 1 / 27 ) 186.084337349398 8.12923105448815 22.8907674172529 Winsorized Mean ( 2 / 27 ) 186.10843373494 8.1154614580869 22.9325756392431 Winsorized Mean ( 3 / 27 ) 186.397590361446 8.05078538958027 23.1527212988053 Winsorized Mean ( 4 / 27 ) 186.493975903614 8.01406296820124 23.2708398528435 Winsorized Mean ( 5 / 27 ) 186.614457831325 7.98825230831606 23.3611121217407 Winsorized Mean ( 6 / 27 ) 186.614457831325 7.94176629430982 23.4978531117231 Winsorized Mean ( 7 / 27 ) 186.698795180723 7.92398381648263 23.5612287335029 Winsorized Mean ( 8 / 27 ) 189.590361445783 7.32740551807951 25.874146173293 Winsorized Mean ( 9 / 27 ) 190.024096385542 7.21882021092215 26.3234283211589 Winsorized Mean ( 10 / 27 ) 190.265060240964 7.17671006134008 26.5114597935194 Winsorized Mean ( 11 / 27 ) 190.530120481928 7.13089360827115 26.7189683297099 Winsorized Mean ( 12 / 27 ) 190.819277108434 7.081431903741 26.9464254831889 Winsorized Mean ( 13 / 27 ) 190.819277108434 7.0375998821041 27.1142549029631 Winsorized Mean ( 14 / 27 ) 190.987951807229 7.00907211908865 27.2486783645853 Winsorized Mean ( 15 / 27 ) 190.987951807229 6.9588964485284 27.4451492732899 Winsorized Mean ( 16 / 27 ) 191.566265060241 6.86217090933452 27.9162771652417 Winsorized Mean ( 17 / 27 ) 192.180722891566 6.70452640244042 28.6643248688846 Winsorized Mean ( 18 / 27 ) 192.397590361446 6.61006053763554 29.1067818919352 Winsorized Mean ( 19 / 27 ) 193.313253012048 6.46166679229128 29.9169330802804 Winsorized Mean ( 20 / 27 ) 198.614457831325 5.63931643895848 35.2195979745388 Winsorized Mean ( 21 / 27 ) 201.650602409639 5.20122371208224 38.7698383250103 Winsorized Mean ( 22 / 27 ) 202.710843373494 5.05452288769571 40.1048423120124 Winsorized Mean ( 23 / 27 ) 202.433734939759 5.02237698468375 40.3063600277521 Winsorized Mean ( 24 / 27 ) 201.855421686747 4.88375396149589 41.3320210801362 Winsorized Mean ( 25 / 27 ) 201.855421686747 4.80871638951162 41.9769862342095 Winsorized Mean ( 26 / 27 ) 202.481927710843 4.72348411846504 42.8670707114905 Winsorized Mean ( 27 / 27 ) 202.156626506024 4.68707785021093 43.1306312731559 Trimmed Mean ( 1 / 27 ) 187.061728395062 8.05401030541277 23.2259112295082 Trimmed Mean ( 2 / 27 ) 188.088607594937 7.96316148820211 23.61984092293 Trimmed Mean ( 3 / 27 ) 189.155844155844 7.86225973490573 24.0587121939075 Trimmed Mean ( 4 / 27 ) 190.173333333333 7.76908573083687 24.4782127423954 Trimmed Mean ( 5 / 27 ) 191.219178082192 7.66868264578864 24.9350751510368 Trimmed Mean ( 6 / 27 ) 192.295774647887 7.55426763515166 25.4552504538088 Trimmed Mean ( 7 / 27 ) 192.295774647887 7.42700994122381 25.8914120446432 Trimmed Mean ( 8 / 27 ) 194.626865671642 7.2760343962841 26.7490304568981 Trimmed Mean ( 9 / 27 ) 195.430769230769 7.22881417923229 27.0349692750747 Trimmed Mean ( 10 / 27 ) 196.222222222222 7.1881467987679 27.2980265589256 Trimmed Mean ( 11 / 27 ) 197.032786885246 7.14054716234396 27.593513831028 Trimmed Mean ( 12 / 27 ) 197.864406779661 7.0846290108641 27.9286899111077 Trimmed Mean ( 13 / 27 ) 198.719298245614 7.0186715885842 28.312950070043 Trimmed Mean ( 14 / 27 ) 198.719298245614 6.93803083079047 28.642031592554 Trimmed Mean ( 15 / 27 ) 200.603773584906 6.83627414154425 29.3440212360459 Trimmed Mean ( 16 / 27 ) 201.647058823529 6.71105751459817 30.046987138003 Trimmed Mean ( 17 / 27 ) 202.714285714286 6.56638004830481 30.8715432586968 Trimmed Mean ( 18 / 27 ) 203.808510638298 6.40822481865543 31.804207312605 Trimmed Mean ( 19 / 27 ) 204.977777777778 6.21715522403018 32.9697056598346 Trimmed Mean ( 20 / 27 ) 206.162790697674 5.99694738076476 34.3779555843599 Trimmed Mean ( 21 / 27 ) 206.926829268293 5.90136303435873 35.0642433050687 Trimmed Mean ( 22 / 27 ) 207.461538461538 5.86313146697076 35.3840843634921 Trimmed Mean ( 23 / 27 ) 207.945945945946 5.82939969634427 35.6719313785179 Trimmed Mean ( 24 / 27 ) 208.514285714286 5.77205254967888 36.124807236186 Trimmed Mean ( 25 / 27 ) 209.212121212121 5.70465612190935 36.6739233253025 Trimmed Mean ( 26 / 27 ) 210 5.60779028031158 37.4479054142396 Trimmed Mean ( 27 / 27 ) 210.827586206897 5.47386737627047 38.5152894132668 Median 212 Midrange 146.5 Midmean - Weighted Average at Xnp 208.155555555556 Midmean - Weighted Average at X(n+1)p 208.155555555556 Midmean - Empirical Distribution Function 208.155555555556 Midmean - Empirical Distribution Function - Averaging 208.155555555556 Midmean - Empirical Distribution Function - Interpolation 209.931818181818 Midmean - Closest Observation 208.155555555556 Midmean - True Basic - Statistics Graphics Toolkit 208.155555555556 Midmean - MS Excel (old versions) 208.155555555556 Number of observations 83

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Aug/16/t1281969945wc6137v3rkb7nhd/10rgy1281969979.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t1281969945wc6137v3rkb7nhd/10rgy1281969979.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t1281969945wc6137v3rkb7nhd/2sjfj1281969979.png (open in new window) http://www.freestatistics.org/blog/date/2010/Aug/16/t1281969945wc6137v3rkb7nhd/2sjfj1281969979.ps (open in new window)

Parameters (Session):

par1 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;

Parameters (R input):

par1 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;

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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