*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 06 Jun 2010 23:08:34 +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/Jun/07/t1275865726lhl97cow80qxuq8.htm/, Retrieved Mon, 07 Jun 2010 01:08:46 +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/Jun/07/t1275865726lhl97cow80qxuq8.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 «

10.383 10.431 10.574 10.653 10.805 10.872 10.625 10.407 10.463 10.556 10.646 10.702 11.353 11.346 11.451 11.964 12.574 13.031 13.812 14.544 14.931 14.886 16.005 17.064 15.168 16.050 15.839 15.137 14.954 15.648 15.305 15.579 16.348 15.928 16.171 15.937 15.713 15.594 15.683 16.438 17.032 17.696 17.745 19.394 20.148 20.108 18.584 18.441 18.391 19.178 18.079 18.483 19.644 19.195 19.650 20.830 23.595 22.937 21.814 21.928 21.777 21.383 21.467 22.052 22.680 24.320 24.977 25.204 25.739 26.434 27.525 30.695

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 1 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 17.0652083333333 0.5718268164707 29.8433159162757 Geometric Mean 16.3963647274193 Harmonic Mean 15.746636233899 Quadratic Mean 17.7323809718423 Winsorized Mean ( 1 / 24 ) 17.0215138888889 0.558532189026574 30.4754394165795 Winsorized Mean ( 2 / 24 ) 16.991875 0.550745796790954 30.8524823957024 Winsorized Mean ( 3 / 24 ) 16.96425 0.543733050119859 31.1995932494088 Winsorized Mean ( 4 / 24 ) 16.9396944444444 0.536260249340784 31.5885700371567 Winsorized Mean ( 5 / 24 ) 16.9251805555556 0.532661464395494 31.7747419080965 Winsorized Mean ( 6 / 24 ) 16.8746805555556 0.520599366351003 32.4139475501746 Winsorized Mean ( 7 / 24 ) 16.8062361111111 0.506493616394113 33.1815358913306 Winsorized Mean ( 8 / 24 ) 16.7339027777778 0.49297416350564 33.9447865964812 Winsorized Mean ( 9 / 24 ) 16.7079027777778 0.486283846459005 34.3583339225444 Winsorized Mean ( 10 / 24 ) 16.6349861111111 0.469143780866387 35.4581831616538 Winsorized Mean ( 11 / 24 ) 16.6262777777778 0.464290609467813 35.8100668821095 Winsorized Mean ( 12 / 24 ) 16.6862777777778 0.447694254627919 37.2715923988032 Winsorized Mean ( 13 / 24 ) 16.6808611111111 0.446405927903027 37.367024200303 Winsorized Mean ( 14 / 24 ) 16.6396388888889 0.433625262493906 38.3733152288901 Winsorized Mean ( 15 / 24 ) 16.7290138888889 0.413171713959675 40.4892525883842 Winsorized Mean ( 16 / 24 ) 16.7416805555556 0.372189238105847 44.981635258337 Winsorized Mean ( 17 / 24 ) 16.6885555555556 0.330929091100814 50.429400147452 Winsorized Mean ( 18 / 24 ) 16.8738055555556 0.300155050333268 56.2169636553515 Winsorized Mean ( 19 / 24 ) 16.9461111111111 0.255185017996437 66.4071552639024 Winsorized Mean ( 20 / 24 ) 17.0394444444444 0.242691821821553 70.2102127568734 Winsorized Mean ( 21 / 24 ) 16.9796527777778 0.230148071136342 73.777080528817 Winsorized Mean ( 22 / 24 ) 16.925875 0.220361452554899 76.8095998812826 Winsorized Mean ( 23 / 24 ) 16.9789027777778 0.212314178313367 79.9706496883952 Winsorized Mean ( 24 / 24 ) 16.7912361111111 0.182868154499329 91.8215429968301 Trimmed Mean ( 1 / 24 ) 16.9659571428571 0.546102182338765 31.0673674113476 Trimmed Mean ( 2 / 24 ) 16.9071323529412 0.531222410389063 31.8268431871286 Trimmed Mean ( 3 / 24 ) 16.8609090909091 0.518390946839958 32.5254698093995 Trimmed Mean ( 4 / 24 ) 16.82215625 0.506162005491277 33.2347273550739 Trimmed Mean ( 5 / 24 ) 16.7880322580645 0.494123608674242 33.9753696511438 Trimmed Mean ( 6 / 24 ) 16.7551166666667 0.480603343790998 34.8626718543037 Trimmed Mean ( 7 / 24 ) 16.7303793103448 0.46759039475824 35.7799892767151 Trimmed Mean ( 8 / 24 ) 16.7164464285714 0.45536942682056 36.7096371517243 Trimmed Mean ( 9 / 24 ) 16.713537037037 0.443609694377238 37.6762213470117 Trimmed Mean ( 10 / 24 ) 16.7144038461538 0.430490629335194 38.8264057500296 Trimmed Mean ( 11 / 24 ) 16.72584 0.417991749122747 40.0147611408671 Trimmed Mean ( 12 / 24 ) 16.7394166666667 0.403177836394868 41.5186926353567 Trimmed Mean ( 13 / 24 ) 16.746347826087 0.388155300631213 43.143421715108 Trimmed Mean ( 14 / 24 ) 16.7545909090909 0.368899956527778 45.4177090905385 Trimmed Mean ( 15 / 24 ) 16.7686666666667 0.34682376890059 48.3492429593921 Trimmed Mean ( 16 / 24 ) 16.773425 0.323002682944124 51.9296770141739 Trimmed Mean ( 17 / 24 ) 16.7771842105263 0.302507815530424 55.4603330863001 Trimmed Mean ( 18 / 24 ) 16.7876111111111 0.286279121420952 58.6407106036427 Trimmed Mean ( 19 / 24 ) 16.7774705882353 0.272607869164286 61.5443370716654 Trimmed Mean ( 20 / 24 ) 16.7575 0.265884305121001 63.0255328247896 Trimmed Mean ( 21 / 24 ) 16.7236666666667 0.258777347750556 64.625697774703 Trimmed Mean ( 22 / 24 ) 16.6923214285714 0.25168303349267 66.3227917946148 Trimmed Mean ( 23 / 24 ) 16.6629230769231 0.243628645044852 68.394761518521 Trimmed Mean ( 24 / 24 ) 16.6217083333333 0.232682353914231 71.4351907384443 Median 16.1105 Midrange 20.539 Midmean - Weighted Average at Xnp 16.6860810810811 Midmean - Weighted Average at X(n+1)p 16.7876111111111 Midmean - Empirical Distribution Function 16.6860810810811 Midmean - Empirical Distribution Function - Averaging 16.7876111111111 Midmean - Empirical Distribution Function - Interpolation 16.7876111111111 Midmean - Closest Observation 16.6860810810811 Midmean - True Basic - Statistics Graphics Toolkit 16.7876111111111 Midmean - MS Excel (old versions) 16.7771842105263 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275865726lhl97cow80qxuq8/1wcio1275865711.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/07/t1275865726lhl97cow80qxuq8/1wcio1275865711.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/07/t1275865726lhl97cow80qxuq8/2wcio1275865711.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/07/t1275865726lhl97cow80qxuq8/2wcio1275865711.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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