WS 3 Y/X gem

*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: Fri, 16 Oct 2009 08:11:04 -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/16/t1255702367px5810kht58rgyp.htm/, Retrieved Fri, 16 Oct 2009 16:12:49 +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/16/t1255702367px5810kht58rgyp.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?

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Dataseries X:

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1315,511354 1293,838312 1347,166144 1547,284007 1623,08315 1296,975676 1634,548618 1492,268898 1609,725632 1406,27471 1377,634297 1515,481164 1293,25295 1333,304497 1272,652699 1335,340949 1448,48779 1349,471922 1422,686782 1473,623501 1821,769029 1366,705713 1681,136994 1575,753383 1432,933154 1481,161069 1483,76285 1901,748081 1747,455446 1724,591013 1665,313776 1688,283252 1887,620957 1808,881231 2123,509758 1876,565678 1949,468617 1661,14422 2045,335405 2253,978337 2089,956435 1867,686835 1988,699442 1777,65877 2254,988745 2351,146178 2441,670675 2473,868639 2371,769264 1826,179863 2104,980374 1982,785287 1878,349467 1986,915838 1509,362064 1613,664842 1825,686834 1540,21893 1461,770805 1715,72719

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 1710.48029153333 41.3404880363023 41.3754257093266 Geometric Mean 1682.43412970830 Harmonic Mean 1655.92223390677 Quadratic Mean 1739.70570753724 Winsorized Mean ( 1 / 20 ) 1710.28699631667 41.1152723168057 41.5973651624726 Winsorized Mean ( 2 / 20 ) 1707.97646135 40.4362705816976 42.2387237195675 Winsorized Mean ( 3 / 20 ) 1707.10217525 40.1253426570688 42.5442391816999 Winsorized Mean ( 4 / 20 ) 1701.92739158333 38.2529956008274 44.4913493662839 Winsorized Mean ( 5 / 20 ) 1703.32595283333 37.9829708796213 44.8444635421397 Winsorized Mean ( 6 / 20 ) 1690.48274013333 34.9668262014981 48.345329667378 Winsorized Mean ( 7 / 20 ) 1689.70058475 34.2824019194167 49.2876954398284 Winsorized Mean ( 8 / 20 ) 1688.00482995 33.822879922878 49.9071880868495 Winsorized Mean ( 9 / 20 ) 1683.8967441 32.0726571277123 52.502564330569 Winsorized Mean ( 10 / 20 ) 1676.2788476 30.0305451813565 55.819128073661 Winsorized Mean ( 11 / 20 ) 1681.20259591667 29.1094887524216 57.754452859527 Winsorized Mean ( 12 / 20 ) 1683.65890011667 28.4443160188886 59.1914004540881 Winsorized Mean ( 13 / 20 ) 1678.66033555 26.8380687680944 62.5477321060308 Winsorized Mean ( 14 / 20 ) 1671.15495888333 24.4303355675826 68.4049121740614 Winsorized Mean ( 15 / 20 ) 1670.94393163333 23.3615434288301 71.5254082729504 Winsorized Mean ( 16 / 20 ) 1671.63225323333 22.4990224682656 74.2979947502669 Winsorized Mean ( 17 / 20 ) 1673.26249061667 22.1036813485839 75.7006248972129 Winsorized Mean ( 18 / 20 ) 1671.37937201667 21.5756391477388 77.4660421678322 Winsorized Mean ( 19 / 20 ) 1660.92907941667 19.2014509516324 86.5001860328405 Winsorized Mean ( 20 / 20 ) 1666.46245841667 18.3393755228357 90.8680045480081 Trimmed Mean ( 1 / 20 ) 1704.86717506897 39.9398560487751 42.685861786456 Trimmed Mean ( 2 / 20 ) 1699.06022373214 38.4754562535615 44.1595861147161 Trimmed Mean ( 3 / 20 ) 1694.10675838889 37.1101624694178 45.6507502435483 Trimmed Mean ( 4 / 20 ) 1689.10852113462 35.5453677487988 47.5197931013584 Trimmed Mean ( 5 / 20 ) 1685.26286 34.3463518310983 49.0667209224272 Trimmed Mean ( 6 / 20 ) 1680.74708679167 32.8999214995184 51.0866594869009 Trimmed Mean ( 7 / 20 ) 1678.63064041304 32.050345918256 52.3748057101902 Trimmed Mean ( 8 / 20 ) 1676.47415775 31.1386082185399 53.839084456955 Trimmed Mean ( 9 / 20 ) 1674.41510914286 30.0641158223367 55.6948063611045 Trimmed Mean ( 10 / 20 ) 1672.83483665 29.1334759519693 57.4196789771295 Trimmed Mean ( 11 / 20 ) 1672.29104544737 28.4389947811092 58.8027480689366 Trimmed Mean ( 12 / 20 ) 1670.94081052778 27.7076656735757 60.3060838907596 Trimmed Mean ( 13 / 20 ) 1669.07050323529 26.8408625554766 62.183936890461 Trimmed Mean ( 14 / 20 ) 1667.68735434375 26.0636516477975 63.9851766314057 Trimmed Mean ( 15 / 20 ) 1667.19198226667 25.6196582017051 65.074716030197 Trimmed Mean ( 16 / 20 ) 1666.6559895 25.2040444102006 66.126529630517 Trimmed Mean ( 17 / 20 ) 1665.93825915385 24.7496788016663 67.3115102827793 Trimmed Mean ( 18 / 20 ) 1664.86116629167 24.062905477213 69.1878695973872 Trimmed Mean ( 19 / 20 ) 1663.87355936364 23.0595229085862 72.155593416206 Trimmed Mean ( 20 / 20 ) 1664.33847725 22.3529580483232 74.4571914666503 Median 1663.228998 Midrange 1873.260669 Midmean - Weighted Average at Xnp 1660.13700832258 Midmean - Weighted Average at X(n+1)p 1667.19198226667 Midmean - Empirical Distribution Function 1660.13700832258 Midmean - Empirical Distribution Function - Averaging 1667.19198226667 Midmean - Empirical Distribution Function - Interpolation 1667.19198226667 Midmean - Closest Observation 1660.13700832258 Midmean - True Basic - Statistics Graphics Toolkit 1667.19198226667 Midmean - MS Excel (old versions) 1667.68735434375 Number of observations 60

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/16/t1255702367px5810kht58rgyp/188xt1255702261.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/16/t1255702367px5810kht58rgyp/188xt1255702261.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/16/t1255702367px5810kht58rgyp/2haz51255702261.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/16/t1255702367px5810kht58rgyp/2haz51255702261.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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