Maximumprijs 2005-Wendy van Weelde-MAR202B

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 01 Jun 2009 14:23:09 -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/Jun/01/t1243887825vli6rs84ejwkisk.htm/, Retrieved Mon, 01 Jun 2009 22:23:47 +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/Jun/01/t1243887825vli6rs84ejwkisk.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:

Dataseries X:

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1528 1816 1420 1757 1544 1678 1655 1391 1403 1744 1266 1358 1596 1819 1416 1521 1638 1543 1623 1530 1336 1700 1615 1494 1578 1607 1767 1505 1938 1862 2571 2082 1781 1869 1785 1682 1556 2080 2027 1887 1935 1798 1590 1592 1387 1849 1470 1437 1500 2081 1552 1586 1914 1639 1633 1693 1224 1417 1577 1225 1510 1515 1393 1455 1532 1268 1365 1282 1063 1296 1639 1247 1515 1547 1299

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1599.90666666667 28.6405192296114 55.861650197058 Geometric Mean 1581.86535669458 Harmonic Mean 1564.48826759246 Quadratic Mean 1618.76558319398 Winsorized Mean ( 1 / 25 ) 1595.53333333333 25.7973553594849 61.8487170913318 Winsorized Mean ( 2 / 25 ) 1595.53333333333 25.7853812437568 61.8774381596412 Winsorized Mean ( 3 / 25 ) 1596.37333333333 25.6086118210144 62.3373630906205 Winsorized Mean ( 4 / 25 ) 1594.56 24.7290414673091 64.4812700123437 Winsorized Mean ( 5 / 25 ) 1588.76 23.4025704293931 67.8882691451942 Winsorized Mean ( 6 / 25 ) 1589.64 23.1498731535840 68.6673308943768 Winsorized Mean ( 7 / 25 ) 1588.98666666667 22.5289842809820 70.5307725749546 Winsorized Mean ( 8 / 25 ) 1586.42666666667 21.9248279464282 72.3575423507536 Winsorized Mean ( 9 / 25 ) 1588.70666666667 20.7686074028437 76.4955798841446 Winsorized Mean ( 10 / 25 ) 1590.70666666667 20.1280027547418 79.0295334340573 Winsorized Mean ( 11 / 25 ) 1589.82666666667 19.6244963057719 81.0123552673844 Winsorized Mean ( 12 / 25 ) 1588.54666666667 18.2504724690991 87.0413995778094 Winsorized Mean ( 13 / 25 ) 1588.72 18.0588583239352 87.9745536235982 Winsorized Mean ( 14 / 25 ) 1585.73333333333 17.4411787077226 90.918931564597 Winsorized Mean ( 15 / 25 ) 1585.13333333333 16.7207303316220 94.8004843027434 Winsorized Mean ( 16 / 25 ) 1587.05333333333 16.1803895690619 98.0849890269575 Winsorized Mean ( 17 / 25 ) 1584.10666666667 15.6399877114918 101.285672079059 Winsorized Mean ( 18 / 25 ) 1582.42666666667 15.1594667396921 104.385378050495 Winsorized Mean ( 19 / 25 ) 1583.44 14.0327832380254 112.838627458398 Winsorized Mean ( 20 / 25 ) 1576.50666666667 11.5973960005681 135.936262466974 Winsorized Mean ( 21 / 25 ) 1578.74666666667 10.7300553441111 147.133133617350 Winsorized Mean ( 22 / 25 ) 1582.56 9.32981735576275 169.623899338447 Winsorized Mean ( 23 / 25 ) 1583.17333333333 8.9193659802415 177.498416013026 Winsorized Mean ( 24 / 25 ) 1577.41333333333 7.68393886730735 205.287074841877 Winsorized Mean ( 25 / 25 ) 1573.74666666667 6.75880722280752 232.843845783332 Trimmed Mean ( 1 / 25 ) 1593.95890410959 25.1278196533497 63.4340315275666 Trimmed Mean ( 2 / 25 ) 1592.29577464789 24.3359567407862 65.429758591708 Trimmed Mean ( 3 / 25 ) 1590.53623188406 23.4014738180856 67.9673530072636 Trimmed Mean ( 4 / 25 ) 1588.35820895522 22.3635386594244 71.0244578527765 Trimmed Mean ( 5 / 25 ) 1586.56923076923 21.4556560728120 73.9464328373388 Trimmed Mean ( 6 / 25 ) 1586.04761904762 20.8008432192929 76.249198281373 Trimmed Mean ( 7 / 25 ) 1585.31147540984 20.0803242330027 78.9484998854908 Trimmed Mean ( 8 / 25 ) 1584.64406779661 19.3707221323173 81.8061431562664 Trimmed Mean ( 9 / 25 ) 1584.35087719298 18.6563281077414 84.9229745555106 Trimmed Mean ( 10 / 25 ) 1583.69090909091 18.0559898513849 87.7100021724613 Trimmed Mean ( 11 / 25 ) 1582.69811320755 17.4564684553603 90.6654239518619 Trimmed Mean ( 12 / 25 ) 1581.74509803922 16.8205719782735 94.0363443099498 Trimmed Mean ( 13 / 25 ) 1580.87755102041 16.3302344863279 96.8067881905774 Trimmed Mean ( 14 / 25 ) 1579.91489361702 15.7431344091406 100.35580288889 Trimmed Mean ( 15 / 25 ) 1579.22222222222 15.1311401724414 104.369016757804 Trimmed Mean ( 16 / 25 ) 1578.53488372093 14.5036883397462 108.836790114628 Trimmed Mean ( 17 / 25 ) 1577.56097560976 13.8029710826297 114.291406260717 Trimmed Mean ( 18 / 25 ) 1576.82051282051 13.0080361227880 121.218952494926 Trimmed Mean ( 19 / 25 ) 1576.18918918919 12.0589043420490 130.707495845462 Trimmed Mean ( 20 / 25 ) 1575.37142857143 11.0817501358959 142.159082207466 Trimmed Mean ( 21 / 25 ) 1575.24242424242 10.4861046497465 150.221886664129 Trimmed Mean ( 22 / 25 ) 1574.83870967742 9.90102598943296 159.058133102387 Trimmed Mean ( 23 / 25 ) 1573.93103448276 9.48980929105003 165.854864540550 Trimmed Mean ( 24 / 25 ) 1572.81481481481 8.9947811771386 174.858596761901 Trimmed Mean ( 25 / 25 ) 1572.24 8.70196912581668 180.676347763121 Median 1577 Midrange 1817 Midmean - Weighted Average at Xnp 1572.07894736842 Midmean - Weighted Average at X(n+1)p 1576.82051282051 Midmean - Empirical Distribution Function 1576.82051282051 Midmean - Empirical Distribution Function - Averaging 1576.82051282051 Midmean - Empirical Distribution Function - Interpolation 1576.18918918919 Midmean - Closest Observation 1572.07894736842 Midmean - True Basic - Statistics Graphics Toolkit 1576.82051282051 Midmean - MS Excel (old versions) 1576.82051282051 Number of observations 75

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243887825vli6rs84ejwkisk/1m6m01243887788.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243887825vli6rs84ejwkisk/1m6m01243887788.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243887825vli6rs84ejwkisk/2slpq1243887788.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243887825vli6rs84ejwkisk/2slpq1243887788.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')

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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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