S&P

*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, 26 Nov 2010 21:56:35 +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/Nov/26/t1290808562ksd9a6nwvwt2pph.htm/, Retrieved Fri, 26 Nov 2010 22:56:02 +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/Nov/26/t1290808562ksd9a6nwvwt2pph.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:

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1198.35 1183.26 1141.2 1049.33 1101.6 1030.71 1089.41 1186.69 1169.43 1104.49 1073.87 1115.1 1095.63 1036.19 1057.08 1020.62 987.48 919.32 919.14 872.81 797.87 735.09 825.88 903.25 896.24 968.75 1166.36 1282.83 1267.38 1280 1400.38 1385.59 1322.7 1330.63 1378.55 1468.36 1481.14 1549.38 1526.75 1473.99 1455.27 1503.35 1530.62 1482.37 1420.86 1406.82 1438.24 1418.3 1400.63 1377.94 1335.85 1303.82 1276.66 1270.2 1270.09 1310.61 1294.87 1280.66 1280.08 1248.29 1249.48 1207.01 1228.81 1220.33 1234.18 1191.33 1191.5 1156.85 1180.59 1203.6 1181.27

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 1216.10295774648 22.6932986442234 53.5886376331649 Geometric Mean 1200.20561010002 Harmonic Mean 1183.1162781983 Quadratic Mean 1230.83524895684 Winsorized Mean ( 1 / 23 ) 1216.72295774648 22.3869611855318 54.3496255549332 Winsorized Mean ( 2 / 23 ) 1217.40295774648 22.1601256392163 54.9366451060218 Winsorized Mean ( 3 / 23 ) 1218.39718309859 21.4894392660006 56.6974860542906 Winsorized Mean ( 4 / 23 ) 1218.53521126761 20.9746322106635 58.095665231646 Winsorized Mean ( 5 / 23 ) 1218.94225352113 20.8514983381425 58.4582572318739 Winsorized Mean ( 6 / 23 ) 1219.68084507042 20.4574031384453 59.6205117930288 Winsorized Mean ( 7 / 23 ) 1219.14352112676 20.3558441878381 59.8915726548525 Winsorized Mean ( 8 / 23 ) 1223.23816901408 18.976729440394 64.4599045824139 Winsorized Mean ( 9 / 23 ) 1223.45366197183 18.157686467075 67.3793803076344 Winsorized Mean ( 10 / 23 ) 1225.67338028169 16.9102684506243 72.4810125788654 Winsorized Mean ( 11 / 23 ) 1226.84 16.5773103023731 74.0071807562394 Winsorized Mean ( 12 / 23 ) 1225.82591549296 16.1052538168802 76.1134179834003 Winsorized Mean ( 13 / 23 ) 1227.09845070423 15.5245371754843 79.0425142362382 Winsorized Mean ( 14 / 23 ) 1228.57732394366 15.269028953717 80.4620469099699 Winsorized Mean ( 15 / 23 ) 1228.99985915493 14.2103125623059 86.4864761958129 Winsorized Mean ( 16 / 23 ) 1230.91535211268 13.4237819156433 91.6966142513266 Winsorized Mean ( 17 / 23 ) 1232.2585915493 13.17833183035 93.5064170042658 Winsorized Mean ( 18 / 23 ) 1223.1014084507 11.3442715479467 107.816654712579 Winsorized Mean ( 19 / 23 ) 1222.47788732394 11.0289761102681 110.842373317483 Winsorized Mean ( 20 / 23 ) 1223.23281690141 10.2644233999639 119.172092696966 Winsorized Mean ( 21 / 23 ) 1227.37661971831 8.63692343582856 142.108081522036 Winsorized Mean ( 22 / 23 ) 1230.12197183099 7.67031665121907 160.374340169578 Winsorized Mean ( 23 / 23 ) 1230.30338028169 6.86062575515237 179.328158128685 Trimmed Mean ( 1 / 23 ) 1218.24405797101 21.7358202245051 56.0477610408996 Trimmed Mean ( 2 / 23 ) 1219.85597014925 20.957673696066 58.2056953381345 Trimmed Mean ( 3 / 23 ) 1221.19569230769 20.1719247214953 60.5393738658155 Trimmed Mean ( 4 / 23 ) 1222.24698412698 19.5421083746174 62.5442741743528 Trimmed Mean ( 5 / 23 ) 1223.32704918033 18.9741142825086 64.4734732259971 Trimmed Mean ( 6 / 23 ) 1224.38237288136 18.3214345209924 66.8278660974105 Trimmed Mean ( 7 / 23 ) 1224.38237288136 17.6390692184729 69.4130941784103 Trimmed Mean ( 8 / 23 ) 1226.50454545455 16.8211728909976 72.9143296607424 Trimmed Mean ( 9 / 23 ) 1227.05150943396 16.1808999921839 75.8333288028902 Trimmed Mean ( 10 / 23 ) 1227.60803921569 15.5874413878977 78.756224877857 Trimmed Mean ( 11 / 23 ) 1227.88836734694 15.1435172204152 81.083433225909 Trimmed Mean ( 12 / 23 ) 1228.03234042553 14.6535404416728 83.8044802424103 Trimmed Mean ( 13 / 23 ) 1228.32244444444 14.1325944816721 86.9141505501623 Trimmed Mean ( 14 / 23 ) 1228.32244444444 13.5938683353463 90.3585656520303 Trimmed Mean ( 15 / 23 ) 1228.4656097561 12.9447475601571 94.9007003842407 Trimmed Mean ( 16 / 23 ) 1228.40076923077 12.3549888866517 99.4254855670434 Trimmed Mean ( 17 / 23 ) 1228.09918918919 11.7645319847232 104.389974100451 Trimmed Mean ( 18 / 23 ) 1227.60285714286 11.013568206256 111.46277338579 Trimmed Mean ( 19 / 23 ) 1228.14090909091 10.5143173163775 116.806528863068 Trimmed Mean ( 20 / 23 ) 1228.8235483871 9.8882851460041 124.270642507075 Trimmed Mean ( 21 / 23 ) 1229.50793103448 9.22984381461543 133.21004729111 Trimmed Mean ( 22 / 23 ) 1229.77481481481 8.8350292094118 139.193067240203 Trimmed Mean ( 23 / 23 ) 1229.73 8.56307635529818 143.608435680845 Median 1228.81 Midrange 1142.235 Midmean - Weighted Average at Xnp 1223.93694444444 Midmean - Weighted Average at X(n+1)p 1228.09918918919 Midmean - Empirical Distribution Function 1228.09918918919 Midmean - Empirical Distribution Function - Averaging 1228.09918918919 Midmean - Empirical Distribution Function - Interpolation 1227.60285714286 Midmean - Closest Observation 1223.93694444444 Midmean - True Basic - Statistics Graphics Toolkit 1228.09918918919 Midmean - MS Excel (old versions) 1228.09918918919 Number of observations 71

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/26/t1290808562ksd9a6nwvwt2pph/1k9331290808591.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290808562ksd9a6nwvwt2pph/1k9331290808591.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290808562ksd9a6nwvwt2pph/2k9331290808591.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/26/t1290808562ksd9a6nwvwt2pph/2k9331290808591.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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