*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Sun, 14 Mar 2010 03:17:07 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/14/t1268558280igvvqx1mnoygven.htm/, Retrieved Sun, 14 Mar 2010 10:18:02 +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/Mar/14/t1268558280igvvqx1mnoygven.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 «

77 70 67 76 85 106 108 120 108 111 109 104 104 117 111 110 116 118 115 111 112 97 106 93 95 97 81 71 75 70 72 80 78 80 81 99 87 100 95 128 112 104 102 108 103 99 96 85 78 74 106 100 109 87 107 106 109 83 84 83 65 68 61 75 66 78 68 68 174 64 48 45

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 92.4305555555556 2.47616386293216 37.3281255490513 Geometric Mean 90.0472883555268 Harmonic Mean 87.5715615902422 Quadratic Mean 94.756192996084 Winsorized Mean ( 1 / 24 ) 91.8333333333333 2.24017590970358 40.9938045202372 Winsorized Mean ( 2 / 24 ) 91.9722222222222 2.10641878242229 43.6628380784082 Winsorized Mean ( 3 / 24 ) 92.0138888888889 2.06633848063937 44.5299208000122 Winsorized Mean ( 4 / 24 ) 92.0138888888889 2.04617023229848 44.9688336954882 Winsorized Mean ( 5 / 24 ) 92.0138888888889 2.02164471688981 45.5143716005884 Winsorized Mean ( 6 / 24 ) 92.0138888888889 1.99299369972664 46.1686802630183 Winsorized Mean ( 7 / 24 ) 91.8194444444444 1.93075819969769 47.5561592636618 Winsorized Mean ( 8 / 24 ) 91.8194444444444 1.93075819969769 47.5561592636618 Winsorized Mean ( 9 / 24 ) 91.6944444444444 1.91267075693856 47.9405271983201 Winsorized Mean ( 10 / 24 ) 91.9722222222222 1.86538061648954 49.304802145583 Winsorized Mean ( 11 / 24 ) 91.9722222222222 1.86538061648954 49.304802145583 Winsorized Mean ( 12 / 24 ) 91.9722222222222 1.81434600259841 50.6916663582934 Winsorized Mean ( 13 / 24 ) 91.9722222222222 1.76027858068562 52.2486742901793 Winsorized Mean ( 14 / 24 ) 92.3611111111111 1.69959324457625 54.343067911016 Winsorized Mean ( 15 / 24 ) 92.5694444444444 1.66828869297315 55.4876651950875 Winsorized Mean ( 16 / 24 ) 92.3472222222222 1.63791631177386 56.3809161422968 Winsorized Mean ( 17 / 24 ) 92.5833333333333 1.60310121010118 57.7526439066752 Winsorized Mean ( 18 / 24 ) 92.8333333333333 1.56709613532150 59.2390800034024 Winsorized Mean ( 19 / 24 ) 92.8333333333333 1.49425084992578 62.1270072143138 Winsorized Mean ( 20 / 24 ) 92.5555555555556 1.45765596460409 63.4961594526141 Winsorized Mean ( 21 / 24 ) 92.5555555555556 1.45765596460409 63.4961594526141 Winsorized Mean ( 22 / 24 ) 93.1666666666667 1.37337184867820 67.8379033007955 Winsorized Mean ( 23 / 24 ) 93.1666666666667 1.37337184867820 67.8379033007955 Winsorized Mean ( 24 / 24 ) 92.8333333333333 1.24234746751742 74.7241297306638 Trimmed Mean ( 1 / 24 ) 91.9428571428571 2.15466999334992 42.671433410511 Trimmed Mean ( 2 / 24 ) 92.0588235294118 2.05241697310587 44.8538599786093 Trimmed Mean ( 3 / 24 ) 92.1060606060606 2.01661268161137 45.6736494052311 Trimmed Mean ( 4 / 24 ) 92.140625 1.99115942777455 46.2748606237836 Trimmed Mean ( 5 / 24 ) 92.1774193548387 1.96687590932967 46.8648880784012 Trimmed Mean ( 6 / 24 ) 92.2166666666667 1.94400304379262 47.4364826542444 Trimmed Mean ( 7 / 24 ) 92.2586206896552 1.92282440361335 47.9807831210608 Trimmed Mean ( 8 / 24 ) 92.3392857142857 1.91071428571429 48.3271028037383 Trimmed Mean ( 9 / 24 ) 92.425925925926 1.89386479605186 48.8028111186216 Trimmed Mean ( 10 / 24 ) 92.5384615384615 1.87494827248135 49.3552077658089 Trimmed Mean ( 11 / 24 ) 92.62 1.85975420803011 49.8022801078132 Trimmed Mean ( 12 / 24 ) 92.7083333333333 1.83831327188246 50.4311940469203 Trimmed Mean ( 13 / 24 ) 92.804347826087 1.81954487201411 51.0041545297858 Trimmed Mean ( 14 / 24 ) 92.9090909090909 1.80404120635489 51.5005370064778 Trimmed Mean ( 15 / 24 ) 92.9761904761905 1.79381052738976 51.8316673118669 Trimmed Mean ( 16 / 24 ) 93.025 1.78328690330165 52.1649095430297 Trimmed Mean ( 17 / 24 ) 93.1052631578947 1.77134994196658 52.5617558405924 Trimmed Mean ( 18 / 24 ) 93.1666666666667 1.75865208124209 52.9761785519654 Trimmed Mean ( 19 / 24 ) 93.2058823529412 1.74475501846159 53.4206128463377 Trimmed Mean ( 20 / 24 ) 93.25 1.73728096786050 53.6758312127481 Trimmed Mean ( 21 / 24 ) 93.3333333333333 1.72828619738648 54.0034014473252 Trimmed Mean ( 22 / 24 ) 93.4285714285714 1.70699507894618 54.7327713951289 Trimmed Mean ( 23 / 24 ) 93.4615384615385 1.69363584245962 55.1839634698607 Trimmed Mean ( 24 / 24 ) 93.5 1.66267638271047 56.2346352978067 Median 95.5 Midrange 109.5 Midmean - Weighted Average at Xnp 93.4871794871795 Midmean - Weighted Average at X(n+1)p 93.9473684210526 Midmean - Empirical Distribution Function 93.4871794871795 Midmean - Empirical Distribution Function - Averaging 93.9473684210526 Midmean - Empirical Distribution Function - Interpolation 93.9473684210526 Midmean - Closest Observation 93.4871794871795 Midmean - True Basic - Statistics Graphics Toolkit 93.9473684210526 Midmean - MS Excel (old versions) 93.4871794871795 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/14/t1268558280igvvqx1mnoygven/1wxbb1268558225.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268558280igvvqx1mnoygven/1wxbb1268558225.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268558280igvvqx1mnoygven/2i8ym1268558225.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/14/t1268558280igvvqx1mnoygven/2i8ym1268558225.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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