WS6 TUT 1

*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: Tue, 16 Nov 2010 09:25:25 +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/16/t1289899434rb6mndjsa2xzaj1.htm/, Retrieved Tue, 16 Nov 2010 10:23:54 +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/16/t1289899434rb6mndjsa2xzaj1.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?

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Dataseries X:

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2981,85 3080,58 3106,22 3119,31 3061,26 3097,31 3161,69 3257,16 3277,01 3295,32 3363,99 3494,17 3667,03 3813,06 3917,96 3895,51 3801,06 3570,12 3701,61 3862,27 3970,10 4138,52 4199,75 4290,89 4443,91 4502,64 4356,98 4591,27 4696,96 4621,40 4562,84 4202,52 4296,49 4435,23 4105,18 4116,68 3844,49 3720,98 3674,40 3857,62 3801,06 3504,37 3032,60 3047,03 2962,34 2197,82 2014,45 1862,83 1905,41 1810,99 1670,07 1864,44 2052,02 2029,60 2070,83 2293,41 2443,27 2513,17 2466,92 2502,66 2539,91

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 3339.97606557377 110.441193198449 30.2421222448425 Geometric Mean 3217.27899536707 Harmonic Mean 3082.96392121021 Quadratic Mean 3447.79285165328 Winsorized Mean ( 1 / 20 ) 3341.04754098361 109.633947788724 30.4745711376018 Winsorized Mean ( 2 / 20 ) 3341.75934426230 109.053708964937 30.6432433704454 Winsorized Mean ( 3 / 20 ) 3340.44032786885 108.771357835636 30.7106612837965 Winsorized Mean ( 4 / 20 ) 3339.17934426230 107.442771784245 31.0786783402021 Winsorized Mean ( 5 / 20 ) 3343.3031147541 104.645940795890 31.9487128628826 Winsorized Mean ( 6 / 20 ) 3343.93950819672 104.182228801538 32.0970240957961 Winsorized Mean ( 7 / 20 ) 3337.53278688525 102.110557360846 32.6854820221068 Winsorized Mean ( 8 / 20 ) 3332.06655737705 100.297319964272 33.2218902615144 Winsorized Mean ( 9 / 20 ) 3349.97655737705 96.3311139310447 34.7756443445159 Winsorized Mean ( 10 / 20 ) 3351.16016393443 90.9382783533037 36.8509303740594 Winsorized Mean ( 11 / 20 ) 3377.68459016393 85.7821085545473 39.3751639715888 Winsorized Mean ( 12 / 20 ) 3370.29180327869 83.0470253792676 40.5829322349223 Winsorized Mean ( 13 / 20 ) 3373.25409836066 80.9589215885112 41.6662429806791 Winsorized Mean ( 14 / 20 ) 3373.0268852459 80.1240895277601 42.0975377708008 Winsorized Mean ( 15 / 20 ) 3346.38590163934 74.0718506536429 45.1775657298872 Winsorized Mean ( 16 / 20 ) 3443.51114754098 53.4644450799809 64.4074981492769 Winsorized Mean ( 17 / 20 ) 3442.69180327869 51.733836218847 66.5462307630783 Winsorized Mean ( 18 / 20 ) 3447.85868852459 48.1243498166145 71.6447848472386 Winsorized Mean ( 19 / 20 ) 3450.90491803279 47.2733585478618 72.9989369073265 Winsorized Mean ( 20 / 20 ) 3451.26557377049 45.9961309405919 75.0338235672063 Trimmed Mean ( 1 / 20 ) 3345.27983050847 108.129938198464 30.9375912558876 Trimmed Mean ( 2 / 20 ) 3349.80912280702 106.238094658457 31.5311483472691 Trimmed Mean ( 3 / 20 ) 3354.27309090909 104.241988206176 32.1777543639593 Trimmed Mean ( 4 / 20 ) 3359.58 101.854101961013 32.9842385855599 Trimmed Mean ( 5 / 20 ) 3365.68019607843 99.347599122925 33.8778211631868 Trimmed Mean ( 6 / 20 ) 3371.25163265306 97.1061672311044 34.7171732628451 Trimmed Mean ( 7 / 20 ) 3377.15957446809 94.3469638214566 35.7951060392263 Trimmed Mean ( 8 / 20 ) 3384.83333333333 91.3590567154641 37.0497841705538 Trimmed Mean ( 9 / 20 ) 3394.19023255814 87.933509525074 38.5995083204349 Trimmed Mean ( 10 / 20 ) 3401.49926829268 84.5611882642229 40.2253012063198 Trimmed Mean ( 11 / 20 ) 3409.37282051282 81.5465446692651 41.8089182606141 Trimmed Mean ( 12 / 20 ) 3414.12216216216 78.919961704411 43.2605653681069 Trimmed Mean ( 13 / 20 ) 3420.488 75.9965362642803 45.0084723349121 Trimmed Mean ( 14 / 20 ) 3427.20424242424 72.4584088787532 47.2989166538156 Trimmed Mean ( 15 / 20 ) 3434.81903225806 67.5797110727655 50.8261869980425 Trimmed Mean ( 16 / 20 ) 3447.22 62.338248897573 55.2986338397806 Trimmed Mean ( 17 / 20 ) 3447.74370370370 62.0031974709644 55.6059017007672 Trimmed Mean ( 18 / 20 ) 3448.4688 61.6603816247245 55.9268157143101 Trimmed Mean ( 19 / 20 ) 3448.55869565217 61.8717135025437 55.73724243972 Trimmed Mean ( 20 / 20 ) 3448.2 61.8843770845506 55.720040540908 Median 3494.17 Midrange 3183.515 Midmean - Weighted Average at Xnp 3416.97633333333 Midmean - Weighted Average at X(n+1)p 3434.81903225806 Midmean - Empirical Distribution Function 3434.81903225806 Midmean - Empirical Distribution Function - Averaging 3434.81903225806 Midmean - Empirical Distribution Function - Interpolation 3434.81903225806 Midmean - Closest Observation 3406.0175 Midmean - True Basic - Statistics Graphics Toolkit 3434.81903225806 Midmean - MS Excel (old versions) 3434.81903225806 Number of observations 61

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899434rb6mndjsa2xzaj1/1ii041289899522.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899434rb6mndjsa2xzaj1/1ii041289899522.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899434rb6mndjsa2xzaj1/2aah71289899522.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/16/t1289899434rb6mndjsa2xzaj1/2aah71289899522.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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