Intermediaire goederen

*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, 05 Dec 2008 08:19:38 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/05/t1228490482kykqwyvx86af3st.htm/, Retrieved Fri, 05 Dec 2008 15:21:24 +0000

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/2008/Dec/05/t1228490482kykqwyvx86af3st.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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103,1 100,6 103,1 95,5 90,5 90,9 88,8 90,7 94,3 104,6 111,1 110,8 107,2 99 99 91 96,2 96,9 96,2 100,1 99 115,4 106,9 107,1 99,3 99,2 108,3 105,6 99,5 107,4 93,1 88,1 110,7 113,1 99,6 93,6 98,6 99,6 114,3 107,8 101,2 112,5 100,5 93,9 116,2 112 106,4 95,7 96 95,8 103 102,2 98,4 111,4 86,6 91,3 107,9 101,8 104,4 93,4 100,1 98,5 112,9 101,4 107,1 110,8 90,3 95,5 111,4 113 107,5 95,9 106,3 105,2 117,2 106,9 108,2 113 97,2 99,9 108,1 118,1 109,1 93,3 112,1

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 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 102.416470588235 0.840357812045329 121.872456137423 Geometric Mean 102.125951119340 Harmonic Mean 101.834857409753 Quadratic Mean 102.705668553109 Winsorized Mean ( 1 / 28 ) 102.423529411765 0.83428401860169 122.768178615518 Winsorized Mean ( 2 / 28 ) 102.416470588235 0.826166685555424 123.965868363939 Winsorized Mean ( 3 / 28 ) 102.441176470588 0.810758012573044 126.352345437177 Winsorized Mean ( 4 / 28 ) 102.398823529412 0.79957182890172 128.067072685721 Winsorized Mean ( 5 / 28 ) 102.34 0.785477784625419 130.290126599576 Winsorized Mean ( 6 / 28 ) 102.347058823529 0.781854056307806 130.903022114957 Winsorized Mean ( 7 / 28 ) 102.355294117647 0.780423116371379 131.153590879719 Winsorized Mean ( 8 / 28 ) 102.374117647059 0.774047083703834 132.258256380473 Winsorized Mean ( 9 / 28 ) 102.522352941176 0.736414541320522 139.218262525528 Winsorized Mean ( 10 / 28 ) 102.498823529412 0.72534256200937 141.310918313501 Winsorized Mean ( 11 / 28 ) 102.498823529412 0.721359776741406 142.091126833311 Winsorized Mean ( 12 / 28 ) 102.442352941176 0.704070550622414 145.500124739794 Winsorized Mean ( 13 / 28 ) 102.488235294118 0.697276437801724 146.98364914958 Winsorized Mean ( 14 / 28 ) 102.504705882353 0.68023909514318 150.689230616446 Winsorized Mean ( 15 / 28 ) 102.663529411765 0.64299031593272 159.665747473726 Winsorized Mean ( 16 / 28 ) 102.663529411765 0.64299031593272 159.665747473726 Winsorized Mean ( 17 / 28 ) 102.683529411765 0.63470773851438 161.780805843189 Winsorized Mean ( 18 / 28 ) 102.365882352941 0.583043672639517 175.571551766469 Winsorized Mean ( 19 / 28 ) 102.209411764706 0.556068188817341 183.807334820010 Winsorized Mean ( 20 / 28 ) 102.209411764706 0.549837316223697 185.890278358486 Winsorized Mean ( 21 / 28 ) 102.234117647059 0.54002944452657 189.312117484047 Winsorized Mean ( 22 / 28 ) 102.182352941176 0.533379312979284 191.575395698080 Winsorized Mean ( 23 / 28 ) 102.344705882353 0.505101442739546 202.622081867873 Winsorized Mean ( 24 / 28 ) 102.344705882353 0.483476282972668 211.685059819447 Winsorized Mean ( 25 / 28 ) 102.668235294118 0.436734802662118 235.081414781472 Winsorized Mean ( 26 / 28 ) 102.637647058824 0.425332219701839 241.311714242512 Winsorized Mean ( 27 / 28 ) 102.637647058824 0.417616205906597 245.770268507681 Winsorized Mean ( 28 / 28 ) 102.769411764706 0.402687134949472 255.209076340621 Trimmed Mean ( 1 / 28 ) 102.418072289157 0.817288839906177 125.314414302921 Trimmed Mean ( 2 / 28 ) 102.412345679012 0.797626461036638 128.396374345344 Trimmed Mean ( 3 / 28 ) 102.410126582278 0.77982012368608 131.325319098208 Trimmed Mean ( 4 / 28 ) 102.398701298701 0.765791808080778 133.716109545925 Trimmed Mean ( 5 / 28 ) 102.398666666667 0.753204549304565 135.950674702126 Trimmed Mean ( 6 / 28 ) 102.412328767123 0.742442760544187 137.939696108099 Trimmed Mean ( 7 / 28 ) 102.425352112676 0.730559495385023 140.201246797422 Trimmed Mean ( 8 / 28 ) 102.437681159420 0.716717027065237 142.926255817969 Trimmed Mean ( 9 / 28 ) 102.447761194030 0.701598479254383 146.020500647187 Trimmed Mean ( 10 / 28 ) 102.436923076923 0.691335695866124 148.172477841734 Trimmed Mean ( 11 / 28 ) 102.428571428571 0.680988365521445 150.411631996297 Trimmed Mean ( 12 / 28 ) 102.419672131148 0.669037395412045 153.085123243477 Trimmed Mean ( 13 / 28 ) 102.416949152542 0.657604674040215 155.742428841495 Trimmed Mean ( 14 / 28 ) 102.408771929825 0.64466812925579 158.855025217465 Trimmed Mean ( 15 / 28 ) 102.398181818182 0.631733710410723 162.090735591120 Trimmed Mean ( 16 / 28 ) 102.369811320755 0.622238951539688 164.518487740839 Trimmed Mean ( 17 / 28 ) 102.339215686275 0.609969966675458 167.777466559637 Trimmed Mean ( 18 / 28 ) 102.304081632653 0.595732836182518 171.728122774333 Trimmed Mean ( 19 / 28 ) 102.297872340426 0.587500777346718 174.123807635498 Trimmed Mean ( 20 / 28 ) 102.306666666667 0.58138983600863 175.969135217472 Trimmed Mean ( 21 / 28 ) 102.316279069767 0.573867320342632 178.292569454345 Trimmed Mean ( 22 / 28 ) 102.324390243902 0.565197790631037 181.041737848371 Trimmed Mean ( 23 / 28 ) 102.338461538462 0.554269593716295 184.636614922889 Trimmed Mean ( 24 / 28 ) 102.337837837838 0.545171975392191 187.716615044669 Trimmed Mean ( 25 / 28 ) 102.337142857143 0.536751600754357 190.660153995474 Trimmed Mean ( 26 / 28 ) 102.303030303030 0.534482985252416 191.405588439296 Trimmed Mean ( 27 / 28 ) 102.267741935484 0.531975161049497 192.241573335354 Trimmed Mean ( 28 / 28 ) 102.227586206897 0.527959557520689 193.627683694107 Median 101.4 Midrange 102.35 Midmean - Weighted Average at Xnp 102.178571428571 Midmean - Weighted Average at X(n+1)p 102.316279069767 Midmean - Empirical Distribution Function 102.316279069767 Midmean - Empirical Distribution Function - Averaging 102.316279069767 Midmean - Empirical Distribution Function - Interpolation 102.316279069767 Midmean - Closest Observation 102.172727272727 Midmean - True Basic - Statistics Graphics Toolkit 102.316279069767 Midmean - MS Excel (old versions) 102.316279069767 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228490482kykqwyvx86af3st/12j9y1228490376.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228490482kykqwyvx86af3st/12j9y1228490376.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228490482kykqwyvx86af3st/2qbml1228490376.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/05/t1228490482kykqwyvx86af3st/2qbml1228490376.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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