Central Tendency Consumptiegoederen

*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: Wed, 10 Dec 2008 05:45:44 -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/10/t1228913185bhkw44fqtsamvcp.htm/, Retrieved Wed, 10 Dec 2008 12:46:27 +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/10/t1228913185bhkw44fqtsamvcp.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)

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

Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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98,5 97,0 103,3 99,6 100,1 102,9 95,9 94,5 107,4 116,0 102,8 99,8 109,6 103,0 111,6 106,3 97,9 108,8 103,9 101,2 122,9 123,9 111,7 120,9 99,6 103,3 119,4 106,5 101,9 124,6 106,5 107,8 127,4 120,1 118,5 127,7 107,7 104,5 118,8 110,3 109,6 119,1 96,5 106,7 126,3 116,2 118,8 115,2 110,0 111,4 129,6 108,1 117,8 122,9 100,6 111,8 127,0 128,6 124,8 118,5 114,7 112,6 128,7 111,0 115,8 126,0 111,1 113,2 120,1 130,6 124,0 119,4 116,7 116,5 119,6 126,5 111,3 123,5 114,2 103,7 129,5

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 112.991358024691 1.08736599505136 103.912903786691 Geometric Mean 112.570828146094 Harmonic Mean 112.149194482513 Quadratic Mean 113.409153831776 Winsorized Mean ( 1 / 27 ) 112.996296296296 1.08138634792127 104.492068457778 Winsorized Mean ( 2 / 27 ) 113.008641975309 1.07803146718037 104.828704370650 Winsorized Mean ( 3 / 27 ) 112.997530864198 1.06897316500266 105.706611319767 Winsorized Mean ( 4 / 27 ) 113.037037037037 1.05994182877368 106.644566681379 Winsorized Mean ( 5 / 27 ) 113.018518518519 1.04342904411178 108.314522349458 Winsorized Mean ( 6 / 27 ) 113.077777777778 1.02575476577307 110.238608243321 Winsorized Mean ( 7 / 27 ) 113.043209876543 1.01978111042712 110.850464595483 Winsorized Mean ( 8 / 27 ) 113.013580246914 1.00818219419234 112.096385849632 Winsorized Mean ( 9 / 27 ) 113.024691358025 0.999052839814467 113.131845337644 Winsorized Mean ( 10 / 27 ) 113.049382716049 0.983049430857173 114.998675720178 Winsorized Mean ( 11 / 27 ) 112.967901234568 0.944053558261247 119.662597790142 Winsorized Mean ( 12 / 27 ) 113.041975308642 0.923512925771184 122.404323918093 Winsorized Mean ( 13 / 27 ) 113.09012345679 0.887206054500765 127.467709314074 Winsorized Mean ( 14 / 27 ) 113.090123456790 0.882052889112777 128.212406367767 Winsorized Mean ( 15 / 27 ) 113.034567901235 0.868122282757708 130.205813335611 Winsorized Mean ( 16 / 27 ) 112.975308641975 0.841919710520886 134.187746444466 Winsorized Mean ( 17 / 27 ) 112.975308641975 0.841919710520886 134.187746444466 Winsorized Mean ( 18 / 27 ) 112.619753086420 0.766178225553295 146.988976363941 Winsorized Mean ( 19 / 27 ) 112.479012345679 0.734485030080038 153.139965743648 Winsorized Mean ( 20 / 27 ) 112.627160493827 0.713113526937667 157.937209489608 Winsorized Mean ( 21 / 27 ) 112.964197530864 0.631970533385715 178.749152948114 Winsorized Mean ( 22 / 27 ) 112.964197530864 0.61773508206272 182.868353783078 Winsorized Mean ( 23 / 27 ) 112.964197530864 0.61773508206272 182.868353783078 Winsorized Mean ( 24 / 27 ) 112.934567901235 0.59848873586414 188.699571326387 Winsorized Mean ( 25 / 27 ) 113.058024691358 0.558828868539705 202.312427034763 Winsorized Mean ( 26 / 27 ) 113.154320987654 0.546730036364112 206.965620071211 Winsorized Mean ( 27 / 27 ) 113.087654320988 0.529731421338435 213.481114703857 Trimmed Mean ( 1 / 27 ) 113.002531645570 1.06657026709126 105.949448556961 Trimmed Mean ( 2 / 27 ) 113.009090909091 1.04917892874972 107.711933410406 Trimmed Mean ( 3 / 27 ) 113.009333333333 1.03080860997102 109.631732059854 Trimmed Mean ( 4 / 27 ) 113.013698630137 1.01311287531535 111.550944997081 Trimmed Mean ( 5 / 27 ) 113.007042253521 0.995299463431024 113.540744675939 Trimmed Mean ( 6 / 27 ) 113.004347826087 0.97900473754763 115.427784455016 Trimmed Mean ( 7 / 27 ) 112.989552238806 0.964090989080129 117.198017115182 Trimmed Mean ( 8 / 27 ) 112.98 0.947484523924757 119.242053191543 Trimmed Mean ( 9 / 27 ) 112.974603174603 0.929964207268018 121.482743412773 Trimmed Mean ( 10 / 27 ) 112.967213114754 0.910580554952302 124.060647353349 Trimmed Mean ( 11 / 27 ) 112.955932203390 0.890219836344856 126.885436149316 Trimmed Mean ( 12 / 27 ) 112.954385964912 0.873126602364102 129.367706423185 Trimmed Mean ( 13 / 27 ) 112.943636363636 0.85587596113627 131.962622496946 Trimmed Mean ( 14 / 27 ) 112.926415094340 0.841253776728901 134.235849179113 Trimmed Mean ( 15 / 27 ) 112.907843137255 0.823544911151998 137.099800640279 Trimmed Mean ( 16 / 27 ) 112.893877551020 0.80366617517238 140.473595926574 Trimmed Mean ( 17 / 27 ) 112.885106382979 0.78342554519262 144.091684367050 Trimmed Mean ( 18 / 27 ) 112.875555555556 0.757042061169225 149.100771734166 Trimmed Mean ( 19 / 27 ) 112.902325581395 0.738945766453542 152.788378669862 Trimmed Mean ( 20 / 27 ) 112.946341463415 0.721288629696165 156.589660245985 Trimmed Mean ( 21 / 27 ) 112.979487179487 0.702157649106989 160.903306149517 Trimmed Mean ( 22 / 27 ) 112.981081081081 0.69436641067944 162.711040372084 Trimmed Mean ( 23 / 27 ) 112.982857142857 0.685387527188065 164.845219180441 Trimmed Mean ( 24 / 27 ) 112.984848484848 0.671245467397952 168.321208816245 Trimmed Mean ( 25 / 27 ) 112.990322580645 0.654929280245424 172.522936428043 Trimmed Mean ( 26 / 27 ) 112.982758620690 0.641255483570928 176.189929778890 Trimmed Mean ( 27 / 27 ) 112.962962962963 0.622629936968003 181.428736808022 Median 111.8 Midrange 112.55 Midmean - Weighted Average at Xnp 112.7675 Midmean - Weighted Average at X(n+1)p 113.116666666667 Midmean - Empirical Distribution Function 113.116666666667 Midmean - Empirical Distribution Function - Averaging 113.116666666667 Midmean - Empirical Distribution Function - Interpolation 113.116666666667 Midmean - Closest Observation 112.902325581395 Midmean - True Basic - Statistics Graphics Toolkit 113.116666666667 Midmean - MS Excel (old versions) 113.116666666667 Number of observations 81

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228913185bhkw44fqtsamvcp/13trv1228913142.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228913185bhkw44fqtsamvcp/13trv1228913142.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228913185bhkw44fqtsamvcp/2wwan1228913142.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228913185bhkw44fqtsamvcp/2wwan1228913142.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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