centrummaten

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 02 Jul 2010 16:53:16 +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/Jul/02/t1278089630absv1en69lcig4e.htm/, Retrieved Fri, 02 Jul 2010 18:53:52 +0200

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/Jul/02/t1278089630absv1en69lcig4e.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:

thomas talboom

Dataseries X:

» Textbox « » Textfile « » CSV «

237 236 235 233 231 230 231 233 234 234 235 237 246 245 240 239 231 224 229 231 238 240 237 239 248 239 237 232 216 209 214 217 217 227 218 220 229 224 216 208 191 190 196 196 200 204 193 194 207 209 193 175 157 150 162 157 160 167 159 161 179 180 169 152 128 125 131 135 141 154 152 147 163 165 147 130 106 107 115 114 124 141 139 129

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 192.976190476190 4.58232454940695 42.1131651404233 Geometric Mean 187.970650192598 Harmonic Mean 182.526644997102 Quadratic Mean 197.440165740457 Winsorized Mean ( 1 / 28 ) 192.964285714286 4.57623154260649 42.1666351271157 Winsorized Mean ( 2 / 28 ) 193.107142857143 4.53655446431226 42.56691821431 Winsorized Mean ( 3 / 28 ) 192.964285714286 4.50554087473273 42.8282177610324 Winsorized Mean ( 4 / 28 ) 193.392857142857 4.42029617991494 43.7511083582138 Winsorized Mean ( 5 / 28 ) 193.392857142857 4.40159889379983 43.936956049147 Winsorized Mean ( 6 / 28 ) 193.607142857143 4.36212305790771 44.3836958029346 Winsorized Mean ( 7 / 28 ) 193.690476190476 4.34710210021249 44.5562288911982 Winsorized Mean ( 8 / 28 ) 193.690476190476 4.31823496799393 44.8540845104722 Winsorized Mean ( 9 / 28 ) 193.690476190476 4.28612941828272 45.1900671417617 Winsorized Mean ( 10 / 28 ) 194.166666666667 4.20378191246472 46.1885679870641 Winsorized Mean ( 11 / 28 ) 194.690476190476 4.11666415310011 47.2932619591671 Winsorized Mean ( 12 / 28 ) 194.976190476190 4.07055447196801 47.8991724146918 Winsorized Mean ( 13 / 28 ) 194.821428571429 4.05145337437291 48.0868001107339 Winsorized Mean ( 14 / 28 ) 195.654761904762 3.87529704032865 50.487681297372 Winsorized Mean ( 15 / 28 ) 195.654761904762 3.87529704032865 50.487681297372 Winsorized Mean ( 16 / 28 ) 196.035714285714 3.76677530808796 52.0433788192222 Winsorized Mean ( 17 / 28 ) 196.440476190476 3.70774534679074 52.9811132688782 Winsorized Mean ( 18 / 28 ) 196.226190476190 3.68177471574633 53.2966315502587 Winsorized Mean ( 19 / 28 ) 196.678571428571 3.61687734054975 54.3780042589658 Winsorized Mean ( 20 / 28 ) 197.154761904762 3.48780738543489 56.5268491396863 Winsorized Mean ( 21 / 28 ) 196.904761904762 3.45791097646771 56.9432710225242 Winsorized Mean ( 22 / 28 ) 197.428571428571 3.38567422166564 58.3129263191316 Winsorized Mean ( 23 / 28 ) 197.702380952381 3.34837882874837 59.0442094708508 Winsorized Mean ( 24 / 28 ) 197.988095238095 3.30976293831831 59.8194187704249 Winsorized Mean ( 25 / 28 ) 197.988095238095 3.23414505225926 61.2180629003598 Winsorized Mean ( 26 / 28 ) 197.988095238095 3.15594377021926 62.7349882169606 Winsorized Mean ( 27 / 28 ) 198.630952380952 3.070587606744 64.6882544385625 Winsorized Mean ( 28 / 28 ) 198.630952380952 2.90388090577883 68.4018934749251 Trimmed Mean ( 1 / 28 ) 193.365853658537 4.52153707930243 42.7655132020655 Trimmed Mean ( 2 / 28 ) 193.7875 4.45702736797305 43.479091331703 Trimmed Mean ( 3 / 28 ) 194.153846153846 4.40514324632828 44.0743547478677 Trimmed Mean ( 4 / 28 ) 194.592105263158 4.35620862160434 44.6700610935139 Trimmed Mean ( 5 / 28 ) 194.932432432432 4.32638817142015 45.0566210679254 Trimmed Mean ( 6 / 28 ) 195.291666666667 4.29430954678026 45.4768489647166 Trimmed Mean ( 7 / 28 ) 195.628571428571 4.26416389920027 45.8773574499003 Trimmed Mean ( 8 / 28 ) 195.970588235294 4.2293743992117 46.3355971208935 Trimmed Mean ( 9 / 28 ) 196.333333333333 4.19147393746565 46.8411199168866 Trimmed Mean ( 10 / 28 ) 196.71875 4.14987501903504 47.4035360336568 Trimmed Mean ( 11 / 28 ) 197.064516129032 4.11359530059300 47.9056644440994 Trimmed Mean ( 12 / 28 ) 197.366666666667 4.08338002971109 48.3341411356785 Trimmed Mean ( 13 / 28 ) 197.655172413793 4.05173379154737 48.7828624936161 Trimmed Mean ( 14 / 28 ) 197.982142857143 4.01243934868824 49.3420898491258 Trimmed Mean ( 15 / 28 ) 198.240740740741 3.99221247391555 49.6568612106727 Trimmed Mean ( 16 / 28 ) 198.519230769231 3.96215985256737 50.1037914057394 Trimmed Mean ( 17 / 28 ) 198.78 3.93915872091636 50.4625515454625 Trimmed Mean ( 18 / 28 ) 199.020833333333 3.91538264564529 50.8304938100201 Trimmed Mean ( 19 / 28 ) 199.304347826087 3.88330622186436 51.3233663376673 Trimmed Mean ( 20 / 28 ) 199.568181818182 3.84866986814771 51.8538062902834 Trimmed Mean ( 21 / 28 ) 199.809523809524 3.8223072392128 52.274584774267 Trimmed Mean ( 22 / 28 ) 200.1 3.78505834389203 52.8657637002882 Trimmed Mean ( 23 / 28 ) 200.368421052632 3.74344777081866 53.5251012755048 Trimmed Mean ( 24 / 28 ) 200.638888888889 3.68742022303325 54.4117233060691 Trimmed Mean ( 25 / 28 ) 200.911764705882 3.61181652665362 55.6262377181237 Trimmed Mean ( 26 / 28 ) 201.21875 3.51744912354018 57.2058736126029 Trimmed Mean ( 27 / 28 ) 201.566666666667 3.39664585512445 59.3428562364155 Trimmed Mean ( 28 / 28 ) 201.892857142857 3.24173319216607 62.2792948015428 Median 205.5 Midrange 177 Midmean - Weighted Average at Xnp 198.813953488372 Midmean - Weighted Average at X(n+1)p 198.813953488372 Midmean - Empirical Distribution Function 198.813953488372 Midmean - Empirical Distribution Function - Averaging 198.813953488372 Midmean - Empirical Distribution Function - Interpolation 198.813953488372 Midmean - Closest Observation 198.813953488372 Midmean - True Basic - Statistics Graphics Toolkit 198.813953488372 Midmean - MS Excel (old versions) 199.568181818182 Number of observations 84

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/02/t1278089630absv1en69lcig4e/172pw1278089595.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/02/t1278089630absv1en69lcig4e/172pw1278089595.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/02/t1278089630absv1en69lcig4e/20coz1278089595.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/02/t1278089630absv1en69lcig4e/20coz1278089595.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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