*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 02 Jun 2010 11:42:38 +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/Jun/02/t1275478995bj5qfw8qduclzt2.htm/, Retrieved Wed, 02 Jun 2010 13:43:16 +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/Jun/02/t1275478995bj5qfw8qduclzt2.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 «

306 303 344 254 309 310 379 294 356 318 405 545 268 243 273 273 236 222 302 285 309 322 362 471 198 253 173 186 185 105 228 214 189 270 277 378 185 182 258 179 197 168 250 211 260 234 305 347 203 217 227 242 185 175 252 319 202 254 336 431 150 280 187 279 193 227 225 205 259 254 275 394 159 230 188 195 189 220 274

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 184.73.237.11 @ 184.73.237.11 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 260.088607594937 8.63858688333538 30.1077723830817 Geometric Mean 249.816231554906 Harmonic Mean 240.090219458319 Quadratic Mean 271.047686028245 Winsorized Mean ( 1 / 26 ) 259.721518987342 8.16899833658106 31.7935575802849 Winsorized Mean ( 2 / 26 ) 258.936708860759 7.81941470153844 33.1145896136976 Winsorized Mean ( 3 / 26 ) 258.291139240506 7.50164218522079 34.4312795602773 Winsorized Mean ( 4 / 26 ) 257.987341772152 7.32713792923117 35.2098383112084 Winsorized Mean ( 5 / 26 ) 257.164556962025 7.09065035248598 36.2681198730753 Winsorized Mean ( 6 / 26 ) 257.392405063291 7.02964506068185 36.6152775625808 Winsorized Mean ( 7 / 26 ) 256.240506329114 6.6918838678921 38.2912362778089 Winsorized Mean ( 8 / 26 ) 255.936708860759 6.52783075874748 39.2070073994791 Winsorized Mean ( 9 / 26 ) 254.911392405063 6.33140756881694 40.2614094313778 Winsorized Mean ( 10 / 26 ) 254.53164556962 6.26121416382401 40.6521225611881 Winsorized Mean ( 11 / 26 ) 253.556962025316 6.0417713664843 41.9673216090037 Winsorized Mean ( 12 / 26 ) 251.582278481013 5.6637526423576 44.419715048906 Winsorized Mean ( 13 / 26 ) 251.253164556962 5.56182881299197 45.1745591252387 Winsorized Mean ( 14 / 26 ) 251.253164556962 5.50846824856508 45.61216534604 Winsorized Mean ( 15 / 26 ) 249.73417721519 5.27918108773309 47.3054765625453 Winsorized Mean ( 16 / 26 ) 250.341772151899 5.13172433367088 48.7831683610374 Winsorized Mean ( 17 / 26 ) 250.772151898734 5.07054900137022 49.4566075253326 Winsorized Mean ( 18 / 26 ) 250.544303797468 4.90668513983308 51.0618261937206 Winsorized Mean ( 19 / 26 ) 250.544303797468 4.83834078323155 51.7831039652665 Winsorized Mean ( 20 / 26 ) 251.050632911392 4.62599581757048 54.2695330501274 Winsorized Mean ( 21 / 26 ) 251.050632911392 4.55172938783173 55.1549996760645 Winsorized Mean ( 22 / 26 ) 249.379746835443 4.16275910757379 59.9073211759282 Winsorized Mean ( 23 / 26 ) 248.506329113924 3.57349112554058 69.5416108180012 Winsorized Mean ( 24 / 26 ) 247.898734177215 3.25571402101951 76.1426625854524 Winsorized Mean ( 25 / 26 ) 248.53164556962 3.09021738820126 80.4252951648441 Winsorized Mean ( 26 / 26 ) 248.860759493671 2.87930613560456 86.4308092898979 Trimmed Mean ( 1 / 26 ) 258.402597402597 7.78200203152638 33.2051567650277 Trimmed Mean ( 2 / 26 ) 257.013333333333 7.31899893054681 35.1159134974941 Trimmed Mean ( 3 / 26 ) 255.972602739726 6.99728074500962 36.5817253970098 Trimmed Mean ( 4 / 26 ) 255.112676056338 6.76336293477102 37.719796869806 Trimmed Mean ( 5 / 26 ) 254.289855072464 6.54944149591948 38.8261892607018 Trimmed Mean ( 6 / 26 ) 253.611940298507 6.36934068641988 39.8176126516886 Trimmed Mean ( 7 / 26 ) 252.846153846154 6.16902275210396 40.9864194065292 Trimmed Mean ( 8 / 26 ) 252.238095238095 6.01583991603824 41.9289905912602 Trimmed Mean ( 9 / 26 ) 251.639344262295 5.86855251546012 42.8792864338142 Trimmed Mean ( 10 / 26 ) 251.152542372881 5.73375853035916 43.8024275077293 Trimmed Mean ( 11 / 26 ) 250.684210526316 5.5829447305047 44.9017897591929 Trimmed Mean ( 12 / 26 ) 250.309090909091 5.44398303923669 45.9790357730775 Trimmed Mean ( 13 / 26 ) 250.150943396226 5.34963315661137 46.7603919882013 Trimmed Mean ( 14 / 26 ) 250.019607843137 5.24942500650167 47.6279987871959 Trimmed Mean ( 15 / 26 ) 249.877551020408 5.1310738566767 48.6988801954703 Trimmed Mean ( 16 / 26 ) 249.893617021277 5.02548859858778 49.7252380776467 Trimmed Mean ( 17 / 26 ) 249.844444444444 4.91708581218587 50.8114875329738 Trimmed Mean ( 18 / 26 ) 249.744186046512 4.78578703045142 52.1845590824284 Trimmed Mean ( 19 / 26 ) 249.658536585366 4.64713519883127 53.7231059359223 Trimmed Mean ( 20 / 26 ) 249.564102564103 4.47557396432173 55.7613625768609 Trimmed Mean ( 21 / 26 ) 249.564102564103 4.2946050833588 58.1110713837556 Trimmed Mean ( 22 / 26 ) 249.228571428571 4.06317459077284 61.3383859986107 Trimmed Mean ( 23 / 26 ) 249.212121212121 3.85405079492265 64.6623862717209 Trimmed Mean ( 24 / 26 ) 249.290322580645 3.7307768363952 66.819950244335 Trimmed Mean ( 25 / 26 ) 249.448275862069 3.63940740009732 68.5409047240489 Trimmed Mean ( 26 / 26 ) 249.555555555556 3.54632884023957 70.3701114019357 Median 253 Midrange 325 Midmean - Weighted Average at Xnp 248.275 Midmean - Weighted Average at X(n+1)p 249.658536585366 Midmean - Empirical Distribution Function 249.658536585366 Midmean - Empirical Distribution Function - Averaging 249.658536585366 Midmean - Empirical Distribution Function - Interpolation 249.564102564103 Midmean - Closest Observation 248.275 Midmean - True Basic - Statistics Graphics Toolkit 249.658536585366 Midmean - MS Excel (old versions) 249.658536585366 Number of observations 79

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/02/t1275478995bj5qfw8qduclzt2/1kzzh1275478956.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275478995bj5qfw8qduclzt2/1kzzh1275478956.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275478995bj5qfw8qduclzt2/2kzzh1275478956.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/02/t1275478995bj5qfw8qduclzt2/2kzzh1275478956.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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