CVWS1EAQ1

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

Title produced by software: Central Tendency

Date of computation: Sun, 06 Jan 2008 06:27:54 -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/Jan/06/t1199626073v7pxfm6d0l7ymjm.htm/, Retrieved Sun, 06 Jan 2008 14:27:55 +0100

User-defined keywords:

Investigating associations Econ Activiteit BE Q1

Dataseries X:

» Textbox « » Textfile « » CSV «

6,6 9,5 10,4 11,9 13,5 16,2 17,6 15,8 17,6 15,2 15,9 12,0 13,3 14,8 16,1 16,9 17,6 13,9 10,0 7,6 7,1 8,1 8,1 7,7 4,0 1,4 0,3 -1,0 -1,9 -1,5 -0,2 3,4 3,0 4,1 3,4 3,2 6,1 5,8 6,2 5,8 5,9 6,7 5,9 3,8 1,7 1,4 1,8 3,0 3,6 4,8 4,3 4,2 2,9 4,9 7,2 8,7 9,1 8,9 9,0 11,6 9,6 9,1 9,2 10,8 11,0 8,5 6,5 7,2 7,8 8,7 7,8 7,5 7,7 7,5 8,3 7,9 10,4 11,5 14,0 11,9 11,9 10,3 11,3 9,9 8,9 9,2 8,8 6,7 7,1 6,6 7,2 5,0 5,3 6,3 8,0 7,7 7,0

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 7.98969072164948 0.448238928352069 17.8246248067370 Geometric Mean NaN Harmonic Mean 8.83474568892373 Quadratic Mean 9.11719797794652 Winsorized Mean ( 1 / 32 ) 7.99381443298969 0.447309190715265 17.8708924361855 Winsorized Mean ( 2 / 32 ) 8.00412371134021 0.445083194098313 17.9834327996941 Winsorized Mean ( 3 / 32 ) 8.00721649484536 0.435308693404884 18.3943408807547 Winsorized Mean ( 4 / 32 ) 7.99896907216495 0.425367475165932 18.8048441386936 Winsorized Mean ( 5 / 32 ) 8.05051546391753 0.414233765864262 19.4347156782858 Winsorized Mean ( 6 / 32 ) 8.03814432989691 0.411751359855856 19.5218403958905 Winsorized Mean ( 7 / 32 ) 8.05257731958763 0.406738485812274 19.7979232368589 Winsorized Mean ( 8 / 32 ) 8.01134020618557 0.395800214626425 20.2408687770598 Winsorized Mean ( 9 / 32 ) 8.07628865979382 0.373058471078432 21.6488547665116 Winsorized Mean ( 10 / 32 ) 8.0041237113402 0.356583629349839 22.4466942745918 Winsorized Mean ( 11 / 32 ) 7.99278350515464 0.354606551434389 22.5398641757286 Winsorized Mean ( 12 / 32 ) 7.9680412371134 0.342539994378189 23.2616376711798 Winsorized Mean ( 13 / 32 ) 7.9680412371134 0.33420594456764 23.8417100791597 Winsorized Mean ( 14 / 32 ) 7.78041237113402 0.305000701281015 25.5094901043046 Winsorized Mean ( 15 / 32 ) 7.7958762886598 0.298197324217497 26.1433475606028 Winsorized Mean ( 16 / 32 ) 7.82886597938144 0.293419958859412 26.6814364292531 Winsorized Mean ( 17 / 32 ) 7.8639175257732 0.288467427925268 27.2610241729284 Winsorized Mean ( 18 / 32 ) 7.82680412371134 0.277880553370335 28.1660736196982 Winsorized Mean ( 19 / 32 ) 7.82680412371134 0.272392809176806 28.7335196085558 Winsorized Mean ( 20 / 32 ) 7.80618556701031 0.263793916365416 29.5919848136184 Winsorized Mean ( 21 / 32 ) 7.84948453608247 0.24020825958133 32.6778294375210 Winsorized Mean ( 22 / 32 ) 7.82680412371134 0.231072667977891 33.8716136019176 Winsorized Mean ( 23 / 32 ) 7.75567010309278 0.215501936828852 35.9888649597252 Winsorized Mean ( 24 / 32 ) 7.8298969072165 0.205801618460031 38.0458470920002 Winsorized Mean ( 25 / 32 ) 7.93298969072165 0.186466059033738 42.5438802741378 Winsorized Mean ( 26 / 32 ) 7.85257731958763 0.176034575540940 44.6081532304510 Winsorized Mean ( 27 / 32 ) 7.85257731958763 0.16914666554884 46.424665210561 Winsorized Mean ( 28 / 32 ) 7.7659793814433 0.158459119401014 49.0093559196796 Winsorized Mean ( 29 / 32 ) 7.7958762886598 0.147610677837723 52.8137693211478 Winsorized Mean ( 30 / 32 ) 7.7340206185567 0.132982947563402 58.157987623709 Winsorized Mean ( 31 / 32 ) 7.7659793814433 0.129173344783065 60.1206030120656 Winsorized Mean ( 32 / 32 ) 7.79896907216495 0.117667176945885 66.27990298222 Trimmed Mean ( 1 / 32 ) 7.99263157894737 0.43384073975342 18.4229622683432 Trimmed Mean ( 2 / 32 ) 7.99139784946237 0.418479895447589 19.0962527385338 Trimmed Mean ( 3 / 32 ) 7.98461538461538 0.402252276514055 19.8497705315942 Trimmed Mean ( 4 / 32 ) 7.97640449438202 0.387944027032363 20.5607096348376 Trimmed Mean ( 5 / 32 ) 7.97011494252874 0.375001077936716 21.2535787533756 Trimmed Mean ( 6 / 32 ) 7.95176470588235 0.363393636316244 21.8819591517621 Trimmed Mean ( 7 / 32 ) 7.95176470588235 0.350631996190719 22.6783773080343 Trimmed Mean ( 8 / 32 ) 7.91481481481481 0.337012616127876 23.48521816706 Trimmed Mean ( 9 / 32 ) 7.9 0.323658693211937 24.4084282785723 Trimmed Mean ( 10 / 32 ) 7.87532467532468 0.312871274153689 25.1711337086707 Trimmed Mean ( 11 / 32 ) 7.85866666666667 0.303594640442986 25.8853932836226 Trimmed Mean ( 12 / 32 ) 7.84246575342466 0.293063633072671 26.7602829842758 Trimmed Mean ( 13 / 32 ) 7.8281690140845 0.282929366721958 27.6682802664930 Trimmed Mean ( 14 / 32 ) 7.8281690140845 0.272448349856692 28.7326717823842 Trimmed Mean ( 15 / 32 ) 7.81641791044776 0.265314274913265 29.4609776010094 Trimmed Mean ( 16 / 32 ) 7.81846153846154 0.257958817409465 30.3089524792288 Trimmed Mean ( 17 / 32 ) 7.81746031746032 0.249941515765842 31.277158152406 Trimmed Mean ( 18 / 32 ) 7.81311475409836 0.241109405475896 32.4048526380670 Trimmed Mean ( 19 / 32 ) 7.81186440677966 0.232286990031613 33.6302278733583 Trimmed Mean ( 20 / 32 ) 7.81052631578947 0.222478691645695 35.1068511685964 Trimmed Mean ( 21 / 32 ) 7.81090909090909 0.212007761869101 36.8425619045577 Trimmed Mean ( 22 / 32 ) 7.80754716981132 0.203611248028406 38.3453627705386 Trimmed Mean ( 23 / 32 ) 7.80588235294118 0.194883811835001 40.0540315762606 Trimmed Mean ( 24 / 32 ) 7.81020408163265 0.186997510304809 41.7663533001156 Trimmed Mean ( 25 / 32 ) 7.81020408163265 0.178953422310015 43.6437816098449 Trimmed Mean ( 26 / 32 ) 7.79777777777778 0.172605958933878 45.1767588207365 Trimmed Mean ( 27 / 32 ) 7.79302325581395 0.166635501477241 46.7668845277747 Trimmed Mean ( 28 / 32 ) 7.79302325581395 0.160266360678898 48.6254459313995 Trimmed Mean ( 29 / 32 ) 7.78974358974359 0.154281884076896 50.4903322664966 Trimmed Mean ( 30 / 32 ) 7.78918918918919 0.148808268108376 52.3437930445935 Trimmed Mean ( 31 / 32 ) 7.78918918918919 0.144881455868244 53.7624994345221 Trimmed Mean ( 32 / 32 ) 7.7969696969697 0.140243622477268 55.595894909471 Median 7.7 Midrange 7.85 Midmean - Weighted Average at Xnp 7.75625 Midmean - Weighted Average at X(n+1)p 7.862 Midmean - Empirical Distribution Function 7.862 Midmean - Empirical Distribution Function - Averaging 7.862 Midmean - Empirical Distribution Function - Interpolation 7.862 Midmean - Closest Observation 7.80588235294117 Midmean - True Basic - Statistics Graphics Toolkit 7.862 Midmean - MS Excel (old versions) 7.862 Number of observations 97

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199626073v7pxfm6d0l7ymjm/1f7v81199626072.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199626073v7pxfm6d0l7ymjm/1f7v81199626072.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199626073v7pxfm6d0l7ymjm/23zhy1199626072.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jan/06/t1199626073v7pxfm6d0l7ymjm/23zhy1199626072.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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As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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