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

Title produced by software: Central Tendency

Date of computation: Sun, 20 Apr 2008 14:34:43 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/20/t1208723827uapdriq3a9vwo4z.htm/, Retrieved Sun, 20 Apr 2008 22:37:07 +0200

User-defined keywords:

Dataseries X:

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47,87 47,87 47,89 47,88 47,91 47,92 47,92 47,91 47,93 48,05 48,03 48,04 48,04 48,06 48,04 48,09 48,12 48,16 48,16 48,16 48,08 48,13 48,16 48,15 48,15 48,15 48,27 48,47 48,51 48,53 48,53 48,53 48,68 48,64 48,67 48,66 48,66 48,67 48,71 48,96 49,01 49,04 49,04 49,04 49,06 49,13 49,19 49,26 49,26 49,26 49,29 49,43 49,43 49,45 49,45 49,46 49,57 49,68 49,71 49,7 49,7 49,8 49,84 50,09 50,2 50,16 50,16 50,29 50,36 51,02 51,03 51,04

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 48.8820833333333 0.101062032094085 483.683954502575 Geometric Mean 48.8747256851132 Harmonic Mean 48.8674276757827 Quadratic Mean 48.8895002218722 Winsorized Mean ( 1 / 24 ) 48.8819444444444 0.101020349769937 483.882153999346 Winsorized Mean ( 2 / 24 ) 48.8819444444444 0.100898281354622 484.467562659879 Winsorized Mean ( 3 / 24 ) 48.8548611111111 0.093583248791879 522.047072973071 Winsorized Mean ( 4 / 24 ) 48.8520833333333 0.0925569100193593 527.805901505521 Winsorized Mean ( 5 / 24 ) 48.8458333333333 0.0912195133113728 535.475706459875 Winsorized Mean ( 6 / 24 ) 48.8433333333333 0.0904089993720157 540.248577825227 Winsorized Mean ( 7 / 24 ) 48.8433333333333 0.0904089993720157 540.248577825227 Winsorized Mean ( 8 / 24 ) 48.8366666666667 0.0886770264695101 550.725127025523 Winsorized Mean ( 9 / 24 ) 48.8179166666667 0.081017091238639 602.563186610484 Winsorized Mean ( 10 / 24 ) 48.81375 0.0798503190639623 611.31565374083 Winsorized Mean ( 11 / 24 ) 48.8 0.0775167203932938 629.541597637325 Winsorized Mean ( 12 / 24 ) 48.7983333333333 0.0772419222572214 631.759696125004 Winsorized Mean ( 13 / 24 ) 48.8001388888889 0.0769932046509558 633.823973298962 Winsorized Mean ( 14 / 24 ) 48.7981944444444 0.0760894597415394 641.326599113755 Winsorized Mean ( 15 / 24 ) 48.7794444444444 0.0718710615411081 678.707721835221 Winsorized Mean ( 16 / 24 ) 48.7572222222222 0.0678862110124497 718.2198195342 Winsorized Mean ( 17 / 24 ) 48.7619444444444 0.0665708345513811 732.482096297121 Winsorized Mean ( 18 / 24 ) 48.7644444444444 0.066232414587812 736.262519612535 Winsorized Mean ( 19 / 24 ) 48.7644444444444 0.0647569456244468 753.03805598322 Winsorized Mean ( 20 / 24 ) 48.7644444444444 0.0647569456244468 753.03805598322 Winsorized Mean ( 21 / 24 ) 48.7236111111111 0.0590334596363252 825.355847535825 Winsorized Mean ( 22 / 24 ) 48.7175 0.0573855771086595 848.950249428589 Winsorized Mean ( 23 / 24 ) 48.7175 0.0573855771086595 848.950249428589 Winsorized Mean ( 24 / 24 ) 48.7175 0.0573855771086595 848.950249428589 Trimmed Mean ( 1 / 24 ) 48.8657142857143 0.0981315235710083 497.961434893599 Trimmed Mean ( 2 / 24 ) 48.8485294117647 0.094650891445119 516.091593707687 Trimmed Mean ( 3 / 24 ) 48.830303030303 0.0905062090612938 539.52434354237 Trimmed Mean ( 4 / 24 ) 48.82109375 0.088963697894314 548.775454545492 Trimmed Mean ( 5 / 24 ) 48.8120967741935 0.0874436094175137 558.212282170699 Trimmed Mean ( 6 / 24 ) 48.804 0.085988174196775 567.566417776439 Trimmed Mean ( 7 / 24 ) 48.7958620689655 0.0844013954416394 578.140465730879 Trimmed Mean ( 8 / 24 ) 48.7871428571429 0.0824115875275597 591.993727105763 Trimmed Mean ( 9 / 24 ) 48.7788888888889 0.080361111382858 606.99619566603 Trimmed Mean ( 10 / 24 ) 48.7728846153846 0.0795771898895252 612.90031330705 Trimmed Mean ( 11 / 24 ) 48.767 0.078766122418311 619.136736743347 Trimmed Mean ( 12 / 24 ) 48.7625 0.0781583793940455 623.893437633316 Trimmed Mean ( 13 / 24 ) 48.7578260869565 0.0773329041988833 630.492629134451 Trimmed Mean ( 14 / 24 ) 48.7525 0.076212624708147 639.690604892504 Trimmed Mean ( 15 / 24 ) 48.7469047619048 0.0748529243904805 651.235808872475 Trimmed Mean ( 16 / 24 ) 48.743 0.0739258117373468 659.350216852274 Trimmed Mean ( 17 / 24 ) 48.7413157894737 0.0734480695893748 663.61602234029 Trimmed Mean ( 18 / 24 ) 48.7388888888889 0.072901082990821 668.561931995243 Trimmed Mean ( 19 / 24 ) 48.7358823529412 0.0720196517633725 676.702554923031 Trimmed Mean ( 20 / 24 ) 48.7325 0.0709540400995716 686.817832101067 Trimmed Mean ( 21 / 24 ) 48.7286666666667 0.0692151955499597 704.016889347574 Trimmed Mean ( 22 / 24 ) 48.7292857142857 0.0682159824160855 714.338253124611 Trimmed Mean ( 23 / 24 ) 48.7307692307692 0.0669349237966896 728.032041670589 Trimmed Mean ( 24 / 24 ) 48.7325 0.064637366363697 753.936967756319 Median 48.67 Midrange 49.455 Midmean - Weighted Average at Xnp 48.7413157894737 Midmean - Weighted Average at X(n+1)p 48.7581081081081 Midmean - Empirical Distribution Function 48.7413157894737 Midmean - Empirical Distribution Function - Averaging 48.7581081081081 Midmean - Empirical Distribution Function - Interpolation 48.7581081081081 Midmean - Closest Observation 48.7413157894737 Midmean - True Basic - Statistics Graphics Toolkit 48.7581081081081 Midmean - MS Excel (old versions) 48.7413157894737 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208723827uapdriq3a9vwo4z/1y5wc1208723678.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208723827uapdriq3a9vwo4z/1y5wc1208723678.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208723827uapdriq3a9vwo4z/24fd51208723678.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/20/t1208723827uapdriq3a9vwo4z/24fd51208723678.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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