WS3_Part 2 Y(t)*X(t)

*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: Mon, 19 Oct 2009 12:24:14 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/19/t12559771216chgjyaq0s6z9yb.htm/, Retrieved Mon, 19 Oct 2009 20:32:01 +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/2009/Oct/19/t12559771216chgjyaq0s6z9yb.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

» Textbox « » Textfile « » CSV «

48246854,6 46836572 48706419,4 29098486,1 49052932,8 57056572,5 59014973 49599878,6 37137255 42934862,8 45962100,1 54001904,7 51320001,6 47080558 53231955 33305395,5 50782946,4 65370895,2 63614700 49042022,4 41331706 46504277,5 50532945,4 60753320,8 52185504 47870250,4 59210970,2 29142323 56739882,7 65978420,1 63272034 54128613,7 47517229,2 42483193,5 48859519,1 52656962,8 57711170 51468259,2 61910246,4 27374413,5 58863542,4 67472116,8 59069290,5 55729814,4 45681286,5 45514393,6 49566048 59893236,7 50817142,5 56704725 60674557,8 27694644,9 58826046 66393003,6 61583100 57988555 43300189,8 47761075,2 50110370,2 56623174,5 48594915,6 49826205 53356834 28378998,2 55668672,6 55357345,4 60244101 50678692,4 37283705 47711900,6 50451563,4 42316229,8 53632584,2 45809243,2 50002626 30064765,1 46262253 56197032,5 52338391,6 43260849,2 36646011 40092049,8 46392769,8 54704844 47483347,5 45971816,6 54050371,2

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 50138769.6356322 984482.780860311 50.929046815646 Geometric Mean 49194865.8509276 Harmonic Mean 48110294.712935 Quadratic Mean 50963202.0806649 Winsorized Mean ( 1 / 29 ) 50130046.8563218 981033.261768053 51.0992326253808 Winsorized Mean ( 2 / 29 ) 50136248.4609195 975081.542370131 51.4174930837613 Winsorized Mean ( 3 / 29 ) 50140109.254023 964814.940141108 51.9686285607163 Winsorized Mean ( 4 / 29 ) 50061380.1367816 950189.112660492 52.6857016879637 Winsorized Mean ( 5 / 29 ) 50094700.6022988 933539.270491838 53.6610533544093 Winsorized Mean ( 6 / 29 ) 50224275.9678161 865056.737829863 58.0589385313753 Winsorized Mean ( 7 / 29 ) 50466738.9988506 803287.10947148 62.825281775099 Winsorized Mean ( 8 / 29 ) 50435609.3252874 782309.962137765 64.4701100155563 Winsorized Mean ( 9 / 29 ) 50442611.4287356 778075.289470183 64.8299876777781 Winsorized Mean ( 10 / 29 ) 50715931.8885057 710467.991323982 71.3838378474938 Winsorized Mean ( 11 / 29 ) 50828307.8758621 677128.795121712 75.0644607673579 Winsorized Mean ( 12 / 29 ) 50869998.537931 641057.655110903 79.3532346620688 Winsorized Mean ( 13 / 29 ) 50873776.6068966 634009.930214963 80.2412930498543 Winsorized Mean ( 14 / 29 ) 50937718.2758621 621658.958313115 81.9383644274711 Winsorized Mean ( 15 / 29 ) 50967814.1034483 609379.692032965 83.6388458128846 Winsorized Mean ( 16 / 29 ) 50968153.2666667 607278.304149236 83.9288229439882 Winsorized Mean ( 17 / 29 ) 51237166.1126437 523086.314912431 97.9516470837537 Winsorized Mean ( 18 / 29 ) 51214305.6781609 510155.976338491 100.389504491818 Winsorized Mean ( 19 / 29 ) 51099292.1701149 485839.214546777 105.177372760623 Winsorized Mean ( 20 / 29 ) 51061629.4344828 471110.020485594 108.385785090819 Winsorized Mean ( 21 / 29 ) 51055488.4551724 469626.617907402 108.715065348445 Winsorized Mean ( 22 / 29 ) 51108310.1770115 457593.886205329 111.689233002729 Winsorized Mean ( 23 / 29 ) 51030156.3885057 437714.987239266 116.583068609006 Winsorized Mean ( 24 / 29 ) 50932029.3816092 416434.842101758 122.304918398648 Winsorized Mean ( 25 / 29 ) 51009946.8241379 402412.852577873 126.760232674891 Winsorized Mean ( 26 / 29 ) 50989821.8678161 381206.032908824 133.759220646993 Winsorized Mean ( 27 / 29 ) 50912325.0712644 339761.071650938 149.847434916177 Winsorized Mean ( 28 / 29 ) 50737776.0965517 314807.893269109 161.170596993829 Winsorized Mean ( 29 / 29 ) 50776585.7298851 303875.629934107 167.096603768113 Trimmed Mean ( 1 / 29 ) 50202663.8588235 949169.918572378 52.8911239984639 Trimmed Mean ( 2 / 29 ) 50278780.4759036 912203.412389898 55.1179482481625 Trimmed Mean ( 3 / 29 ) 50355325.4469136 872843.144036291 57.6911507995071 Trimmed Mean ( 4 / 29 ) 50434328.8594937 831368.123817706 60.6642561996428 Trimmed Mean ( 5 / 29 ) 50539674.7649351 787709.062448695 64.1603317445987 Trimmed Mean ( 6 / 29 ) 50642908.7706667 741188.155767046 68.3266568368958 Trimmed Mean ( 7 / 29 ) 50726061.8616438 706150.993377203 71.834582599741 Trimmed Mean ( 8 / 29 ) 50771456.4070423 680961.403508762 74.5584935437372 Trimmed Mean ( 9 / 29 ) 50824388.8275362 655962.962727969 77.4805769767422 Trimmed Mean ( 10 / 29 ) 50879471.138806 626984.28404261 81.1495159188842 Trimmed Mean ( 11 / 29 ) 50901360.2384615 607294.084275479 83.8166574587804 Trimmed Mean ( 12 / 29 ) 50910531.3142857 590459.212875624 86.2219272798605 Trimmed Mean ( 13 / 29 ) 50915348.7344262 577121.946534949 88.2228600733743 Trimmed Mean ( 14 / 29 ) 50920064.2169491 562163.187704575 90.5787951446377 Trimmed Mean ( 15 / 29 ) 50918139.5263158 546163.060658376 93.2288233937612 Trimmed Mean ( 16 / 29 ) 50912901.1163636 528765.062849444 96.2864317131712 Trimmed Mean ( 17 / 29 ) 50907232.5584906 507497.046027655 100.310401719494 Trimmed Mean ( 18 / 29 ) 50874125.0392157 497260.34555105 102.308831770686 Trimmed Mean ( 19 / 29 ) 50840569.8061225 486539.518274783 104.494224819389 Trimmed Mean ( 20 / 29 ) 50815363.9319149 477419.973767155 106.437448628193 Trimmed Mean ( 21 / 29 ) 50791558.2666667 468235.836390322 108.474307857818 Trimmed Mean ( 22 / 29 ) 50766129.7767442 456211.860338128 111.277531757105 Trimmed Mean ( 23 / 29 ) 50733125.6804878 442585.879290277 114.628884594878 Trimmed Mean ( 24 / 29 ) 50704316.6820513 428821.291935613 118.241135959416 Trimmed Mean ( 25 / 29 ) 50682006.9918919 415184.028673417 122.071186490072 Trimmed Mean ( 26 / 29 ) 50649400.4028571 399491.046006429 126.784820108439 Trimmed Mean ( 27 / 29 ) 50614882.1424242 383088.379430583 132.123251082837 Trimmed Mean ( 28 / 29 ) 50583965.1354839 371586.475415981 136.129726139404 Trimmed Mean ( 29 / 29 ) 50567485.3896552 362044.472541841 139.672027125925 Median 50451563.4 Midrange 47423265.15 Midmean - Weighted Average at Xnp 50657168.1136364 Midmean - Weighted Average at X(n+1)p 50791558.2666667 Midmean - Empirical Distribution Function 50791558.2666667 Midmean - Empirical Distribution Function - Averaging 50791558.2666667 Midmean - Empirical Distribution Function - Interpolation 50766129.7767442 Midmean - Closest Observation 50657168.1136364 Midmean - True Basic - Statistics Graphics Toolkit 50791558.2666667 Midmean - MS Excel (old versions) 50791558.2666667 Number of observations 87

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/19/t12559771216chgjyaq0s6z9yb/1ofgg1255976649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t12559771216chgjyaq0s6z9yb/1ofgg1255976649.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t12559771216chgjyaq0s6z9yb/2pbyi1255976649.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t12559771216chgjyaq0s6z9yb/2pbyi1255976649.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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