*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Mon, 15 Mar 2010 11:41:31 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Mar/15/t1268674991p1v1gi9hynejah9.htm/, Retrieved Mon, 15 Mar 2010 18:43:13 +0100

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/Mar/15/t1268674991p1v1gi9hynejah9.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 «

8027,7 8059,6 8059,5 7988,9 7950,2 8003,8 8037,5 8069 8157,6 8244,3 8329,4 8417 8432,5 8486,4 8531,1 8643,8 8727,9 8847,3 8904,3 9003,2 9025,3 9044,7 9120,7 9184,3 9247,2 9407,1 9488,9 9592,5 9666,2 9809,6 9932,7 10008,9 10103,4 10194,3 10328,8 10507,6 10601,2 10684 10819,9 11014,3 11043 11258,5 11267,9 11334,5 11297,2 11371,3 11340,1 11380,1 11477,9 11538,8 11596,4 11598,8 11645,8 11738,7 11935,5 12042,8 12127,6 12213,8 12303,5 12410,3 12534,1 12587,5 12683,2 12748,7 12915,9 12962,5 12965,9 13060,7 13099,9 13204 13321,1 13391,2 13366,9 13415,3 13324,6 13141,9 12925,4 12901,5 12973 13155

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 10728.7925 204.665950282367 52.4209937471185 Geometric Mean 10570.6613457301 Harmonic Mean 10410.7145387657 Quadratic Mean 10881.9186016644 Winsorized Mean ( 1 / 26 ) 10728.975 204.533522495377 52.4558266493576 Winsorized Mean ( 2 / 26 ) 10728.74 204.370824608763 52.4964364191344 Winsorized Mean ( 3 / 26 ) 10728.05 203.962682962201 52.5981019870589 Winsorized Mean ( 4 / 26 ) 10728.365 203.852499636162 52.6280767670159 Winsorized Mean ( 5 / 26 ) 10722.42125 202.466199622399 52.9590680814743 Winsorized Mean ( 6 / 26 ) 10718.75375 201.899193882314 53.0896312357141 Winsorized Mean ( 7 / 26 ) 10718.43 201.587456751704 53.1701236411843 Winsorized Mean ( 8 / 26 ) 10723.09 199.492944186955 53.7517256246959 Winsorized Mean ( 9 / 26 ) 10728.43375 197.258987818397 54.3875534831242 Winsorized Mean ( 10 / 26 ) 10728.10875 193.954817508590 55.3124118689389 Winsorized Mean ( 11 / 26 ) 10739.1775 191.946417224610 55.9488301750032 Winsorized Mean ( 12 / 26 ) 10740.9925 191.516130618971 56.0840095572401 Winsorized Mean ( 13 / 26 ) 10743.7225 189.304499902842 56.7536561757066 Winsorized Mean ( 14 / 26 ) 10749.8825 187.886881087347 57.2146519107018 Winsorized Mean ( 15 / 26 ) 10768.31375 184.371316232187 58.4055804886644 Winsorized Mean ( 16 / 26 ) 10754.57375 177.517200234050 60.5832772025497 Winsorized Mean ( 17 / 26 ) 10766.0275 171.918845707545 62.6227302521234 Winsorized Mean ( 18 / 26 ) 10757.32 167.099929999076 64.3765679618146 Winsorized Mean ( 19 / 26 ) 10768.12625 162.078246728178 66.437825355177 Winsorized Mean ( 20 / 26 ) 10742.70125 157.100723903264 68.3809786682772 Winsorized Mean ( 21 / 26 ) 10719.75875 152.670031343908 70.2152128720825 Winsorized Mean ( 22 / 26 ) 10715.99125 146.563093492294 73.1152092567113 Winsorized Mean ( 23 / 26 ) 10709.49375 140.867868686592 76.0250996188979 Winsorized Mean ( 24 / 26 ) 10702.92375 135.068841791596 79.2405088252258 Winsorized Mean ( 25 / 26 ) 10719.36125 124.128589989689 86.3569081940786 Winsorized Mean ( 26 / 26 ) 10681.98625 112.803645476258 94.6953992922881 Trimmed Mean ( 1 / 26 ) 10729.9730769231 203.938537518436 52.6137590643117 Trimmed Mean ( 2 / 26 ) 10731.0236842105 203.133096907391 52.8275492649179 Trimmed Mean ( 3 / 26 ) 10732.2581081081 202.178851663577 53.0829907272717 Trimmed Mean ( 4 / 26 ) 10733.8166666667 201.121008467411 53.3699425458377 Trimmed Mean ( 5 / 26 ) 10735.3742857143 199.800280048856 53.7305267194281 Trimmed Mean ( 6 / 26 ) 10738.4220588235 198.523570338655 54.0914211874448 Trimmed Mean ( 7 / 26 ) 10742.3954545455 197.030583091412 54.5214620288747 Trimmed Mean ( 8 / 26 ) 10746.675 195.203184449553 55.0537893646777 Trimmed Mean ( 9 / 26 ) 10750.4790322581 193.355104897262 55.5996648651726 Trimmed Mean ( 10 / 26 ) 10753.745 191.467645072858 56.1648157102886 Trimmed Mean ( 11 / 26 ) 10757.2810344828 189.702089661345 56.706181010903 Trimmed Mean ( 12 / 26 ) 10759.6321428571 187.790823809869 57.2958354650537 Trimmed Mean ( 13 / 26 ) 10761.9333333333 185.374529039918 58.055081186563 Trimmed Mean ( 14 / 26 ) 10764.0884615385 182.667177662759 58.9273267330554 Trimmed Mean ( 15 / 26 ) 10765.712 179.424717420848 60.0012760490998 Trimmed Mean ( 16 / 26 ) 10765.4229166667 175.908617204314 61.1989514087469 Trimmed Mean ( 17 / 26 ) 10766.6021739130 172.680424539722 62.349870882072 Trimmed Mean ( 18 / 26 ) 10766.6636363636 169.515050816711 63.5144996535152 Trimmed Mean ( 19 / 26 ) 10767.6523809524 166.230676668644 64.775362747371 Trimmed Mean ( 20 / 26 ) 10767.6025 162.807446653208 66.137039314521 Trimmed Mean ( 21 / 26 ) 10770.2236842105 159.157272899623 67.670320607988 Trimmed Mean ( 22 / 26 ) 10775.5638888889 155.03723020119 69.5030727452081 Trimmed Mean ( 23 / 26 ) 10781.9352941176 150.689343048604 71.5507485532006 Trimmed Mean ( 24 / 26 ) 10789.809375 145.885539697152 73.9607873227112 Trimmed Mean ( 25 / 26 ) 10799.4633333333 140.442260437727 76.8961087615213 Trimmed Mean ( 26 / 26 ) 10808.6178571429 135.733863185182 79.6309602003783 Median 11028.65 Midrange 10682.75 Midmean - Weighted Average at Xnp 10724.5682926829 Midmean - Weighted Average at X(n+1)p 10767.6025 Midmean - Empirical Distribution Function 10724.5682926829 Midmean - Empirical Distribution Function - Averaging 10767.6025 Midmean - Empirical Distribution Function - Interpolation 10767.6025 Midmean - Closest Observation 10724.5682926829 Midmean - True Basic - Statistics Graphics Toolkit 10767.6025 Midmean - MS Excel (old versions) 10767.6523809524 Number of observations 80

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Mar/15/t1268674991p1v1gi9hynejah9/1jdw31268674889.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/15/t1268674991p1v1gi9hynejah9/1jdw31268674889.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/15/t1268674991p1v1gi9hynejah9/2ayjj1268674889.png (open in new window) http://www.freestatistics.org/blog/date/2010/Mar/15/t1268674991p1v1gi9hynejah9/2ayjj1268674889.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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