gehuwde mannen

*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: Thu, 25 Nov 2010 20:24:08 +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/Nov/25/t1290716540jehw2c1ek0753zu.htm/, Retrieved Thu, 25 Nov 2010 21:22:20 +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/Nov/25/t1290716540jehw2c1ek0753zu.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 54 222 522 1084 2023 3229 5198 8080 11132 14877 18448 21418 24525 26708 30336 33613 36727 39660 42131 43769 45025 46760 49385 51382 53800 54017 53313 53577 53629 54090 53725 52995 52453 52220 51870 51122 51296 49265 50020 50058 50799 50216 50571 42873 42535 40069 35293 31552 34590 36992 37279 35618 33745 32570 32227 31114 30698 29453 27620 24178 22031 19962 17784 16259 14147 11990 9988 8383 6661 4111 2154 1601 1295 1137 876 515 342 206 126 52 33 17

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 22634.21 2082.96186886133 10.8663583037039 Geometric Mean 0 Harmonic Mean 0 Quadratic Mean 30689.4403156851 Winsorized Mean ( 1 / 33 ) 22633.48 2082.85063952306 10.8665881127140 Winsorized Mean ( 2 / 33 ) 22629.14 2082.19223503509 10.8679398660896 Winsorized Mean ( 3 / 33 ) 22626.89 2081.85237223410 10.8686332910908 Winsorized Mean ( 4 / 33 ) 22623.05 2081.27374821892 10.8698099033632 Winsorized Mean ( 5 / 33 ) 22620.45 2080.88277349914 10.8706027499869 Winsorized Mean ( 6 / 33 ) 22604.61 2078.51069918956 10.8753878480462 Winsorized Mean ( 7 / 33 ) 22582.35 2075.20209941323 10.8820003634273 Winsorized Mean ( 8 / 33 ) 22538.99 2068.82621190121 10.8945787086133 Winsorized Mean ( 9 / 33 ) 22518.02 2065.77204561404 10.9005347651060 Winsorized Mean ( 10 / 33 ) 22483.02 2060.70961274915 10.9103290734913 Winsorized Mean ( 11 / 33 ) 22429.34 2053.01998500558 10.925047083718 Winsorized Mean ( 12 / 33 ) 22419.02 2051.55130498013 10.927837849133 Winsorized Mean ( 13 / 33 ) 22396.4 2048.34114351151 10.9339208807794 Winsorized Mean ( 14 / 33 ) 22351.18 2041.95652989376 10.9459626944962 Winsorized Mean ( 15 / 33 ) 22316.98 2037.15452570789 10.9549765215995 Winsorized Mean ( 16 / 33 ) 22260.18 2029.22371256407 10.9698008465871 Winsorized Mean ( 17 / 33 ) 22233.49 2025.47242343109 10.9769403635411 Winsorized Mean ( 18 / 33 ) 22229.53 2024.20431343186 10.9818607995710 Winsorized Mean ( 19 / 33 ) 22111.92 2007.22141690971 11.0161837721138 Winsorized Mean ( 20 / 33 ) 22091.72 2003.50823711253 11.0265181798497 Winsorized Mean ( 21 / 33 ) 21566.09 1932.77010683572 11.1581247680343 Winsorized Mean ( 22 / 33 ) 21200.23 1881.43355733807 11.2681257955210 Winsorized Mean ( 23 / 33 ) 20929.75 1842.78567651550 11.3576691346851 Winsorized Mean ( 24 / 33 ) 20718.55 1815.63444321507 11.4111902191678 Winsorized Mean ( 25 / 33 ) 20664.05 1801.82738443728 11.4683849177115 Winsorized Mean ( 26 / 33 ) 20603.99 1783.86539814131 11.5501932048619 Winsorized Mean ( 27 / 33 ) 20049.14 1716.90854789130 11.6774653050823 Winsorized Mean ( 28 / 33 ) 20033.74 1692.09392201891 11.839614656908 Winsorized Mean ( 29 / 33 ) 19403.57 1605.85994139111 12.0829777864633 Winsorized Mean ( 30 / 33 ) 19333.37 1594.37059863411 12.1260201464846 Winsorized Mean ( 31 / 33 ) 19300.2 1579.55473204164 12.2187598875119 Winsorized Mean ( 32 / 33 ) 19043.24 1529.06796415795 12.4541488320874 Winsorized Mean ( 33 / 33 ) 19075.25 1501.33319772155 12.7055406680868 Trimmed Mean ( 1 / 33 ) 22544.193877551 2088.17969630696 10.7960985912378 Trimmed Mean ( 2 / 33 ) 22451.1875 2092.99299786302 10.7268335455126 Trimmed Mean ( 3 / 33 ) 22356.5319148936 2097.58512570407 10.658223898012 Trimmed Mean ( 4 / 33 ) 22258.5760869565 2101.66041928107 10.5909479394253 Trimmed Mean ( 5 / 33 ) 22157.3333333333 2105.17634414556 10.5251673547218 Trimmed Mean ( 6 / 33 ) 22052.0795454545 2107.95810813162 10.4613462005658 Trimmed Mean ( 7 / 33 ) 21945 2110.32294343340 10.3988823456075 Trimmed Mean ( 8 / 33 ) 21836.6071428571 2112.31335065182 10.3377688429223 Trimmed Mean ( 9 / 33 ) 21729.5365853659 2114.35354210033 10.2771538215792 Trimmed Mean ( 10 / 33 ) 21620.025 2115.72622799537 10.2187252367168 Trimmed Mean ( 11 / 33 ) 21509.3846153846 2116.59627915544 10.1622519264596 Trimmed Mean ( 12 / 33 ) 21399.3421052632 2117.21480587799 10.1073079811517 Trimmed Mean ( 13 / 33 ) 21284.5135135135 2116.47571210424 10.0565829278296 Trimmed Mean ( 14 / 33 ) 21165.7222222222 2114.38232898104 10.0103571298869 Trimmed Mean ( 15 / 33 ) 21044.7571428571 2111.12740345958 9.96849224180898 Trimmed Mean ( 16 / 33 ) 20920.0294117647 2106.20606945541 9.93256534351072 Trimmed Mean ( 17 / 33 ) 20793.1212121212 2099.72388888734 9.90278832477334 Trimmed Mean ( 18 / 33 ) 20660.734375 2090.70471147800 9.88218673903217 Trimmed Mean ( 19 / 33 ) 20520.1612903226 2078.23596689729 9.87383608847758 Trimmed Mean ( 20 / 33 ) 20380.5333333333 2063.99250911063 9.87432524264116 Trimmed Mean ( 21 / 33 ) 20233.0172413793 2045.44604736049 9.8917384144591 Trimmed Mean ( 22 / 33 ) 20119.6607142857 2032.22523905635 9.9003104221007 Trimmed Mean ( 23 / 33 ) 20028.7037037037 2021.87065924211 9.9060261902269 Trimmed Mean ( 24 / 33 ) 19953.3653846154 2012.67738133787 9.91384191506737 Trimmed Mean ( 25 / 33 ) 19889.6 2002.86204890371 9.93058908419918 Trimmed Mean ( 26 / 33 ) 19825.0625 1989.88414886195 9.96292297284656 Trimmed Mean ( 27 / 33 ) 19759.9347826087 1973.53467206377 10.0124588953612 Trimmed Mean ( 28 / 33 ) 19735.5909090909 1961.54017352304 10.0612728586867 Trimmed Mean ( 29 / 33 ) 19735.5909090909 1946.89087101922 10.1369785039667 Trimmed Mean ( 30 / 33 ) 19736.675 1940.03292015007 10.1733711809763 Trimmed Mean ( 31 / 33 ) 19772.0526315789 1928.24213865948 10.2539262238738 Trimmed Mean ( 32 / 33 ) 19814.3333333333 1910.44278919670 10.3715920965447 Trimmed Mean ( 33 / 33 ) 19885.2058823529 1892.16540958189 10.5092323227423 Median 20690 Midrange 27045 Midmean - Weighted Average at Xnp 19503.9607843137 Midmean - Weighted Average at X(n+1)p 19889.6 Midmean - Empirical Distribution Function 19503.9607843137 Midmean - Empirical Distribution Function - Averaging 19889.6 Midmean - Empirical Distribution Function - Interpolation 19889.6 Midmean - Closest Observation 19503.9607843137 Midmean - True Basic - Statistics Graphics Toolkit 19889.6 Midmean - MS Excel (old versions) 19953.3653846154 Number of observations 100

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/25/t1290716540jehw2c1ek0753zu/1u3qe1290716644.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/25/t1290716540jehw2c1ek0753zu/1u3qe1290716644.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/25/t1290716540jehw2c1ek0753zu/2ndpz1290716644.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/25/t1290716540jehw2c1ek0753zu/2ndpz1290716644.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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