paper central tendensy export

*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Wed, 10 Dec 2008 05:01:01 -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/Dec/10/t1228912249hno1fk57zl53ab6.htm/, Retrieved Wed, 10 Dec 2008 12:30:51 +0000

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/2008/Dec/10/t1228912249hno1fk57zl53ab6.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

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Dataseries X:

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12,5 14,8 15,9 14,8 12,9 14,3 14,2 15,9 15,3 15,5 15,1 15 12,1 15,8 16,9 15,1 13,7 14,8 14,7 16 15,4 15 15,5 15,1 11,7 16,3 16,7 15 14,9 14,6 15,3 17,9 16,4 15,4 17,9 15,9 13,9 17,8 17,9 17,4 16,7 16 16,6 19,1 17,8 17,2 18,6 16,3 15,1 19,2 17,7 19,1 18 17,5 17,8 21,1 17,2 19,4 19,8 17,6 16,2 19,5 19,9 20 17,3 18,9 18,6 21,4 18,6 19,8 20,8 19,6 17,7 19,8 22,2 20,7 17,9 21,2 21,4 21,7 23,2 21,5 22,9 23,2 18,6

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 17.3141176470588 0.283851822220829 60.9970283494917 Geometric Mean 17.1198428169265 Harmonic Mean 16.9265661302997 Quadratic Mean 17.5084752586384 Winsorized Mean ( 1 / 28 ) 17.3188235294118 0.282780779964301 61.244698213217 Winsorized Mean ( 2 / 28 ) 17.3211764705882 0.279064534355668 62.068712925421 Winsorized Mean ( 3 / 28 ) 17.3105882352941 0.270641025175704 63.9614346127156 Winsorized Mean ( 4 / 28 ) 17.3247058823529 0.258940449781801 66.906139604499 Winsorized Mean ( 5 / 28 ) 17.3247058823529 0.254686636052270 68.023615808398 Winsorized Mean ( 6 / 28 ) 17.3388235294118 0.250036939106563 69.3450479411851 Winsorized Mean ( 7 / 28 ) 17.3470588235294 0.248821244799492 69.7169521738716 Winsorized Mean ( 8 / 28 ) 17.3564705882353 0.241229617700829 71.9499983196948 Winsorized Mean ( 9 / 28 ) 17.3564705882353 0.237808900157045 72.984949582515 Winsorized Mean ( 10 / 28 ) 17.3329411764706 0.229775119847872 75.434368994982 Winsorized Mean ( 11 / 28 ) 17.32 0.227468100389215 76.142544692483 Winsorized Mean ( 12 / 28 ) 17.2211764705882 0.210940896827034 81.639818212725 Winsorized Mean ( 13 / 28 ) 17.2211764705882 0.206491934702183 83.3987850199855 Winsorized Mean ( 14 / 28 ) 17.2211764705882 0.201785406978799 85.3440133676148 Winsorized Mean ( 15 / 28 ) 17.2211764705882 0.201785406978799 85.3440133676148 Winsorized Mean ( 16 / 28 ) 17.2211764705882 0.201785406978799 85.3440133676148 Winsorized Mean ( 17 / 28 ) 17.2011764705882 0.193178442621555 89.0429399738258 Winsorized Mean ( 18 / 28 ) 17.18 0.190074436252029 90.3856422713268 Winsorized Mean ( 19 / 28 ) 17.1576470588235 0.186853471483859 91.8240743539286 Winsorized Mean ( 20 / 28 ) 17.1105882352941 0.180242783119601 94.9307813558354 Winsorized Mean ( 21 / 28 ) 17.1352941176471 0.170390110001792 100.565074566046 Winsorized Mean ( 22 / 28 ) 17.1352941176471 0.170390110001792 100.565074566046 Winsorized Mean ( 23 / 28 ) 17.1082352941176 0.159596934224132 107.196515881010 Winsorized Mean ( 24 / 28 ) 17.0235294117647 0.148575373535975 114.578405603959 Winsorized Mean ( 25 / 28 ) 17.0529411764706 0.144784087632710 117.781874067064 Winsorized Mean ( 26 / 28 ) 17.0529411764706 0.144784087632710 117.781874067064 Winsorized Mean ( 27 / 28 ) 17.1482352941176 0.132932995955639 128.999088381640 Winsorized Mean ( 28 / 28 ) 16.9835294117647 0.104450637810410 162.598618522481 Trimmed Mean ( 1 / 28 ) 17.3108433734940 0.273504331949317 63.2927575593277 Trimmed Mean ( 2 / 28 ) 17.3024691358025 0.262725360690835 65.8576282483948 Trimmed Mean ( 3 / 28 ) 17.2924050632911 0.252503030545368 68.4839505725622 Trimmed Mean ( 4 / 28 ) 17.2857142857143 0.244381249481491 70.7325718417012 Trimmed Mean ( 5 / 28 ) 17.2746666666667 0.239045348581977 72.265228205194 Trimmed Mean ( 6 / 28 ) 17.2630136986301 0.234037642587851 73.761697083195 Trimmed Mean ( 7 / 28 ) 17.2478873239437 0.229327238929019 75.2108096905237 Trimmed Mean ( 8 / 28 ) 17.2304347826087 0.224000140320735 76.9215356648317 Trimmed Mean ( 9 / 28 ) 17.2104477611940 0.219329745911704 78.4683704877974 Trimmed Mean ( 10 / 28 ) 17.1892307692308 0.214421438420784 80.1656350028694 Trimmed Mean ( 11 / 28 ) 17.1698412698413 0.210145085821451 81.7047003632033 Trimmed Mean ( 12 / 28 ) 17.1508196721311 0.205386786263606 83.5049809393226 Trimmed Mean ( 13 / 28 ) 17.1423728813559 0.202803313689466 84.5270847378977 Trimmed Mean ( 14 / 28 ) 17.1333333333333 0.200333890048810 85.5238887896548 Trimmed Mean ( 15 / 28 ) 17.1236363636364 0.198002884656803 86.4817519871828 Trimmed Mean ( 16 / 28 ) 17.1132075471698 0.194966368575551 87.7751771867175 Trimmed Mean ( 17 / 28 ) 17.1019607843137 0.191044398824419 89.5182527702966 Trimmed Mean ( 18 / 28 ) 17.0918367346939 0.187646467389044 91.0853104378337 Trimmed Mean ( 19 / 28 ) 17.0829787234043 0.183811006509725 92.9377356001826 Trimmed Mean ( 20 / 28 ) 17.0755555555556 0.179425445408830 95.1679708340587 Trimmed Mean ( 21 / 28 ) 17.0720930232558 0.175028097139949 97.5391568680846 Trimmed Mean ( 22 / 28 ) 17.0658536585366 0.171208393774227 99.6788374817731 Trimmed Mean ( 23 / 28 ) 17.0589743589744 0.165951960786973 102.794653814741 Trimmed Mean ( 24 / 28 ) 17.0540540540541 0.161337995734999 105.703891859830 Trimmed Mean ( 25 / 28 ) 17.0571428571429 0.157570083875503 108.251150457087 Trimmed Mean ( 26 / 28 ) 17.0575757575758 0.153064052684028 111.440769132044 Trimmed Mean ( 27 / 28 ) 17.0580645161290 0.146410396360132 116.508560458853 Trimmed Mean ( 28 / 28 ) 17.0482758620690 0.140251418304181 121.555104883818 Median 17.2 Midrange 17.45 Midmean - Weighted Average at Xnp 17.0720930232558 Midmean - Weighted Average at X(n+1)p 17.0720930232558 Midmean - Empirical Distribution Function 17.0720930232558 Midmean - Empirical Distribution Function - Averaging 17.0720930232558 Midmean - Empirical Distribution Function - Interpolation 17.0720930232558 Midmean - Closest Observation 16.9042553191489 Midmean - True Basic - Statistics Graphics Toolkit 17.0720930232558 Midmean - MS Excel (old versions) 17.0720930232558 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228912249hno1fk57zl53ab6/11l1a1228910459.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228912249hno1fk57zl53ab6/11l1a1228910459.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228912249hno1fk57zl53ab6/20cqj1228910459.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/10/t1228912249hno1fk57zl53ab6/20cqj1228910459.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')

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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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