central tend bob

*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: Wed, 29 Oct 2008 13:48:42 -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/Oct/29/t1225309779uv7p55imxgvze3o.htm/, Retrieved Wed, 29 Oct 2008 19:49:39 +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/Oct/29/t1225309779uv7p55imxgvze3o.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}, }

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Dataseries X:

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0.797974 0.806243 0.795912 0.80236 0.80157 0.807034 0.803075 0.804388 0.807334 0.808039 0.800208 0.808518 0.800323 0.807641 0.807843 0.808647 0.802774 0.800387 0.799744 0.801755 0.799294 0.800994 0.801697 0.805512 0.799396 0.808458 0.804788 0.803232 0.805114 0.804385 0.803292 0.798574 0.802943 0.801767 0.798419 0.803301 0.805025 0.812093 0.80564 0.807676 0.800135 0.794657 0.779268 0.787052 0.796981 0.784986 0.79138 0.801543 0.798333 0.80404 0.799443 0.802055 0.804435 0.803417 0.809433 0.810135 0.809626 0.815044 0.806292 0.809363 0.812224 0.810642 0.812912 0.805542 0.802734 0.797022 0.7978 0.796909 0.806619 0.806229

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 0.802851714285714 0.000742503393316199 1081.27682851385 Geometric Mean 0.80282788043578 Harmonic Mean 0.802803901291459 Quadratic Mean 0.802875404786108 Winsorized Mean ( 1 / 23 ) 0.802902942857143 0.000701698546425883 1144.22774130964 Winsorized Mean ( 2 / 23 ) 0.802942314285714 0.000676730028510429 1186.50315555391 Winsorized Mean ( 3 / 23 ) 0.803122185714286 0.000618220622439485 1299.08669585492 Winsorized Mean ( 4 / 23 ) 0.803226528571429 0.000554421021459134 1448.76636614082 Winsorized Mean ( 5 / 23 ) 0.803279957142857 0.000528381805394091 1520.26422738712 Winsorized Mean ( 6 / 23 ) 0.803321785714286 0.000503784854952844 1594.57311552067 Winsorized Mean ( 7 / 23 ) 0.803309685714286 0.000498992514390076 1609.86319944334 Winsorized Mean ( 8 / 23 ) 0.803306371428572 0.000496714025631844 1617.24116891350 Winsorized Mean ( 9 / 23 ) 0.803314342857143 0.0004630606929288 1734.79277149671 Winsorized Mean ( 10 / 23 ) 0.803320771428571 0.000455741347755963 1762.66817874670 Winsorized Mean ( 11 / 23 ) 0.803367757142857 0.000444754442419698 1806.31755530561 Winsorized Mean ( 12 / 23 ) 0.803310671428571 0.000430655913493217 1865.31903141096 Winsorized Mean ( 13 / 23 ) 0.803303057142857 0.000420192277729178 1911.75111899748 Winsorized Mean ( 14 / 23 ) 0.803413657142857 0.000392216587757977 2048.39285797523 Winsorized Mean ( 15 / 23 ) 0.803428014285714 0.000387724662445761 2072.16123219427 Winsorized Mean ( 16 / 23 ) 0.803368585714286 0.000375198907354296 2141.18050444021 Winsorized Mean ( 17 / 23 ) 0.803368828571429 0.000353154382379085 2274.83748937051 Winsorized Mean ( 18 / 23 ) 0.803362657142857 0.000322534129919652 2490.78340125737 Winsorized Mean ( 19 / 23 ) 0.803293714285714 0.000306870892351509 2617.69276365766 Winsorized Mean ( 20 / 23 ) 0.803312571428571 0.000300123014510887 2676.61103143902 Winsorized Mean ( 21 / 23 ) 0.803327571428571 0.000296763735187322 2706.96003647985 Winsorized Mean ( 22 / 23 ) 0.803333228571429 0.000243923072056207 3293.38763159852 Winsorized Mean ( 23 / 23 ) 0.803481414285714 0.000215121789851915 3735.0071084794 Trimmed Mean ( 1 / 23 ) 0.803019235294118 0.000655241883142996 1225.53099237533 Trimmed Mean ( 2 / 23 ) 0.803142575757576 0.000597589055524224 1343.97136013984 Trimmed Mean ( 3 / 23 ) 0.80325209375 0.000543236477873345 1478.64167166123 Trimmed Mean ( 4 / 23 ) 0.803300983870968 0.000506595954772462 1585.68377086977 Trimmed Mean ( 5 / 23 ) 0.8033227 0.000487694093652006 1647.18562405476 Trimmed Mean ( 6 / 23 ) 0.80333301724138 0.000473317408002619 1697.23953452592 Trimmed Mean ( 7 / 23 ) 0.803335357142857 0.000462829790056785 1735.70365261989 Trimmed Mean ( 8 / 23 ) 0.803340111111111 0.000451029892720704 1781.1238768792 Trimmed Mean ( 9 / 23 ) 0.803345788461538 0.000436812566442997 1839.10869369728 Trimmed Mean ( 10 / 23 ) 0.80335068 0.000427214819012255 1880.43729816628 Trimmed Mean ( 11 / 23 ) 0.803355041666667 0.000416601855908060 1928.35204710168 Trimmed Mean ( 12 / 23 ) 0.803353282608696 0.000405448164587277 1981.39578070717 Trimmed Mean ( 13 / 23 ) 0.803358931818182 0.000394182797173405 2038.03650889609 Trimmed Mean ( 14 / 23 ) 0.803366095238095 0.000381766868267486 2104.33686632863 Trimmed Mean ( 15 / 23 ) 0.80336015 0.000371945559757174 2159.88638370754 Trimmed Mean ( 16 / 23 ) 0.803351815789474 0.000359560599662529 2234.25986201901 Trimmed Mean ( 17 / 23 ) 0.803349777777778 0.000345763792460065 2323.40631175418 Trimmed Mean ( 18 / 23 ) 0.803347470588235 0.000332522590430623 2415.91847804351 Trimmed Mean ( 19 / 23 ) 0.803345625 0.000322287044437249 2492.64014444867 Trimmed Mean ( 20 / 23 ) 0.803352 0.00031167134178066 2577.56133563721 Trimmed Mean ( 21 / 23 ) 0.803356928571429 0.000297648522032579 2699.01198596745 Trimmed Mean ( 22 / 23 ) 0.803360692307692 0.000277094572965376 2899.22925487276 Trimmed Mean ( 23 / 23 ) 0.803364333333333 0.000266183157675221 3018.08852351787 Median 0.803262 Midrange 0.797156 Midmean - Weighted Average at Xnp 0.803244514285714 Midmean - Weighted Average at X(n+1)p 0.803349777777778 Midmean - Empirical Distribution Function 0.803349777777778 Midmean - Empirical Distribution Function - Averaging 0.803349777777778 Midmean - Empirical Distribution Function - Interpolation 0.803347470588235 Midmean - Closest Observation 0.803349777777778 Midmean - True Basic - Statistics Graphics Toolkit 0.803349777777778 Midmean - MS Excel (old versions) 0.803349777777778 Number of observations 70

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/29/t1225309779uv7p55imxgvze3o/1a1801225309716.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/29/t1225309779uv7p55imxgvze3o/1a1801225309716.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/29/t1225309779uv7p55imxgvze3o/2krns1225309716.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Oct/29/t1225309779uv7p55imxgvze3o/2krns1225309716.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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