*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 11:56:20 -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/t12559751064loo3hee2vs4gvl.htm/, Retrieved Mon, 19 Oct 2009 19:58:28 +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/t12559751064loo3hee2vs4gvl.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:

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1027387 1032760 1026564 1031480 1039048 1029781 1036585 1039113 1038981 1048472 1050976 1058369 1063014 1069895 1068642 1068381 1071410 1075303 1074652 1076742 1058112 1070165 1082079 1089077 1089392 1089298 1091254 1095112 1094153 1098756 1101085 1103418 1099897 1098269 1095835 1105013 1099386 1108399 1106298 1110539 1111430 1111951 1115406 1116142 1120071 1114196 1120541 1123962 1123389 1120435 1116495 1110012 1106820 1104494 1103760 1091570 1048367 1061626 1047607 1023650 1001154 993397 977486 971751 961207 957734 966893 974422

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 1069250.88235294 5448.08312640398 196.261851653997 Geometric Mean 1068294.75127949 Harmonic Mean 1067311.89450500 Quadratic Mean 1070180.41341913 Winsorized Mean ( 1 / 22 ) 1069293.52941176 5431.43844031535 196.871149542050 Winsorized Mean ( 2 / 22 ) 1069377 5370.59882088653 199.11690216762 Winsorized Mean ( 3 / 22 ) 1069586.64705882 5309.93570529489 201.431186067332 Winsorized Mean ( 4 / 22 ) 1069722.35294118 5264.04457148258 203.213012050902 Winsorized Mean ( 5 / 22 ) 1069684.70588235 5167.04764351299 207.020484362148 Winsorized Mean ( 6 / 22 ) 1071057.47058824 4805.87637931451 222.864132585326 Winsorized Mean ( 7 / 22 ) 1071780.22058824 4607.47573387114 232.617659320311 Winsorized Mean ( 8 / 22 ) 1074284.45588235 4032.54099979505 266.403852046874 Winsorized Mean ( 9 / 22 ) 1074373 3918.04274187113 274.211658928180 Winsorized Mean ( 10 / 22 ) 1074417.41176471 3885.15666434604 276.544166577529 Winsorized Mean ( 11 / 22 ) 1074660.54411765 3795.57518266558 283.135096104967 Winsorized Mean ( 12 / 22 ) 1074867.36764706 3729.98849701204 288.169083767442 Winsorized Mean ( 13 / 22 ) 1074803.70588235 3644.77932704717 294.888554131783 Winsorized Mean ( 14 / 22 ) 1075266.11764706 3466.91368970141 310.150818245396 Winsorized Mean ( 15 / 22 ) 1075679.5 3364.22476419864 319.740675904639 Winsorized Mean ( 16 / 22 ) 1075392.91176471 3320.99097659253 323.816872537276 Winsorized Mean ( 17 / 22 ) 1075279.41176471 3301.12966459039 325.730740994122 Winsorized Mean ( 18 / 22 ) 1077333.52941176 2919.73324431213 368.983547216341 Winsorized Mean ( 19 / 22 ) 1077450.32352941 2874.66872927837 374.808517084291 Winsorized Mean ( 20 / 22 ) 1076795.02941176 2778.94751411448 387.483039511413 Winsorized Mean ( 21 / 22 ) 1077201.44117647 2614.51353643723 412.008362612787 Winsorized Mean ( 22 / 22 ) 1079344.82352941 2257.18774423056 478.181235162316 Trimmed Mean ( 1 / 22 ) 1070111.57575758 5283.37323023889 202.543248247709 Trimmed Mean ( 2 / 22 ) 1070980.75 5103.20471980131 209.864351677763 Trimmed Mean ( 3 / 22 ) 1071860.22580645 4923.14616264567 217.718546310727 Trimmed Mean ( 4 / 22 ) 1072719.13333333 4731.19522389336 226.733221219855 Trimmed Mean ( 5 / 22 ) 1073597.5 4511.55748035175 237.966047130202 Trimmed Mean ( 6 / 22 ) 1074547.75 4270.20180826143 251.638634015166 Trimmed Mean ( 7 / 22 ) 1075280.27777778 4087.53530576833 263.063239175045 Trimmed Mean ( 8 / 22 ) 1075934.13461538 3917.08598721594 274.677180467029 Trimmed Mean ( 9 / 22 ) 1076214.58 3859.23723785318 278.867173399964 Trimmed Mean ( 10 / 22 ) 1076504.45833333 3809.70725639066 282.568813267090 Trimmed Mean ( 11 / 22 ) 1076812.97826087 3749.82077877548 287.163851764805 Trimmed Mean ( 12 / 22 ) 1077115.38636364 3689.38805224075 291.949605493369 Trimmed Mean ( 13 / 22 ) 1077418.69047619 3621.49970434637 297.506220746924 Trimmed Mean ( 14 / 22 ) 1077760.65 3546.90387205915 303.859560020810 Trimmed Mean ( 15 / 22 ) 1078079.5 3485.5808432344 309.296943174501 Trimmed Mean ( 16 / 22 ) 1078381.72222222 3421.87342650218 315.143661910528 Trimmed Mean ( 17 / 22 ) 1078755.32352941 3336.78547418765 323.291782427828 Trimmed Mean ( 18 / 22 ) 1079189.8125 3214.83265205528 335.690821047889 Trimmed Mean ( 19 / 22 ) 1079423.56666667 3153.11566392301 342.335544178447 Trimmed Mean ( 20 / 22 ) 1079675.78571429 3066.20856454063 352.12079119479 Trimmed Mean ( 21 / 22 ) 1080052.5 2953.98442173383 365.625658704749 Trimmed Mean ( 22 / 22 ) 1080437.16666667 2832.62479461244 381.426148892584 Median 1079410.5 Midrange 1040848 Midmean - Weighted Average at Xnp 1077620.82857143 Midmean - Weighted Average at X(n+1)p 1078755.32352941 Midmean - Empirical Distribution Function 1077620.82857143 Midmean - Empirical Distribution Function - Averaging 1078755.32352941 Midmean - Empirical Distribution Function - Interpolation 1078755.32352941 Midmean - Closest Observation 1077620.82857143 Midmean - True Basic - Statistics Graphics Toolkit 1078755.32352941 Midmean - MS Excel (old versions) 1078381.72222222 Number of observations 68

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/19/t12559751064loo3hee2vs4gvl/1naqq1255974978.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t12559751064loo3hee2vs4gvl/1naqq1255974978.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t12559751064loo3hee2vs4gvl/2j93j1255974978.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/19/t12559751064loo3hee2vs4gvl/2j93j1255974978.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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