*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: Sat, 20 Dec 2008 05:03:40 -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/20/t12297780079d1m9qbylv6pr9j.htm/, Retrieved Sat, 20 Dec 2008 14:00:07 +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/2008/Dec/20/t12297780079d1m9qbylv6pr9j.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

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Dataseries X:

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655362 873127 1107897 1555964 1671159 1493308 2957796 2638691 1305669 1280496 921901 867888 652586 913831 1108544 1555827 1699283 1509458 3268975 2425016 1312703 1365498 934453 775019 651142 843192 1146766 1652601 1465906 1652734 2922334 2702805 1458956 1410363 1019279 936574 708917 885295 1099663 1576220 1487870 1488635 2882530 2677026 1404398 1344370 936865 872705 628151 953712 1160384 1400618 1661511 1495347 2918786 2775677 1407026 1370199 964526 850851 683118 847224 1073256 1514326 1503734 1507712 2865698 2788128 1391596 1366378 946295 859626

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 1458492.72222222 80643.2784865955 18.0857319989124 Geometric Mean 1325283.82422712 Harmonic Mean 1215709.26841541 Quadratic Mean 1609017.72665652 Winsorized Mean ( 1 / 24 ) 1454490.11111111 79336.4552776498 18.3331875116037 Winsorized Mean ( 2 / 24 ) 1453545.16666667 79070.4235665334 18.3829186831608 Winsorized Mean ( 3 / 24 ) 1453513 79015.2996246343 18.3953361805243 Winsorized Mean ( 4 / 24 ) 1453040.77777778 78276.6836695357 18.562881175602 Winsorized Mean ( 5 / 24 ) 1453663.48611111 77731.8323395118 18.7010062976761 Winsorized Mean ( 6 / 24 ) 1452707.81944444 75377.303617358 19.2724832241135 Winsorized Mean ( 7 / 24 ) 1458125.23611111 74268.6901918644 19.6331082767747 Winsorized Mean ( 8 / 24 ) 1450476.34722222 72215.5165534759 20.0853835359349 Winsorized Mean ( 9 / 24 ) 1447707.34722222 71377.7731501898 20.2823271633317 Winsorized Mean ( 10 / 24 ) 1443601.79166667 69947.9096002281 20.6382406553284 Winsorized Mean ( 11 / 24 ) 1412219.25 62108.7450898853 22.73784871931 Winsorized Mean ( 12 / 24 ) 1292066.58333333 37781.831849471 34.1980925774361 Winsorized Mean ( 13 / 24 ) 1287064.83333333 37013.2104518093 34.7731206675270 Winsorized Mean ( 14 / 24 ) 1287554.83333333 36369.6193445089 35.4019331667195 Winsorized Mean ( 15 / 24 ) 1291671.29166667 35192.3259316271 36.7032089375443 Winsorized Mean ( 16 / 24 ) 1293435.06944444 34918.0774319205 37.041989839396 Winsorized Mean ( 17 / 24 ) 1278364.33333333 31976.8815102184 39.9777674669378 Winsorized Mean ( 18 / 24 ) 1273830.58333333 31242.0657022953 40.7729308129502 Winsorized Mean ( 19 / 24 ) 1273871.22222222 31225.7934117448 40.795479731288 Winsorized Mean ( 20 / 24 ) 1264962.61111111 29403.9338933078 43.0201827993842 Winsorized Mean ( 21 / 24 ) 1265706.06944444 28905.2696571878 43.7880734016852 Winsorized Mean ( 22 / 24 ) 1268476.84722222 28341.1339146537 44.757448697787 Winsorized Mean ( 23 / 24 ) 1284696.63888889 25588.2064202875 50.206591966146 Winsorized Mean ( 24 / 24 ) 1299893.30555556 22665.8837903728 57.350214868201 Trimmed Mean ( 1 / 24 ) 1444490.71428571 77838.3262782522 18.5575767536680 Trimmed Mean ( 2 / 24 ) 1433903.11764706 76030.9745988852 18.8594599136979 Trimmed Mean ( 3 / 24 ) 1423189.27272727 74017.9714451074 19.2276179006436 Trimmed Mean ( 4 / 24 ) 1411817.875 71597.4329345973 19.7188337225675 Trimmed Mean ( 5 / 24 ) 1399849.93548387 68922.9862977039 20.310349430267 Trimmed Mean ( 6 / 24 ) 1386934.68333333 65806.2183754434 21.0760429268321 Trimmed Mean ( 7 / 24 ) 1373326.44827586 62662.4892363086 21.9162447105615 Trimmed Mean ( 8 / 24 ) 1357751.16071429 58996.1583731857 23.0142300474160 Trimmed Mean ( 9 / 24 ) 1342296.96296296 54935.8913960696 24.4338797251044 Trimmed Mean ( 10 / 24 ) 1326079.98076923 49889.330193368 26.5804326421987 Trimmed Mean ( 11 / 24 ) 1309156.84 43546.0638573928 30.0637238829967 Trimmed Mean ( 12 / 24 ) 1295102.875 37641.5513237574 34.4062035026329 Trimmed Mean ( 13 / 24 ) 1295498.91304348 37136.0401127383 34.8852195632754 Trimmed Mean ( 14 / 24 ) 1296560.54545455 36604.9911187513 35.4203212684395 Trimmed Mean ( 15 / 24 ) 1297663.28571429 36008.44810268 36.0377454205727 Trimmed Mean ( 16 / 24 ) 1298382.325 35439.8771853407 36.6361970785006 Trimmed Mean ( 17 / 24 ) 1298968.18421053 34691.4292001847 37.4434900538375 Trimmed Mean ( 18 / 24 ) 1301392.16666667 34297.5185568568 37.9442076694056 Trimmed Mean ( 19 / 24 ) 1304634.70588235 33827.5264015091 38.5672511314381 Trimmed Mean ( 20 / 24 ) 1308277.75 33073.8651083547 39.5562401223411 Trimmed Mean ( 21 / 24 ) 1313475.56666667 32356.3420422935 40.5940685430324 Trimmed Mean ( 22 / 24 ) 1319324.89285714 31329.3363260886 42.1114855139307 Trimmed Mean ( 23 / 24 ) 1325725.34615385 29861.1551760138 44.3963181711987 Trimmed Mean ( 24 / 24 ) 1331076.91666667 28656.9475606257 46.4486635867509 Median 1368288.5 Midrange 1948563 Midmean - Weighted Average at Xnp 1291474.89189189 Midmean - Weighted Average at X(n+1)p 1301392.16666667 Midmean - Empirical Distribution Function 1291474.89189189 Midmean - Empirical Distribution Function - Averaging 1301392.16666667 Midmean - Empirical Distribution Function - Interpolation 1301392.16666667 Midmean - Closest Observation 1291474.89189189 Midmean - True Basic - Statistics Graphics Toolkit 1301392.16666667 Midmean - MS Excel (old versions) 1298968.18421053 Number of observations 72

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297780079d1m9qbylv6pr9j/16hbb1229774615.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297780079d1m9qbylv6pr9j/16hbb1229774615.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297780079d1m9qbylv6pr9j/2mqgh1229774615.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/20/t12297780079d1m9qbylv6pr9j/2mqgh1229774615.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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