Central tendency auto's

*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: Tue, 16 Dec 2008 11:02:42 -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/16/t1229450642h7iueqirn9vmed2.htm/, Retrieved Tue, 16 Dec 2008 19:04:02 +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/16/t1229450642h7iueqirn9vmed2.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)

User-defined keywords:

Dataseries X:

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58608 46865 51378 46235 47206 45382 41227 33795 31295 42625 33625 21538 56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972 58552 54955 65540 51570 51145 46641 35704 33253 35193 41668 34865 21210 56126 49231 59723 48103 47472 50497 40059 34149 36860 46356 36577 23872 57276 56389 57657 62300 48929 51168 39636 33213 38127 43291

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 42098.4787234043 1087.44419903055 38.7132312268848 Geometric Mean 40691.3284412912 Harmonic Mean 39168.2190626265 Quadratic Mean 43384.9934334835 Winsorized Mean ( 1 / 31 ) 42091.5106382979 1073.82523912774 39.1977289269978 Winsorized Mean ( 2 / 31 ) 42078.8085106383 1069.22894936612 39.3543483232327 Winsorized Mean ( 3 / 31 ) 42033.6808510638 1056.61283320726 39.7815354215167 Winsorized Mean ( 4 / 31 ) 42085.5531914894 1028.41482512259 40.9227406717642 Winsorized Mean ( 5 / 31 ) 42147.5744680851 1015.84120839341 41.4903176991048 Winsorized Mean ( 6 / 31 ) 42174.7021276596 991.270561437902 42.5461057438067 Winsorized Mean ( 7 / 31 ) 42149.085106383 986.076603449222 42.7442299705202 Winsorized Mean ( 8 / 31 ) 42168.4893617021 958.800187966661 43.9804767363775 Winsorized Mean ( 9 / 31 ) 42308.3723404255 935.65803531238 45.2177726730049 Winsorized Mean ( 10 / 31 ) 42372.8404255319 917.320699972895 46.1919592861951 Winsorized Mean ( 11 / 31 ) 42283.7872340426 888.777713513628 47.5752109792233 Winsorized Mean ( 12 / 31 ) 42253.1489361702 847.38223205976 49.8631518783018 Winsorized Mean ( 13 / 31 ) 42252.5957446809 840.009909453259 50.300115830993 Winsorized Mean ( 14 / 31 ) 42260.3404255319 822.943838778158 51.3526421052945 Winsorized Mean ( 15 / 31 ) 42291.6170212766 791.163474916357 53.4549664666303 Winsorized Mean ( 16 / 31 ) 42352.2127659574 778.409255670944 54.408670577089 Winsorized Mean ( 17 / 31 ) 42207.8936170213 756.881781233826 55.7655034954288 Winsorized Mean ( 18 / 31 ) 42207.5106382979 750.56986597644 56.2339530956106 Winsorized Mean ( 19 / 31 ) 42244.2978723404 742.611260391874 56.8861531268032 Winsorized Mean ( 20 / 31 ) 42216 734.686452029503 57.461247425187 Winsorized Mean ( 21 / 31 ) 42231.6382978723 731.430288981272 57.7384324030279 Winsorized Mean ( 22 / 31 ) 42104.7872340426 712.233169400136 59.1165773274845 Winsorized Mean ( 23 / 31 ) 42165.4680851064 701.086318517799 60.1430479691152 Winsorized Mean ( 24 / 31 ) 42150.914893617 677.853940865926 62.1828868321858 Winsorized Mean ( 25 / 31 ) 42113.9468085106 648.371146611402 64.953456100895 Winsorized Mean ( 26 / 31 ) 42106.7553191489 625.461831782516 67.3210629002702 Winsorized Mean ( 27 / 31 ) 42052.4680851064 611.044970526701 68.820578048222 Winsorized Mean ( 28 / 31 ) 42000.6382978723 591.80061791819 70.9709267381645 Winsorized Mean ( 29 / 31 ) 42046.2978723404 585.831153127576 71.7720415649934 Winsorized Mean ( 30 / 31 ) 41910.6595744681 567.036311110555 73.91177381989 Winsorized Mean ( 31 / 31 ) 41710.1489361702 542.018135193271 76.953419503754 Trimmed Mean ( 1 / 31 ) 42101.4130434783 1049.76392804433 40.1056008105664 Trimmed Mean ( 2 / 31 ) 42111.7555555556 1022.31869086682 41.1923952205637 Trimmed Mean ( 3 / 31 ) 42111.7555555556 993.71567000891 42.3780733528917 Trimmed Mean ( 4 / 31 ) 42164.2093023256 966.358330828283 43.6320647913139 Trimmed Mean ( 5 / 31 ) 42186.2142857143 944.637014385752 44.6586505115362 Trimmed Mean ( 6 / 31 ) 42186.2142857143 923.235392256684 45.6938876472203 Trimmed Mean ( 7 / 31 ) 42199.0625 904.741749002036 46.6421081447243 Trimmed Mean ( 8 / 31 ) 42207.6666666667 884.427279435462 47.723162376457 Trimmed Mean ( 9 / 31 ) 42213.7236842105 866.594951742452 48.7121735469747 Trimmed Mean ( 10 / 31 ) 42200.3648648649 850.30903121459 49.6294444910051 Trimmed Mean ( 11 / 31 ) 42177.8472222222 834.556175249922 50.5392548435596 Trimmed Mean ( 12 / 31 ) 42177.8472222222 821.075666678243 51.3690137631987 Trimmed Mean ( 13 / 31 ) 42154.75 812.057591412882 51.911034938613 Trimmed Mean ( 14 / 31 ) 42144.0303030303 802.229995089212 52.5336007890651 Trimmed Mean ( 15 / 31 ) 42131.828125 792.942415865312 53.1335280873113 Trimmed Mean ( 16 / 31 ) 42115.6774193548 786.451106608187 53.5515521123642 Trimmed Mean ( 17 / 31 ) 42092.5166666667 780.04154839786 53.9618905597031 Trimmed Mean ( 18 / 31 ) 42081.5172413793 775.064872581546 54.2941871448984 Trimmed Mean ( 19 / 31 ) 42069.7678571429 769.263122697464 54.6883980472414 Trimmed Mean ( 20 / 31 ) 42053.7777777778 762.656410584502 55.1411844103528 Trimmed Mean ( 21 / 31 ) 42039.1153846154 755.03213832582 55.6785774415263 Trimmed Mean ( 22 / 31 ) 42021.88 745.308476138626 56.3818624708408 Trimmed Mean ( 23 / 31 ) 42014.5 735.737110484907 57.1053157456054 Trimmed Mean ( 24 / 31 ) 42014.5 724.774210268698 57.9690880342221 Trimmed Mean ( 25 / 31 ) 41987.75 714.249986680095 58.7857903857489 Trimmed Mean ( 26 / 31 ) 41976.4523809524 705.360437183876 59.5106418904663 Trimmed Mean ( 27 / 31 ) 41964.675 697.110881614988 60.1979916061287 Trimmed Mean ( 28 / 31 ) 41956.6315789474 687.865228394291 60.9954244625626 Trimmed Mean ( 29 / 31 ) 41952.5277777778 678.272191565429 61.8520533488964 Trimmed Mean ( 30 / 31 ) 41943.5882352941 664.99420355541 63.073614793996 Trimmed Mean ( 31 / 31 ) 41943.5882352941 649.914000882691 64.5371359569539 Median 41706.5 Midrange 41963.5 Midmean - Weighted Average at Xnp 41834.0212765957 Midmean - Weighted Average at X(n+1)p 42014.5 Midmean - Empirical Distribution Function 42014.5 Midmean - Empirical Distribution Function - Averaging 42014.5 Midmean - Empirical Distribution Function - Interpolation 42001.0869565217 Midmean - Closest Observation 42014.5 Midmean - True Basic - Statistics Graphics Toolkit 42014.5 Midmean - MS Excel (old versions) 42014.5 Number of observations 94

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229450642h7iueqirn9vmed2/1tfli1229450557.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229450642h7iueqirn9vmed2/1tfli1229450557.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229450642h7iueqirn9vmed2/2ivyj1229450557.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t1229450642h7iueqirn9vmed2/2ivyj1229450557.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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