Paper: Central Tendency Uitvoer Amerika

*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 08:59:22 -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/t122944320453yx340bdmam52f.htm/, Retrieved Tue, 16 Dec 2008 17:00:06 +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/t122944320453yx340bdmam52f.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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1190,8 728,8 995,6 1260,3 994 957,3 975,6 884,9 908,4 1022,8 958,6 825,1 1116,6 724,2 1004,5 1058,9 854,7 943,4 792,4 873,2 1101,4 987,1 1038,8 1060,7 1047,7 840 1044 1097,4 987,5 934 977 881,1 1083,3 1074,7 1182,2 1117,5 1117,4 936,2 1246,3 1175,1 1177,7 1035,8 1091,6 998,7 1247,9 1034,7 1287,7 994,0 1122,8 1017,3 1106,0 1191,8 1030,1 989,4 979,6 1088,0 1389,2 1043,9 1182,1 1109,6 1463,3 1276,2 1082,4 1360,4 1130,2 1019,6 1077,0 958,8 959,6 907,2 880,8 759,6 1137,2

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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 1042.87260273973 17.0695655915298 61.0954389640247 Geometric Mean 1032.82095493291 Harmonic Mean 1022.69675824341 Quadratic Mean 1052.88266703747 Winsorized Mean ( 1 / 24 ) 1041.92054794521 16.733017238426 62.2673444423711 Winsorized Mean ( 2 / 24 ) 1041.97534246575 16.3008988346949 63.9213428064476 Winsorized Mean ( 3 / 24 ) 1040.33561643836 15.2418320778968 68.2552865771969 Winsorized Mean ( 4 / 24 ) 1041.49726027397 14.7152684211159 70.7766403213864 Winsorized Mean ( 5 / 24 ) 1041.42876712329 14.2743188146926 72.9582112213541 Winsorized Mean ( 6 / 24 ) 1041.61780821918 13.8282771667534 75.3252046989253 Winsorized Mean ( 7 / 24 ) 1043.23835616438 13.4742017198357 77.4248729428334 Winsorized Mean ( 8 / 24 ) 1038.09863013699 12.1726360681491 85.281333009969 Winsorized Mean ( 9 / 24 ) 1038.01232876712 12.1444163757080 85.4723929626964 Winsorized Mean ( 10 / 24 ) 1037.35479452055 11.8482164173370 87.5536669808486 Winsorized Mean ( 11 / 24 ) 1040.7 11.2683042364544 92.356398812272 Winsorized Mean ( 12 / 24 ) 1040.17397260274 11.1106213028755 93.6197845509808 Winsorized Mean ( 13 / 24 ) 1044.26986301370 10.3147669197771 101.240277277760 Winsorized Mean ( 14 / 24 ) 1037.42328767123 9.04848127567832 114.651647725652 Winsorized Mean ( 15 / 24 ) 1037.46438356164 8.60327854435782 120.589421603934 Winsorized Mean ( 16 / 24 ) 1038.88904109589 7.91230871680317 131.300367349119 Winsorized Mean ( 17 / 24 ) 1037.95753424658 7.68933835546207 134.986586135759 Winsorized Mean ( 18 / 24 ) 1037.98219178082 7.6787301711511 135.176281578497 Winsorized Mean ( 19 / 24 ) 1037.98219178082 7.61906837988865 136.234791450447 Winsorized Mean ( 20 / 24 ) 1040.44794520548 6.73750100165444 154.426388203874 Winsorized Mean ( 21 / 24 ) 1039.81506849315 6.53706318586684 159.064558338863 Winsorized Mean ( 22 / 24 ) 1039.21232876712 6.23932145442023 166.558549092048 Winsorized Mean ( 23 / 24 ) 1040.31506849315 5.75660089357584 180.716900081454 Winsorized Mean ( 24 / 24 ) 1038.53972602740 5.48004986274727 189.512824160099 Trimmed Mean ( 1 / 24 ) 1041.43943661972 15.8779539755661 65.5902793409243 Trimmed Mean ( 2 / 24 ) 1040.93043478261 14.8470830510608 70.1100971283538 Trimmed Mean ( 3 / 24 ) 1040.36119402985 13.8892677698422 74.9039626328457 Trimmed Mean ( 4 / 24 ) 1040.37076923077 13.2504948606931 78.515616221774 Trimmed Mean ( 5 / 24 ) 1040.04444444444 12.6841874494720 81.995354340789 Trimmed Mean ( 6 / 24 ) 1039.71311475410 12.1454519305734 85.6051401543044 Trimmed Mean ( 7 / 24 ) 1039.32033898305 11.6232650722157 89.417244855531 Trimmed Mean ( 8 / 24 ) 1038.60350877193 11.0796749850860 93.7395284762382 Trimmed Mean ( 9 / 24 ) 1038.68727272727 10.7539963770566 96.5861653945955 Trimmed Mean ( 10 / 24 ) 1038.79056603774 10.3547957183976 100.31975466132 Trimmed Mean ( 11 / 24 ) 1038.99607843137 9.9262484119411 104.671577348546 Trimmed Mean ( 12 / 24 ) 1038.76530612245 9.52531962031832 109.053065674214 Trimmed Mean ( 13 / 24 ) 1038.58297872340 9.05072217394932 114.751393177525 Trimmed Mean ( 14 / 24 ) 1037.87333333333 8.6311717195596 120.247095881704 Trimmed Mean ( 15 / 24 ) 1037.92790697674 8.39569995247158 123.626131573603 Trimmed Mean ( 16 / 24 ) 1037.98292682927 8.18427768647035 126.826455136681 Trimmed Mean ( 17 / 24 ) 1037.87692307692 8.05459731721514 128.855221707814 Trimmed Mean ( 18 / 24 ) 1037.86756756757 7.91861574305111 131.066792637127 Trimmed Mean ( 19 / 24 ) 1037.85428571429 7.7212609921258 134.415128147164 Trimmed Mean ( 20 / 24 ) 1037.83939393939 7.4506354459957 139.295420029868 Trimmed Mean ( 21 / 24 ) 1037.53225806452 7.30255425500163 142.077993786064 Trimmed Mean ( 22 / 24 ) 1037.25862068966 7.12660234724778 145.547425006845 Trimmed Mean ( 23 / 24 ) 1037.01851851852 6.93889084677021 149.450184679186 Trimmed Mean ( 24 / 24 ) 1036.6 6.78943787560257 152.678324626102 Median 1035.8 Midrange 1093.75 Midmean - Weighted Average at Xnp 1035.65833333333 Midmean - Weighted Average at X(n+1)p 1037.86756756757 Midmean - Empirical Distribution Function 1037.86756756757 Midmean - Empirical Distribution Function - Averaging 1037.86756756757 Midmean - Empirical Distribution Function - Interpolation 1037.86756756757 Midmean - Closest Observation 1035.78157894737 Midmean - True Basic - Statistics Graphics Toolkit 1037.86756756757 Midmean - MS Excel (old versions) 1037.86756756757 Number of observations 73

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t122944320453yx340bdmam52f/17q411229443151.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t122944320453yx340bdmam52f/17q411229443151.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t122944320453yx340bdmam52f/2t33z1229443151.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/16/t122944320453yx340bdmam52f/2t33z1229443151.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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