invoer

*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: Thu, 18 Dec 2008 10:20:12 -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/18/t122962091599e3fnf8vutq03g.htm/, Retrieved Thu, 18 Dec 2008 18:21:57 +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/18/t122962091599e3fnf8vutq03g.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:

» Textbox « » Textfile « » CSV «

11554,5 13182,1 14800,1 12150,7 14478,2 13253,9 12036,8 12653,2 14035,4 14571,4 15400,9 14283,2 14485,3 14196,3 15559,1 13767,4 14634 14381,1 12509,9 12122,3 13122,3 13908,7 13456,5 12441,6 12953 13057,2 14350,1 13830,2 13755,5 13574,4 12802,6 11737,3 13850,2 15081,8 13653,3 14019,1 13962 13768,7 14747,1 13858,1 13188 13693,1 12970 11392,8 13985,2 14994,7 13584,7 14257,8 13553,4 14007,3 16535,8 14721,4 13664,6 16405,9 13829,4 13735,6 15870,5 15962,4 15744,1 16083,7 14863,9 15533,1 17473,1 15925,5 15573,7 17495 14155,8 14913,9 17250,4 15879,8 17647,8 17749,9 17111,8 16934,8 20280 16238,2 17896,1 18089,3 15660 16162,4 17850,1 18520,4 18524,7 16843,7

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 17 seconds R Server 'George Udny Yule' @ 72.249.76.132 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 14746.8964285714 198.823802012823 74.170679160538 Geometric Mean 14639.2674449403 Harmonic Mean 14535.0679154510 Quadratic Mean 14857.7259137292 Winsorized Mean ( 1 / 28 ) 14727.925 192.433322283777 76.5352113927599 Winsorized Mean ( 2 / 28 ) 14732.175 191.566625663017 76.9036618409473 Winsorized Mean ( 3 / 28 ) 14727.475 186.114835908820 79.1311177751307 Winsorized Mean ( 4 / 28 ) 14722.3464285714 183.452388715844 80.2515929698544 Winsorized Mean ( 5 / 28 ) 14721.2988095238 182.59669176376 80.621936067549 Winsorized Mean ( 6 / 28 ) 14734.9202380952 177.747336436819 82.898121195379 Winsorized Mean ( 7 / 28 ) 14732.1035714286 175.147117830243 84.1127376455449 Winsorized Mean ( 8 / 28 ) 14731.1988095238 170.216475654739 86.5439068272337 Winsorized Mean ( 9 / 28 ) 14744.8595238095 167.460597759094 88.0497246583415 Winsorized Mean ( 10 / 28 ) 14736.2523809524 159.890143084683 92.1648582999117 Winsorized Mean ( 11 / 28 ) 14720.3285714286 156.196500895692 94.2423709047027 Winsorized Mean ( 12 / 28 ) 14707.5 149.932866158695 98.0939028033587 Winsorized Mean ( 13 / 28 ) 14703.4761904762 146.101744236735 100.638608165085 Winsorized Mean ( 14 / 28 ) 14662.1261904762 136.001634586536 107.808455648722 Winsorized Mean ( 15 / 28 ) 14639.9833333333 132.068361299444 110.851555885815 Winsorized Mean ( 16 / 28 ) 14620.5928571429 125.353947350791 116.634483126634 Winsorized Mean ( 17 / 28 ) 14646.2547619048 117.777414771705 124.355376540523 Winsorized Mean ( 18 / 28 ) 14650.1547619048 112.695022538731 129.998241553835 Winsorized Mean ( 19 / 28 ) 14627.4678571429 107.990620132517 135.451281224177 Winsorized Mean ( 20 / 28 ) 14621.1345238095 106.39953541905 137.417277868976 Winsorized Mean ( 21 / 28 ) 14626.8595238095 102.730367395965 142.381068953366 Winsorized Mean ( 22 / 28 ) 14627.3833333333 102.035460476189 143.355881034582 Winsorized Mean ( 23 / 28 ) 14600.5773809524 96.1260065918212 151.889981687793 Winsorized Mean ( 24 / 28 ) 14588.6916666667 91.33150241801 159.733402828484 Winsorized Mean ( 25 / 28 ) 14568.9297619048 87.0636476545397 167.336542338691 Winsorized Mean ( 26 / 28 ) 14568.0940476190 86.022004188924 169.353111276321 Winsorized Mean ( 27 / 28 ) 14560.1547619048 84.8175831802398 171.664343830265 Winsorized Mean ( 28 / 28 ) 14536.3214285714 76.5060172801278 190.002328514194 Trimmed Mean ( 1 / 28 ) 14720.3231707317 187.571671780410 78.4783919181824 Trimmed Mean ( 2 / 28 ) 14712.34125 181.931247800498 80.867588321789 Trimmed Mean ( 3 / 28 ) 14701.6615384615 175.897143104950 83.5810137614894 Trimmed Mean ( 4 / 28 ) 14692.1513157895 171.290260172029 85.7734193469841 Trimmed Mean ( 5 / 28 ) 14683.5824324324 166.838515163659 88.0107475065256 Trimmed Mean ( 6 / 28 ) 14674.7819444444 161.853779312212 90.6669093968892 Trimmed Mean ( 7 / 28 ) 14662.7542857143 157.269450408606 93.2333281995875 Trimmed Mean ( 8 / 28 ) 14650.5161764706 152.465982771867 96.0903928215382 Trimmed Mean ( 9 / 28 ) 14637.6803030303 147.880894826334 98.9829032358795 Trimmed Mean ( 10 / 28 ) 14622.05 142.951297484077 102.286934482905 Trimmed Mean ( 11 / 28 ) 14606.5774193548 138.631810456840 105.362379465586 Trimmed Mean ( 12 / 28 ) 14592.1 134.162310123325 108.764525495921 Trimmed Mean ( 13 / 28 ) 14578.1724137931 129.990120286155 112.148310823171 Trimmed Mean ( 14 / 28 ) 14563.7142857143 125.614104862652 115.940119158103 Trimmed Mean ( 15 / 28 ) 14552.7796296296 122.281173491644 119.010794663531 Trimmed Mean ( 16 / 28 ) 14543.3884615385 118.902283404894 122.313786119770 Trimmed Mean ( 17 / 28 ) 14535.282 115.978302991621 125.327596844128 Trimmed Mean ( 18 / 28 ) 14523.8583333333 113.646289672492 127.798790221735 Trimmed Mean ( 19 / 28 ) 14511.0456521739 111.543570469599 130.093071174630 Trimmed Mean ( 20 / 28 ) 14499.3477272727 109.691857584724 132.182534296803 Trimmed Mean ( 21 / 28 ) 14487.1690476190 107.469030273480 134.803198751799 Trimmed Mean ( 22 / 28 ) 14473.2 105.142864651766 137.652707560664 Trimmed Mean ( 23 / 28 ) 14457.7078947368 102.008398001811 141.730565109749 Trimmed Mean ( 24 / 28 ) 14443.2138888889 99.1369111943438 145.689569252113 Trimmed Mean ( 25 / 28 ) 14428.2382352941 96.25116236673 149.901963576508 Trimmed Mean ( 26 / 28 ) 14413.465625 93.2331799248459 154.595881387061 Trimmed Mean ( 27 / 28 ) 14396.8133333333 88.9574905238817 161.839247583860 Trimmed Mean ( 28 / 28 ) 14378.6642857143 82.854113712646 173.541947905957 Median 14316.65 Midrange 15836.4 Midmean - Weighted Average at Xnp 14466.1813953488 Midmean - Weighted Average at X(n+1)p 14487.1690476190 Midmean - Empirical Distribution Function 14466.1813953488 Midmean - Empirical Distribution Function - Averaging 14487.1690476190 Midmean - Empirical Distribution Function - Interpolation 14487.1690476190 Midmean - Closest Observation 14466.1813953488 Midmean - True Basic - Statistics Graphics Toolkit 14487.1690476190 Midmean - MS Excel (old versions) 14499.3477272727 Number of observations 84

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t122962091599e3fnf8vutq03g/1wm5x1229620794.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t122962091599e3fnf8vutq03g/1wm5x1229620794.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t122962091599e3fnf8vutq03g/2eg3p1229620794.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t122962091599e3fnf8vutq03g/2eg3p1229620794.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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