*Unverified author*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Tue, 12 Apr 2011 18:41:57 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Apr/12/t13026335229yol17loj6ibi5l.htm/, Retrieved Tue, 12 Apr 2011 20:38:44 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

7989 41102 9123 22109 47115 9105 5496 23102 6994 84101 5884 6383 6292 36109 49127 26116 63120 60115 77117 18110 3999 79105 2286 7487 7789 3788 83108 52100 93102 598 8983 3488 2780 7974 9171 3071 4166 7968 6580 7183 2779 5273 1568 1860 9853 6757 6745 5144 9444 2248 7349 8149 7949 3545 1043 4038 4335 5432 8027 8626 24 4829 931 232 9034 1337 5138 9736 7730 7133 8126 424

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 'Herman Ole Andreas Wold' @ www.yougetit.org Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 16169.0694444444 2732.43526886965 5.91745745220645 Geometric Mean 7035.81374800811 Harmonic Mean 1143.50470360894 Quadratic Mean 28134.3061776405 Winsorized Mean ( 1 / 24 ) 16046.9444444444 2685.07261552844 5.97635399193339 Winsorized Mean ( 2 / 24 ) 16024.6944444444 2674.83729278899 5.99090437674282 Winsorized Mean ( 3 / 24 ) 15865.1527777778 2616.38112827543 6.06377740854413 Winsorized Mean ( 4 / 24 ) 15773.2083333333 2577.55854247419 6.11943747287024 Winsorized Mean ( 5 / 24 ) 14808.9722222222 2267.03832133036 6.53229902771645 Winsorized Mean ( 6 / 24 ) 14583.0555555556 2190.69805680544 6.65680763729765 Winsorized Mean ( 7 / 24 ) 13826.2777777778 1967.56455484273 7.02710248756382 Winsorized Mean ( 8 / 24 ) 13528.3888888889 1875.28119274432 7.21405885220404 Winsorized Mean ( 9 / 24 ) 13325.3888888889 1804.25920216732 7.38551804135575 Winsorized Mean ( 10 / 24 ) 12495.5277777778 1587.39842416181 7.87170226931263 Winsorized Mean ( 11 / 24 ) 11808.0277777778 1389.60087518715 8.4974239644081 Winsorized Mean ( 12 / 24 ) 10142.6944444444 993.080216482482 10.2133687451454 Winsorized Mean ( 13 / 24 ) 9651.04166666667 866.234321881734 11.1413752871181 Winsorized Mean ( 14 / 24 ) 9539.04166666667 815.58170083355 11.6959976626713 Winsorized Mean ( 15 / 24 ) 8717.79166666667 636.858554808788 13.6887407742903 Winsorized Mean ( 16 / 24 ) 6936.90277777778 284.90328312502 24.3482725144088 Winsorized Mean ( 17 / 24 ) 6959.09722222222 273.254909137335 25.4674188441557 Winsorized Mean ( 18 / 24 ) 6895.84722222222 261.522934313676 26.3680401121196 Winsorized Mean ( 19 / 24 ) 6857.58333333333 246.619636702667 27.8063151216181 Winsorized Mean ( 20 / 24 ) 6891.19444444444 237.692884889203 28.9920097846289 Winsorized Mean ( 21 / 24 ) 7030.02777777778 215.697506495511 32.5920679009985 Winsorized Mean ( 22 / 24 ) 7102.75 199.403081001354 35.6200614570834 Winsorized Mean ( 23 / 24 ) 7088.375 196.921748554584 35.9958971115635 Winsorized Mean ( 24 / 24 ) 7012.375 175.120378268153 40.0431695576988 Trimmed Mean ( 1 / 24 ) 15300.6714285714 2571.34633123664 5.95045142021489 Trimmed Mean ( 2 / 24 ) 14510.5 2431.3259926937 5.96814250479163 Trimmed Mean ( 3 / 24 ) 13684.5757575758 2263.68020940926 6.04527781825992 Trimmed Mean ( 4 / 24 ) 12866.859375 2082.68678596807 6.17800980046034 Trimmed Mean ( 5 / 24 ) 12023.0806451613 1866.4034521697 6.44184440999851 Trimmed Mean ( 6 / 24 ) 11354.4666666667 1715.34884569015 6.61933384290605 Trimmed Mean ( 7 / 24 ) 10686.4827586207 1547.03956795824 6.90769840665714 Trimmed Mean ( 8 / 24 ) 10109.7857142857 1406.79047783093 7.18641892563388 Trimmed Mean ( 9 / 24 ) 9540.01851851852 1252.19176888335 7.61865614803224 Trimmed Mean ( 10 / 24 ) 8957.65384615385 1064.45419343815 8.4152553499939 Trimmed Mean ( 11 / 24 ) 8448.2 883.900272331993 9.55786559236047 Trimmed Mean ( 12 / 24 ) 7990.04166666667 700.430441339146 11.4073306856718 Trimmed Mean ( 13 / 24 ) 7709.26086956522 600.916563561123 12.8291701994017 Trimmed Mean ( 14 / 24 ) 7464.84090909091 507.032985261214 14.7225942415663 Trimmed Mean ( 15 / 24 ) 7210.85714285714 383.625354968811 18.7966125008692 Trimmed Mean ( 16 / 24 ) 7030.025 277.218525501833 25.3591457759684 Trimmed Mean ( 17 / 24 ) 7041.05263157895 268.552886488317 26.2184954466511 Trimmed Mean ( 18 / 24 ) 7050.69444444444 259.550077192334 27.1650639472539 Trimmed Mean ( 19 / 24 ) 7068.91176470588 249.894706409932 28.2875610542542 Trimmed Mean ( 20 / 24 ) 7093.9375 240.128136734143 29.5423001922262 Trimmed Mean ( 21 / 24 ) 7118.26666666667 228.572888514768 31.1422177534706 Trimmed Mean ( 22 / 24 ) 7129.07142857143 219.012097275092 32.551039496311 Trimmed Mean ( 23 / 24 ) 7132.38461538462 210.015084270873 33.9612968284955 Trimmed Mean ( 24 / 24 ) 7138.125 196.388943360555 36.3468781788542 Median 7266 Midrange 46563 Midmean - Weighted Average at Xnp 6968.21621621622 Midmean - Weighted Average at X(n+1)p 7050.69444444444 Midmean - Empirical Distribution Function 6968.21621621622 Midmean - Empirical Distribution Function - Averaging 7050.69444444444 Midmean - Empirical Distribution Function - Interpolation 7050.69444444444 Midmean - Closest Observation 6968.21621621622 Midmean - True Basic - Statistics Graphics Toolkit 7050.69444444444 Midmean - MS Excel (old versions) 7041.05263157895 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Apr/12/t13026335229yol17loj6ibi5l/17s7z1302633716.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t13026335229yol17loj6ibi5l/17s7z1302633716.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t13026335229yol17loj6ibi5l/2glf61302633716.png (open in new window) http://www.freestatistics.org/blog/date/2011/Apr/12/t13026335229yol17loj6ibi5l/2glf61302633716.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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