Elisa Somers

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

Title produced by software: Central Tendency

Date of computation: Mon, 21 Apr 2008 14:14:13 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/21/t12088088920zb6ff9snndwxac.htm/, Retrieved Mon, 21 Apr 2008 22:14:52 +0200

User-defined keywords:

Dataseries X:

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4,07 4,07 4,08 4,09 4,08 4,09 4,12 4,14 4,14 4,14 4,14 4,14 4,23 4,29 4,32 4,33 4,35 4,35 4,35 4,35 4,36 4,36 4,38 4,4 4,4 4,4 4,43 4,44 4,46 4,47 4,49 4,49 4,57 4,62 4,64 4,66 4,67 4,68 4,72 4,74 4,75 4,76 4,77 4,76 4,77 4,77 4,78 4,81 4,81 4,85 4,92 4,96 4,95 4,96 4,97 5 5 5,01 5,01 5,02 5,04 5,04 5,19 5,22 5,22 5,22 5,24 5,28 5,34 5,36 5,38 5,39 5,41 5,44 5,51 5,55 5,56 5,57 5,58 5,58 5,59 5,61 5,63 5,64 5,64

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 4.78952941176471 0.0528699863711864 90.5907063818528 Geometric Mean 4.76523240385374 Harmonic Mean 4.74123000294116 Quadratic Mean 4.81397878731366 Winsorized Mean ( 1 / 28 ) 4.78952941176471 0.0528699863711864 90.5907063818528 Winsorized Mean ( 2 / 28 ) 4.78952941176471 0.0527872708433683 90.7326583709227 Winsorized Mean ( 3 / 28 ) 4.78882352941176 0.0526548434849895 90.947445903565 Winsorized Mean ( 4 / 28 ) 4.78835294117647 0.0524067391102397 91.3690304428974 Winsorized Mean ( 5 / 28 ) 4.78776470588235 0.052300140181855 91.544012869461 Winsorized Mean ( 6 / 28 ) 4.78988235294118 0.0519694734027623 92.1672289387981 Winsorized Mean ( 7 / 28 ) 4.79070588235294 0.0515707852271401 92.895732753585 Winsorized Mean ( 8 / 28 ) 4.78976470588235 0.0514021810321548 93.1821298183067 Winsorized Mean ( 9 / 28 ) 4.78870588235294 0.0512140529764746 93.5037475856999 Winsorized Mean ( 10 / 28 ) 4.784 0.0503940216987014 94.9318954657528 Winsorized Mean ( 11 / 28 ) 4.77494117647059 0.0488829343977391 97.681148550105 Winsorized Mean ( 12 / 28 ) 4.78341176470588 0.0463105317232737 103.289933989291 Winsorized Mean ( 13 / 28 ) 4.78952941176471 0.044552837696881 107.502230146387 Winsorized Mean ( 14 / 28 ) 4.79282352941176 0.043640244245179 109.825772341804 Winsorized Mean ( 15 / 28 ) 4.79105882352941 0.0428517813969395 111.805359482012 Winsorized Mean ( 16 / 28 ) 4.79105882352941 0.0417820889377964 114.667766627517 Winsorized Mean ( 17 / 28 ) 4.77905882352941 0.0399469618710688 119.635101136204 Winsorized Mean ( 18 / 28 ) 4.77058823529412 0.0387028299478388 123.26200026519 Winsorized Mean ( 19 / 28 ) 4.76611764705882 0.0380627132946596 125.217495930001 Winsorized Mean ( 20 / 28 ) 4.76847058823529 0.0377580777275453 126.290078182571 Winsorized Mean ( 21 / 28 ) 4.76847058823529 0.0377580777275453 126.290078182571 Winsorized Mean ( 22 / 28 ) 4.76588235294118 0.0359969241284975 132.396933024847 Winsorized Mean ( 23 / 28 ) 4.73070588235294 0.0299204305359 158.109552490457 Winsorized Mean ( 24 / 28 ) 4.73070588235294 0.0299204305359 158.109552490457 Winsorized Mean ( 25 / 28 ) 4.72482352941176 0.0292044909273881 161.784142759386 Winsorized Mean ( 26 / 28 ) 4.73094117647059 0.0276338725333241 171.200803317214 Winsorized Mean ( 27 / 28 ) 4.73411764705882 0.0272236787883053 173.897057920493 Winsorized Mean ( 28 / 28 ) 4.73741176470588 0.0259843483061573 182.317898024146 Trimmed Mean ( 1 / 28 ) 4.78795180722892 0.0524407951677861 91.3020443704124 Trimmed Mean ( 2 / 28 ) 4.7862962962963 0.051930462896843 92.1674105968208 Trimmed Mean ( 3 / 28 ) 4.78455696202532 0.0513753703123151 93.129391242138 Trimmed Mean ( 4 / 28 ) 4.78298701298701 0.050773600163033 94.2022428511852 Trimmed Mean ( 5 / 28 ) 4.78146666666667 0.0501431081135912 95.356407820493 Trimmed Mean ( 6 / 28 ) 4.78 0.0494232335261116 96.7156468520944 Trimmed Mean ( 7 / 28 ) 4.77802816901408 0.048649206163042 98.2138979411318 Trimmed Mean ( 8 / 28 ) 4.77579710144928 0.047816966760679 99.8766217303547 Trimmed Mean ( 9 / 28 ) 4.77358208955224 0.0468562577148853 101.877152003878 Trimmed Mean ( 10 / 28 ) 4.77138461538462 0.0457416853116272 104.311517664430 Trimmed Mean ( 11 / 28 ) 4.76968253968254 0.0445711018028789 107.012892810616 Trimmed Mean ( 12 / 28 ) 4.76901639344262 0.0434626307158801 109.726823132686 Trimmed Mean ( 13 / 28 ) 4.76728813559322 0.0426070560119235 111.889639459227 Trimmed Mean ( 14 / 28 ) 4.76473684210526 0.0418712560613813 113.794934527887 Trimmed Mean ( 15 / 28 ) 4.76163636363636 0.041109825507906 115.827209305976 Trimmed Mean ( 16 / 28 ) 4.75849056603774 0.0402931891322966 118.096647808491 Trimmed Mean ( 17 / 28 ) 4.75509803921569 0.0394515066428862 120.530201349689 Trimmed Mean ( 18 / 28 ) 4.75265306122449 0.0387350755878915 122.696367287074 Trimmed Mean ( 19 / 28 ) 4.75085106382979 0.0380440245821158 124.877720378278 Trimmed Mean ( 20 / 28 ) 4.74933333333333 0.0372561431447245 127.477858212112 Trimmed Mean ( 21 / 28 ) 4.74744186046512 0.0362639105677102 130.913676604208 Trimmed Mean ( 22 / 28 ) 4.74536585365854 0.0349339054693072 135.838400828897 Trimmed Mean ( 23 / 28 ) 4.74333333333333 0.0335693399517375 141.299570982116 Trimmed Mean ( 24 / 28 ) 4.74459459459459 0.0331540099771770 143.107714507558 Trimmed Mean ( 25 / 28 ) 4.746 0.0325142502695085 145.966767207016 Trimmed Mean ( 26 / 28 ) 4.74818181818182 0.0317287704778023 149.64909596808 Trimmed Mean ( 27 / 28 ) 4.75 0.0309908068227802 153.271259672673 Trimmed Mean ( 28 / 28 ) 4.75172413793103 0.0299715339722472 158.541239241575 Median 4.76 Midrange 4.855 Midmean - Weighted Average at Xnp 4.72744186046511 Midmean - Weighted Average at X(n+1)p 4.7595652173913 Midmean - Empirical Distribution Function 4.7595652173913 Midmean - Empirical Distribution Function - Averaging 4.7595652173913 Midmean - Empirical Distribution Function - Interpolation 4.7595652173913 Midmean - Closest Observation 4.7595652173913 Midmean - True Basic - Statistics Graphics Toolkit 4.7595652173913 Midmean - MS Excel (old versions) 4.7595652173913 Number of observations 85

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t12088088920zb6ff9snndwxac/1hhia1208808848.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t12088088920zb6ff9snndwxac/1hhia1208808848.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t12088088920zb6ff9snndwxac/24vq81208808848.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/21/t12088088920zb6ff9snndwxac/24vq81208808848.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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