*Unverified author*

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

Title produced by software: Central Tendency

Date of computation: Fri, 27 Nov 2009 02:18:20 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/27/t1259313584qv9yl93j8in0can.htm/, Retrieved Fri, 27 Nov 2009 10:19:46 +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/2009/Nov/27/t1259313584qv9yl93j8in0can.htm/}, year = {2009}, } @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 = {2009}, 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:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

929 978 927 982 1002 983 982 897 872 927 1019 928 867 975 986 856 834 798 907 938 876 987 943 912 1022 1044 1007 964 986 978 914 927 847 823 937 916 1024 1033 1196 938 917 816 1099 1138 829 729 914 967 937 944 865 976 954 918 889 892 928 927 838 829 1007 928 967 927 926 927 936 827 929 867 927 983

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 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 934.972222222222 8.94483992457661 104.526434246556 Geometric Mean 931.970687223687 Harmonic Mean 928.987673666957 Quadratic Mean 938.005212020582 Winsorized Mean ( 1 / 24 ) 935.125 8.37351667428463 111.676495834994 Winsorized Mean ( 2 / 24 ) 934.541666666667 7.9189936659118 118.012680157771 Winsorized Mean ( 3 / 24 ) 932.541666666667 7.27102040129557 128.254579852438 Winsorized Mean ( 4 / 24 ) 932.152777777778 7.09707062610468 131.343314289293 Winsorized Mean ( 5 / 24 ) 931.666666666667 6.94703863908177 134.109901365081 Winsorized Mean ( 6 / 24 ) 931.5 6.91607978730821 134.686126916784 Winsorized Mean ( 7 / 24 ) 931.694444444444 6.7624758319346 137.774162540394 Winsorized Mean ( 8 / 24 ) 930.805555555556 6.43957829204502 144.544489303811 Winsorized Mean ( 9 / 24 ) 931.930555555556 6.2170674262223 149.898737083800 Winsorized Mean ( 10 / 24 ) 932.486111111111 5.86480421032887 158.996972050465 Winsorized Mean ( 11 / 24 ) 931.569444444444 5.2528711274621 177.344812358747 Winsorized Mean ( 12 / 24 ) 931.736111111111 5.16901328867927 180.254152789996 Winsorized Mean ( 13 / 24 ) 931.736111111111 5.16901328867927 180.254152789996 Winsorized Mean ( 14 / 24 ) 932.125 4.91376884046527 189.696550705413 Winsorized Mean ( 15 / 24 ) 932.958333333333 4.77188712043159 195.511400372135 Winsorized Mean ( 16 / 24 ) 935.625 4.27252557221817 218.986401411812 Winsorized Mean ( 17 / 24 ) 936.333333333333 4.16497618289335 224.811209528424 Winsorized Mean ( 18 / 24 ) 936.583333333333 3.82662967625380 244.754108071997 Winsorized Mean ( 19 / 24 ) 939.222222222222 3.46038514404934 271.421296510118 Winsorized Mean ( 20 / 24 ) 940.055555555556 3.19537817203529 294.192269253936 Winsorized Mean ( 21 / 24 ) 940.347222222222 3.07789837718446 305.516007023732 Winsorized Mean ( 22 / 24 ) 937.902777777778 2.69789227722746 347.642782365511 Winsorized Mean ( 23 / 24 ) 938.541666666667 2.61929292415629 358.318711897786 Winsorized Mean ( 24 / 24 ) 937.875 2.42653703124561 386.507598245291 Trimmed Mean ( 1 / 24 ) 934.185714285714 7.8601727641875 118.850531955487 Trimmed Mean ( 2 / 24 ) 933.191176470588 7.23150534825343 129.045216940339 Trimmed Mean ( 3 / 24 ) 932.454545454545 6.77635343548447 137.604178166347 Trimmed Mean ( 4 / 24 ) 932.421875 6.54217107122313 142.524838444140 Trimmed Mean ( 5 / 24 ) 932.5 6.3257989548128 147.412209376419 Trimmed Mean ( 6 / 24 ) 932.7 6.11224112134197 152.595419827813 Trimmed Mean ( 7 / 24 ) 932.948275862069 5.85984842822839 159.210308472796 Trimmed Mean ( 8 / 24 ) 933.178571428571 5.59226664212826 166.869470135535 Trimmed Mean ( 9 / 24 ) 933.574074074074 5.34632862865974 174.619657510300 Trimmed Mean ( 10 / 24 ) 933.826923076923 5.09766760863725 183.187095505146 Trimmed Mean ( 11 / 24 ) 934.02 4.87429660022231 191.621494670103 Trimmed Mean ( 12 / 24 ) 934.354166666667 4.73747785632031 197.22607577366 Trimmed Mean ( 13 / 24 ) 934.695652173913 4.58013665230998 204.075931162993 Trimmed Mean ( 14 / 24 ) 935.068181818182 4.37431936442455 213.763126081488 Trimmed Mean ( 15 / 24 ) 935.428571428571 4.16850963057969 224.403600885645 Trimmed Mean ( 16 / 24 ) 935.725 3.93244027779972 237.950212564590 Trimmed Mean ( 17 / 24 ) 935.736842105263 3.75260634140093 249.356515705277 Trimmed Mean ( 18 / 24 ) 935.666666666667 3.53508492073746 264.680110279069 Trimmed Mean ( 19 / 24 ) 935.558823529412 3.33222562070632 280.760947792937 Trimmed Mean ( 20 / 24 ) 935.125 3.14878048590039 296.980054401157 Trimmed Mean ( 21 / 24 ) 934.533333333333 2.95939312407717 315.785464840785 Trimmed Mean ( 22 / 24 ) 933.821428571429 2.70852737836169 344.770902458542 Trimmed Mean ( 23 / 24 ) 933.307692307692 2.49477560623071 374.104865374166 Trimmed Mean ( 24 / 24 ) 932.625 2.17013031399272 429.755298097333 Median 928 Midrange 962.5 Midmean - Weighted Average at Xnp 934.486486486486 Midmean - Weighted Average at X(n+1)p 935.666666666667 Midmean - Empirical Distribution Function 934.486486486486 Midmean - Empirical Distribution Function - Averaging 935.666666666667 Midmean - Empirical Distribution Function - Interpolation 935.666666666667 Midmean - Closest Observation 934.486486486486 Midmean - True Basic - Statistics Graphics Toolkit 935.666666666667 Midmean - MS Excel (old versions) 936.923076923077 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259313584qv9yl93j8in0can/1360q1259313498.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259313584qv9yl93j8in0can/1360q1259313498.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259313584qv9yl93j8in0can/2iz181259313498.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259313584qv9yl93j8in0can/2iz181259313498.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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