# ::Free Statistics and Forecasting Software::

v1.1.23-r7
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### :: Central Tendency - Free Statistics Software (Calculator) ::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the following statistics: arithmetic mean, geometric mean, harmonic mean, quadratic mean, winsorized mean, trimmed mean, median, midrange, and midmean.

Enter (or paste) your data delimited by hard returns.

 Send output to: Browser Blue - Charts White Browser Black/White CSV MS Excel MS Word Data (click to load default data) 101 100.88 100.55 100.83 101.51 102.16 102.39 102.54 102.85 103.47 103.57 103.69 103.5 103.47 103.45 103.48 103.93 103.89 104.4 104.79 104.77 105.13 105.26 104.96 104.75 105.01 105.15 105.2 105.77 105.78 106.26 106.13 106.12 106.57 106.44 106.54 107.1 108.1 108.4 108.84 109.62 110.42 110.67 111.66 112.28 112.87 112.18 112.36 112.16 111.49 111.25 111.36 111.74 111.1 111.33 111.25 111.04 110.97 111.31 111.02 Sample Range:(leave blank to include all observations) From: To: Chart options Width: Height: Title: Y-axis minimum Y-axis maximum

Click here to edit the underlying code of this R Module.

 Source code of R 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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 Cite this software as: Wessa, P., (2012), Central Tendency (v1.0.4) in Free Statistics Software (v1.1.23-r7), Office for Research Development and Education, URL http://www.wessa.net/rwasp_centraltendency.wasp/ The R code is based on : Borghers, E, and P. Wessa, Statistics - Econometrics - Forecasting, Office for Research Development and Education, http://www.xycoon.com/
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 To cite Wessa.net in publications use:Wessa, P. (2013), Free Statistics Software, Office for Research Development and Education, version 1.1.23-r7, URL http://www.wessa.net/ © All rights reserved. Academic license for non-commercial use only. The free use of the scientific content, services, and applications in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission. Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. We make no warranties or representations as to the accuracy or completeness of such information (or software), and it assumes no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site. Software Version : 1.1.23-r7Algorithms & Software : Patrick Wessa, PhDServer : www.wessa.net
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