# ::Free Statistics and Forecasting Software::

v1.2.1

### :: 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 Data[reset data] 2 0 0 0 2 0 2 13 8 7 0 35 27 21 17 38 Chart options Width: Height: Title: Y-axis minimum Y-axis maximum

 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,"Arithmetic Mean",header=TRUE) a<-table.element(a,signif(arm,6)) a<-table.element(a, signif(armse,6)) a<-table.element(a,signif(armose,6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, "Geometric Mean",header=TRUE) a<-table.element(a,signif(geo,6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, "Harmonic Mean",header=TRUE) a<-table.element(a,signif(har,6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, "Quadratic Mean",header=TRUE) a<-table.element(a,signif(qua,6)) 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, mylabel,header=TRUE) a<-table.element(a,signif(win[j,1],6)) a<-table.element(a,signif(win[j,2],6)) a<-table.element(a,signif(win[j,1]/win[j,2],6)) 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, mylabel,header=TRUE) a<-table.element(a,signif(tri[j,1],6)) a<-table.element(a,signif(tri[j,2],6)) a<-table.element(a,signif(tri[j,1]/tri[j,2],6)) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a, "Median",header=TRUE) a<-table.element(a,signif(median(x),6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, "Midrange",header=TRUE) a<-table.element(a,signif(midr,6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- "Midmean" mylabel <- paste(mymid,"Weighted Average at Xnp",sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[1],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- "Midmean" mylabel <- paste(mymid,"Weighted Average at X(n+1)p",sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[2],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- "Midmean" mylabel <- paste(mymid,"Empirical Distribution Function",sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[3],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- "Midmean" mylabel <- paste(mymid,"Empirical Distribution Function - Averaging",sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[4],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- "Midmean" mylabel <- paste(mymid,"Empirical Distribution Function - Interpolation",sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[5],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- "Midmean" mylabel <- paste(mymid,"Closest Observation",sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[6],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- "Midmean" mylabel <- paste(mymid,"True Basic - Statistics Graphics Toolkit",sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[7],6)) a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) mymid <- "Midmean" mylabel <- paste(mymid,"MS Excel (old versions)",sep=" - ") a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,signif(midm[8],6)) 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,signif(length(x),6)) 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., (2017), Central Tendency (v1.0.7) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL https://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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