::Free Statistics and Forecasting Software::

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 arithmetic mean and the median of a univariate dataset. It displays the Kernel Density Plot and the Harrell-Davis quantiles with an indication of the arithmetic mean and the median.

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

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Source code of R module

library(Hmisc) m <- mean(x) e <- median(x) bitmap(file="test1.png") op <- par(mfrow=c(2,1)) mydensity1 <- density(x,kernel='gaussian',na.rm=TRUE) plot(mydensity1,main="Density Plot - Gaussian Kernel",xlab="Median (0 -> full line) | Mean (0 -> dashed line)",ylab="density") abline(v=e,lty=1) abline(v=m,lty=5) grid() myseq <- seq(0.01, 0.99, 0.01) hd <- hdquantile(x, probs = myseq, se = TRUE, na.rm = FALSE, names = TRUE, weights=FALSE) plot(myseq,hd,col=2,main="Harrell-Davis Quantiles",xlab="quantiles",ylab="Median (0 -> full) | Mean (0 -> dashed)") abline(h=m,lty=5) abline(h=e,lty=1) grid() par(op) dev.off() load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Median versus Mean",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"mean",header=TRUE) a<-table.element(a,mean(x)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"median",header=TRUE) a<-table.element(a,median(x)) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab")

Cite this software as:

Wessa P., (2012), Mean versus Median (v1.0.2) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_meanversusmedian.wasp/

The R code is based on :

Harrell FE, Davis CE (1982): A new distribution-free quantile estimator. Biometrika 69:635-640.

Hutson AD, Ernst MD (2000): The exact bootstrap mean and variance of an L-estimator. J Roy Statist Soc B 62:89-94.

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988), The New S Language, Wadsworth & Brooks/Cole (for S version)

Sheather, S. J. and Jones M. C. (1991), A reliable data-based bandwidth selection method for kernel density estimation., J. Roy. Statist. Soc. B, 683-690.

Silverman, B. W. (1986), Density Estimation, London: Chapman and Hall.

Venables, W. N. and Ripley, B. D. (2002), Modern Applied Statistics with S, New York: Springer.

To cite Wessa.net in publications use:
Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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Software Version : 1.2.1
Algorithms & Software : Patrick Wessa, PhD
Server : wessa.net

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