Instructions

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This Java applet shows how the relationship between the mean and the median and illustrates several aspects of these measures of central tendency.

The applet begins by showing a histogram of 9 numbers. As can be seen in the histogram, the numbers are: 3, 4, 4, 5, 5, 5, 6, 6, and 7. The mean and median of the numbers are both 5.0. The mean is shown on the histogram as a small blue line; the median is shown as a small purple line. The standard deviation is 1.15. Note that the standard deviation is calculated using N rather than N-1 since the numers are considered to be the entire populaiton of interest. A red line extends one sd in each direction from the mean. You can change the values of the data set by "painting" the histogram with the mouse.

Below the histogram are shown:
  1. X: the nine numbers,
  2. X-M: the deviations from the mean,
  3. (X-M)^2: the squared deviations from the mean,
  4. X-Med: the deviations from the median, and
  5. (X-Med)^2: the squared deviation from the median.

The means of these 5 quantities are displayed at the bottom of the screen.

Credits

The simulations were developed as part of a grant from NSF to David Lane of Rice University. Partial support for this work was provided by the National Science Foundation's Division of Undergraduate Education through grant DUE 9751307. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.