Mean and Median Simulation

We recommend that you begin by answering questions before interacting with the simulation.


General Instructions


This demonstration shows how the relative size of the mean and the median depends on the skew of the distribution.


The demonstration begins by showing a histogram of a symmetric distribution (no skew). The mean and median 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 1.81. A red line extends one sd in each direction from the mean. The standard deviation is calculated assuming the data portrayed in the graph represent the entire population.


You can change the values of the data set by “painting” the histogram with the mouse.


Change the distribution in various ways and note how the skew affects whether the mean is bigger than the median or vice versa.


Step By Step Instructions


Notice that the mean and median are equal and are both 5. Change the distribution so that it has a positive skew such as the one shown below.


Check to see which is bigger, the mean or the median.


Next, make up a distribution with a negative skew such as the following:


Which is bigger, the mean or the median.


Try out other variations to confirm the relationship between skew and the relative size of the mean and median.


Summary


In general, the mean will be higher than the median when a distribution has a positive skew. The mean will be less than the median when a distribution has a negative skew. The mean and median are equal for symmetric distributions.






Questions


Begin by answering the questions, even if you have to guess. The first time you answer the questions you should not check your answers. Once you have answered all the questions, answer them again using the simulation to help you. The second time through click the “Check Answer” button to get feedback.