Sampling distributions

The applet below allows for the investigation of sampling distributions by repeatedly taking samples from a population. The top plot displays the distribution of a population. Several options are available for the population distribution: Uniform, Bell shaped, Skewed, Binary (with several values for p) and Custom. Each distribution can be changed interactively by clicking and dragging the mouse on the plot. The Custom option provides a blank plot on which a distribution can be constructed. When the Sample button is clicked, N random samples of size n will be repeatedly selected from the population. The sample statistics specified in the bottom two plots will be updated for each sample. If N is set to 1 and n is less than or equal to 50, the display will show in an animated fashion the points selected from the population dropping into the second plot and the corresponding summary statistic values dropping into the third and fourth plots. To stop an animation click the Reset button. Summary statistics for each plot are shown in the panel to the left of the plot. Things to try with the applet:

  • Compare the sampling distributions of the mean and the median in terms of center and spread for bell shaped and skewed distributions.
  • For a binary population distribution, compare the shape of the sampling distribution for the count of 1s when the sample size is 3 to the sampling distribution when the sample size is 50.