Standard deviation

The applet below is designed to allow one to interactively investigate the standard deviation as a measure of spread for a data set. Points can be added to the plot by clicking the mouse above the horizontal axis. The mean of the points is shown as a green arrow. Recall that standard deviation is directly proportional to the square root of the sum of squared deviations from the mean. A numeric value for the standard deviation is shown above the plot. Points on the plot can be removed by clicking on the point and then dragging the point into the trash can. All of the points on the plot can be removed by simply clicking inside the trash can. The range of values for the horizontal axis can be specified by inputing lower and upper limits and then clicking the Update button. Things to try with the applet:

  • Create a set of points that are very close together and then add a point that is far away from the set. What is the impact of the new point on the standard deviation?
  • Try to create a data set with at least 10 points that has a mean of approximately 5 and a standard deviation of approximately 1. Try to create a data set with at least 10 points that has a mean of approximately 5 and a standard deviation of approximately 2. What did you do differently to create the data set with a larger standard deviation?