Positive skew - response rate

Learning Objectives

• Use of statistics to compare distributions.
• Identify positive skew.

Instructions

1. Open the model.
2. This model shows a frequency distribution of the response rates of 80 people.
   • The response rates were measured by dividing the group into pairs with one person holding a ruler upright in between the hands of the other person. When the first person dropped the ruler, the second person had to try to catch it as quickly as they could; and the response rate was recorded as the distance that the ruler fell before it was caught.
3. Discuss the shape of the distribution shown on the graph.
   • The distribution shows positive skew because the tail to the left of the peak is shorter than the tail to the right. This happened because some long distances are measured, but the shortest distance is limited by zero.
4. The median and mean values of the distribution are also shown on the model.
   • Check the boxes to display the positions of these values on the graph.
5. Discuss the relationship between median, mean and skew.
   • As is shown in this case, the median is often smaller than the mean in distributions that show positive skew.
6. Try the activity with the class and find out if the data you collect shows a similar distribution.
   • To enter class data, click on a cell in the Frequency column of the data set and change the number to the number in that group in the class.

Discussion Questions

• Can you think of some more examples of data sets that would show positive skew?
• Are there any circumstances in which the median would not be smaller than the mean for distributions showing positive skew?