Chapter 13.2, Problem 1EE

This exercise makes use of the geometric procedure just explained to calculate the variance and standard deviation of the population 2, 5, 7, 11, 15. The following figure shows the given set of data labeled on a number line, along with its mean, which is 8.

a. Draw the tile associated with each of the five data values 2, 5, 7, 11, and 15.

b. Label each tile with its area.

c Find the sum of the areas of all the tiles.

d. Find the average (mean) of the areas of all 5 tiles.

e. To the right of the above number line, draw a tile whose area is the average found in part d.

f. What is the variance of the data? What geometric figure represents the variance?

g. What is the standard deviation of the data? What geometric figure represents the standard deviation?