The article “The Distribution of Buying Frequency Rates” (Journal of Marketing Research [1980]:

210–216) reported the results of a 3 1 2-year study of toothpaste purchases. The investigators conducted their research using a national sample of 2071 households and recorded the number of toothpaste purchases for each household participating in the study. The results are given in the following frequency distribution:

Number of Purchases Number of Households

(Frequency)

Number of Purchases Number of Households

(Frequency)

10 to ,20 904 90 to ,100 13 20 to ,30 500 100 to ,110 9 30 to ,40 258 110 to ,120 7 40 to ,50 167 120 to ,130 6 50 to ,60 94 130 to ,140 6 60 to ,70 56 140 to ,150 3 70 to ,80 26 150 to ,160 0 80 to ,90 20 160 to ,170 2

a. Draw a histogram for this frequency distribution.
Would you describe the histogram as positively or negatively skewed?

b. Does the square-root transformation result in a histogram that is more symmetric than that of the original data? (Be careful! This one is a bit tricky because you don’t have the raw data; transforming the endpoints of the class intervals results in class intervals that are not necessarily of equal widths, so the histogram of the transformed values has to be drawn with this in mind.)