CMA Foundation · Fundamentals of Business Mathematics and Statistics · Statistical Representation of Data
A histogram for the ages of employees in a firm has bars with these widths and heights (frequency densities per year): 20-30 height 2; 30-40 height 5; 40-50 height 4; 50-60 height 1. A histogram with such heights was drawn using one-year units. If the total number of employees is represented by the areas, how many employees are aged 35 to 50?
The number of employees aged 35 to 50 is 65. Area equals frequency, so 35-40 contributes 5 x 5 = 25 and 40-50 contributes 4 x 10 = 40. Adding gives 65. Counting the whole 30-40 bar would wrongly give 90.
- A65Correct
- B45
- C90
- D70
Explanation
Density times width gives frequency. For 35-40: 5 x 5 = 25. For 40-50: 4 x 10 = 40. Total = 25 + 40 = 65. Taking the full 30-40 class would give 50+40 = 90, which ignores the partial class.
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