Answer to Question #135977 in Statistics and Probability for Juli

Question

The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean height. Round your answer to one decimal place.



Height (inches) Frequency
70 -71 1
72 -73 8
74 - 75 13
76 - 77 8
78 - 79 15
80 - 81 6
82 - 83 3

Answer 1

$$1+8+13+8+15+6+3=54$$

1. Determine the midpoint for each interval

70-71, the midpoint is 70.5.

72-73, the midpoint is 72.5.

74-75, the midpoint is 74.5.

76-77, the midpoint is 76.5.

78-79, the midpoint is 78.5.

80-81, the midpoint is 80.5.

82-83, the midpoint is 82.5.

2. Multiply each midpoint by the frequency for the class, add the results, and divide the sum by 54.

$$1\cdot 70.5+8\cdot 72.5+13\cdot 74.5+8\cdot 76.5+$$

$$+15\cdot 78.5+6\cdot 80.5+3\cdot 82.5=4139,$$

$$\dfrac{4139}{54}\approx76.7(inches)$$

The mean height is 76.7 inches.