Example 2.31 from Statistics, 2.5 Measures of the Center of the Data

Measures of the Center of the Data: example 2.31

A frequency table displaying Professor Blount’s last statistic test is shown. Find the best estimate of the class mean.

Grade Interval	Number of Students
50–56.5	1
56.5–62.5	0
62.5–68.5	4
68.5–74.5	4
74.5–80.5	2
80.5–86.5	3
86.5–92.5	4
92.5–98.5	1

Table 2.27

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
- Find the midpoints for all intervals.
Grade Interval Midpoint

50–56.5 53.25

56.5–62.5 59.5

62.5–68.5 65.5

68.5–74.5 71.5

74.5–80.5 77.5

80.5–86.5 83.5

86.5–92.5 89.5

92.5–98.5 95.5

Table 2.28
- Calculate the sum of the product of each interval frequency and midpoint. $\sum^{} f m$
  
  $53.25 (1) + 59.5 (0) + 65.5 (4) + 71.5 (4) + 77.5 (2) + 83.5 (3) + 89.5 (4) + 95.5 (1) = 1460.25$
- $μ = \frac{\sum f m}{\sum f} = \frac{1460.25}{19} = 76.86$

How did it go?