Question

Estimating a Mean: Consider the frequency distribution for 22 test scores (it was a difficult exam).

Score	Frequency
60 − 64	8
65 − 69	4
70 − 74	2
75 − 79	4
80 − 84	4

(a) The class midpoint for the first class is  .

(b) The class midpoint for the second class is  .

(c) Use the frequency table to estimate the mean score. Round your answer to 1 decimal place.

x =

Answer 1

(a) The class midpoint for the first class is 62.

(b) The class midpoint for the second class is 67.

(c) The mean score is 70.2

We need to compute the sample mean for these provided grouped data:

Classes	Frequencies
60-64	8
65-69	4
70-74	2
75-79	4
80-84	4

Now, we need to construct the midpoints based on the lower and upper limits of all the classes provided:

Classes	Lower	Upper	Midpoints (MM)
60-64	60	64	(60 + 64)/2 = 62
65-69	65	69	(65 + 69)/2 = 67
70-74	70	74	(70 + 74)/2 = 72
75-79	75	79	(75 + 79)/2 = 77
80-84	80	84	(80 + 84)/2 = 82

Now, with the midpoints, we need to multiply each midpoint for its corresponding frequency, as shown in the table below:

Classes	Lower	Upper	MM	Frequencies	Mi​⋅fi​
60-64	60	64	62	8	62⋅8=496
65-69	65	69	67	4	67⋅4=268
70-74	70	74	72	2	72⋅2=144
75-79	75	79	77	4	77⋅4=308
80-84	80	84	82	4	82⋅4=328
			Sum =	22	1544

Therefore, the sample mean for these grouped data is