Answer: Choice A
Interval 60-70 70-80 80-90 90-100
Frequency 8 0 10 2
======================================================
Reason:
The original data set is
82, 83, 89, 67, 65, 88, 66, 69, 83, 81, 94, 68, 82, 69, 86, 83, 88, 62, 64, 93
which sorts to
62, 64, 65, 66, 67, 68, 69, 69, 81, 82, 82, 83, 83, 83, 86, 88, 88, 89, 93, 94
We can eliminate choice B since the interval 77-84 should have 6 items in it (and not 5). Those 6 items are 81, 82, 82, 83, 83, 83
Choice C is eliminated because the spacing from 50 to 70 is different from 70 to 80. The spacing must be consistent.
-----------------
In contrast, choices A and D are both correct. Their intervals are spaced out consistently. Choice A has a class width of 10, while D has a class width of 15. The larger the width, the fewer histogram bars because more of the data clumps together.
Also, notice the frequencies are correct for each bin. For example, we have 8 values in the range [tex]60 \le x < 70[/tex] and those values are: 62, 64, 65, 66, 67, 68, 69, 69
This helps justify the "8" in the frequency portion of frequency table A. The other items are going to follow the same idea.
Since choices A and D are both valid, it's simply a matter of preference of which is better.
I'd say choice A is a better one to go with since we're involving more class intervals. Also, we can see that there aren't any data values from 70 to 80. Unfortunately table D does not show this.
Therefore, I'd go with choice A as the final answer.
The frequency table and histogram are shown below for choice A.
