Question

(a) complete the grouped frequency distribution for the data. (note that the class width is 6.)
test scores frequency
66 to 71 4
72 to 77 5
78 to 83 4
84 to 89
(b) construct a histogram for the data.

Explanation:

Step1: Assume total number of scores

Let's assume we have a total of 20 test - scores for simplicity (this is an assumption as the total is not given, but we need to have a total to find the missing frequency).

Step2: Calculate sum of known frequencies

Sum of known frequencies = 4 + 5+4=13.

Step3: Find missing frequency

Let the missing frequency be $x$. Then $13 + x=20$ (based on our assumed total), so $x = 20 - 13=7$.

Answer:

7

For part (b), to construct a histogram:

1. On the x - axis, label the test - score intervals: 66 to 71, 72 to 77, 78 to 83, 84 to 89.
2. On the y - axis, label the frequency from 0 to 8.
3. For the interval 66 to 71, draw a bar with height 4.
4. For the interval 72 to 77, draw a bar with height 5.
5. For the interval 78 to 83, draw a bar with height 4.
6. For the interval 84 to 89, draw a bar with height 7.