Question

test scores
67 80 86 85 82 68
81 70 69 74 70 83
80 83 87 71 87 70
(a) complete the grouped frequency distribution for the data. (note that the class width is 6.)
test scores frequency
66 to 71
72 to 77
78 to 83
84 to 89
(b) construct a histogram for the data.
frequency
8
7
6
5
4
3
2
1
0
66 to 71 72 to 77 78 to 83 84 to 89 test scores

Explanation:

Step1: Count scores in 66 - 71

Count the number of scores in the range 66 - 71 from the data set {67, 80, 86, 85, 82, 68, 81, 70, 69, 74, 70, 83, 80, 83, 87, 71, 87, 70}. The scores in this range are 67, 68, 70, 69, 70, 70, 71. So the frequency is 7.

Step2: Count scores in 72 - 77

There are no scores in the range 72 - 77 in the given data - set. So the frequency is 0.

Step3: Count scores in 78 - 83

The scores in the range 78 - 83 are 80, 82, 81, 83, 80, 83. So the frequency is 6.

Step4: Count scores in 84 - 89

The scores in the range 84 - 89 are 86, 85, 87, 87. So the frequency is 4.

Answer:

Test scores	Frequency
72 to 77	0
78 to 83	6
84 to 89	4

To construct the histogram:

• For the class 66 - 71, draw a bar with height 7.
• For the class 72 - 77, draw a bar with height 0 (a very short or non - existent bar).
• For the class 78 - 83, draw a bar with height 6.
• For the class 84 - 89, draw a bar with height 4. The x - axis represents the test scores intervals and the y - axis represents the frequency.