Question

84 68 70 85 72 80 87 75 86 73 88 77 76 69 80 69 88 84 (a) complete the grouped frequency - distribution for the data. (note that the class width is 6.) (b) construct a histogram for the data. test scores frequency 65.5 - 71.5 71.5 - 77.5 77.5 - 83.5 83.5 - 89.5

Explanation:

Step1: Count scores in 65.5 - 71.5

The scores in the range 65.5 - 71.5 are 68, 70, 69, 69. So the frequency is 4.

Step2: Count scores in 71.5 - 77.5

The scores in the range 71.5 - 77.5 are 72, 75, 73, 77, 76. So the frequency is 5.

Step3: Count scores in 77.5 - 83.5

The scores in the range 77.5 - 83.5 are 80, 80. So the frequency is 2.

Step4: Count scores in 83.5 - 89.5

The scores in the range 83.5 - 89.5 are 84, 85, 87, 86, 88, 88, 84. So the frequency is 7.

Answer:

Test scores	Frequency
71.5 - 77.5	5
77.5 - 83.5	2
83.5 - 89.5	7

To construct the histogram:

• On the x - axis, label the intervals 65.5 - 71.5, 71.5 - 77.5, 77.5 - 83.5, 83.5 - 89.5.
• On the y - axis, label the frequencies from 0 to 8.
• For the interval 65.5 - 71.5, draw a bar with height 4.
• For the interval 71.5 - 77.5, draw a bar with height 5.
• For the interval 77.5 - 83.5, draw a bar with height 2.
• For the interval 83.5 - 89.5, draw a bar with height 7.