Question

constructing a frequency distribution and a histogram
number of miles
21 16 9 24 15 6
22 9 12 10 17 18
13 18 11 19 9 24
(a) complete the grouped frequency distribution for the data. (note that the class width is 6.)
number of miles frequency
1.5 - 7.5
7.5 - 13.5
13.5 - 19.5
19.5 - 25.5
(b) construct a histogram for the data.
frequency

Explanation:

Step1: Count data in 1.5 - 7.5

The numbers in the range 1.5 - 7.5 are 6. So the frequency is 1.

Step2: Count data in 7.5 - 13.5

The numbers in the range 7.5 - 13.5 are 9, 9, 12, 10, 11, 9. So the frequency is 6.

Step3: Count data in 13.5 - 19.5

The numbers in the range 13.5 - 19.5 are 16, 15, 17, 18, 13, 18, 19. So the frequency is 7.

Step4: Count data in 19.5 - 25.5

The numbers in the range 19.5 - 25.5 are 21, 24, 22, 24. So the frequency is 4.

Answer:

Number of miles	Frequency
7.5 - 13.5	6
13.5 - 19.5	7
19.5 - 25.5	4

For constructing the histogram:

• On the x - axis, label the intervals 1.5 - 7.5, 7.5 - 13.5, 13.5 - 19.5, 19.5 - 25.5.
• On the y - axis, label the frequencies from 0 to 8.
• Draw bars with heights corresponding to the frequencies calculated above for each interval.