Question

descriptive statistics
constructing a frequency distribution and a histogram
number of miles
10 6 19 11 9 8 7 6
3 13 14 3 9 13 8 14
(a) complete the grouped frequency distribution for the data. (note that the class width is 4.)
number of miles frequency
0.5 - 4.5
4.5 - 8.5
8.5 - 12.5
12.5 - 16.5
16.5 - 20.5
(b) construct a histogram for the data.
frequency
6
5
4
3
2
1
0
0.5 4.5 8.5 12.5 16.5 20.5
number of miles

Explanation:

Step1: Count data in 0.5 - 4.5

The values in the range 0.5 - 4.5 are 3, 3. So the frequency is 2.

Step2: Count data in 4.5 - 8.5

The values in the range 4.5 - 8.5 are 6, 6, 7, 8, 8. So the frequency is 5.

Step3: Count data in 8.5 - 12.5

The values in the range 8.5 - 12.5 are 9, 9, 10, 11. So the frequency is 4.

Step4: Count data in 12.5 - 16.5

The values in the range 12.5 - 16.5 are 13, 13, 14, 14. So the frequency is 4.

Step5: Count data in 16.5 - 20.5

The value in the range 16.5 - 20.5 is 19. So the frequency is 1.

Answer:

Number of miles	Frequency
4.5 - 8.5	5
8.5 - 12.5	4
12.5 - 16.5	4
16.5 - 20.5	1

For part (b), to construct the histogram:

• Draw bars with bases on the intervals 0.5 - 4.5, 4.5 - 8.5, 8.5 - 12.5, 12.5 - 16.5, 16.5 - 20.5.
• The heights of the bars should be 2, 5, 4, 4, 1 respectively corresponding to the frequencies calculated above.