Question

fifteen cyclists were each asked the number of miles they biked last week. their responses are given below.
number of miles
2 3 17 9 18
15 2 10 19 12
7 13 12 2 8
(a) complete the grouped frequency distribution for the data. (note that the class width is 5.)
number of miles frequency
1 to 5
6 to 10
11 to 15
16 to 20
(b) construct a histogram for the data.
frequency
↑
5
4
3
2
1
0
1 to 5 6 to 10 11 to 15 16 to 20
number of miles

Explanation:

Step1: Count data in 1 - 5 range

The numbers 2, 3, 2, 2 in the data set fall in the 1 - 5 range. So the frequency is 4.

Step2: Count data in 6 - 10 range

The numbers 9, 10, 7, 8 fall in the 6 - 10 range. So the frequency is 4.

Step3: Count data in 11 - 15 range

The numbers 15, 12, 13, 12 fall in the 11 - 15 range. So the frequency is 4.

Step4: Count data in 16 - 20 range

The numbers 17, 18, 19 fall in the 16 - 20 range. So the frequency is 3.

Answer:

Number of miles	Frequency
6 to 10	4
11 to 15	4
16 to 20	3

For part (b), to construct the histogram:

• Draw a bar for the interval 1 - 5 with height 4.
• Draw a bar for the interval 6 - 10 with height 4.
• Draw a bar for the interval 11 - 15 with height 4.
• Draw a bar for the interval 16 - 20 with height 3. The x - axis is labeled "Number of miles" and the y - axis is labeled "Frequency".