Question

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

Explanation:

Step1: Count for 0 - 3

The values 2, 2 are in the 0 - 3 range. So frequency is 2.

Step2: Count for 4 - 7

The values 5, 7, 7, 6, 5 are in the 4 - 7 range. So frequency is 5.

Step3: Count for 8 - 11

The values 8, 10, 9, 8 are in the 8 - 11 range. So frequency is 4.

Step4: Count for 12 - 15

The values 12, 12, 13, 13 are in the 12 - 15 range. So frequency is 4.

Step5: Count for 16 - 19

The value 18 is in the 16 - 19 range. So frequency is 1.

Answer:

Number of miles	Frequency
4 to 7	5
8 to 11	4
12 to 15	4
16 to 19	1

To construct the histogram:

• For the class 0 - 3, draw a bar with height 2.
• For the class 4 - 7, draw a bar with height 5.
• For the class 8 - 11, draw a bar with height 4.
• For the class 12 - 15, draw a bar with height 4.
• For the class 16 - 19, draw a bar with height 1.

The x - axis is labeled "Number of miles" and the y - axis is labeled "Frequency".