Question

sixteen cyclists were each asked the number of miles they biked last week. their responses are given below. 9 10 5 18 12 19 2 19 16 3 14 19 5 11 17 3 (a) complete the grouped - frequency distribution for the data. (note that the class width is 4.) 0 to 3 4 to 7 8 to 11 12 to 15 16 to 19 number of miles frequency (b) construct a histogram for the data. 0 to 3 4 to 7 8 to 11 12 to 15 16 to 19 number of miles frequency

Explanation:

Step1: Count data in each class

For the class 0 - 3: Count the number of values in the range 0 to 3. The values are 2, 3, 3. So the frequency is 3.

Step2: Count data in 4 - 7 class

For the class 4 - 7: The values in the range 4 to 7 are 5, 5, 6. So the frequency is 3.

Step3: Count data in 8 - 11 class

For the class 8 - 11: The values in the range 8 to 11 are 9, 10, 11. So the frequency is 3.

Step4: Count data in 12 - 15 class

For the class 12 - 15: The values in the range 12 to 15 are 12, 12, 14. So the frequency is 3.

Step5: Count data in 16 - 19 class

For the class 16 - 19: The values in the range 16 to 19 are 16, 17, 18, 19, 19, 19. So the frequency is 6.

Answer:

Class Interval	Frequency
4 - 7	3
8 - 11	3
12 - 15	3
16 - 19	6

To construct the histogram:

• On the x - axis, label the class intervals (0 - 3, 4 - 7, 8 - 11, 12 - 15, 16 - 19).
• On the y - axis, label the frequency.
• For each class interval, draw a bar with height equal to the frequency of that class. For example, for the class 0 - 3, draw a bar of height 3; for 4 - 7, a bar of height 3; for 8 - 11, a bar of height 3; for 12 - 15, a bar of height 3; and for 16 - 19, a bar of height 6.