Question

fifteen cyclists were each asked the number of miles they biked last week. their responses are given below. number of miles 11 15 10 3 18 14 9 17 14 20 17 12 13 9 14 (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 8 7 6 5 4 3 2 1 0 1 to 5 6 to 10 11 to 15 16 to 20 number of miles

Explanation:

Step1: Count 1 to 5

Check data for values in 1 - 5. Only 3. So frequency = 1.

Step2: Count 6 to 10

Values: 10, 9, 9. Wait, data: 10, 9, 9? Wait original data: 11,15,10,3,18,14,9,17,14,20,17,12,13,9,14. So 10,9,9? Wait 10,9,9? Wait 10 is 10 (6 - 10? 6 to 10: 10 is included? 6 ≤ x ≤10. So 10,9,9. Wait data points: 10, 9, 9? Wait original data: 10, 9, 9? Wait the data is: 11,15,10,3,18,14,9,17,14,20,17,12,13,9,14. So numbers in 6 - 10: 10, 9, 9. Wait 10, 9, 9: that's three? Wait 10 is 10 (6 ≤10 ≤10), 9 is 9, another 9. So 10,9,9: three? Wait no, let's list all:

Data: 11,15,10,3,18,14,9,17,14,20,17,12,13,9,14.

Numbers between 6 and 10 (inclusive? The class is 6 to 10, so 6 ≤ x ≤10): 10, 9, 9. Wait 10, 9, 9: three values? Wait 10 is 10, 9, 9: that's three? Wait no, 10, 9, 9: three? Wait the data has 10, 9, 9? Wait the data is: 10, 9, 9? Wait the original data: 11,15,10,3,18,14,9,17,14,20,17,12,13,9,14. So 10, 9, 9: three? Wait 10, 9, 9: yes, three. Wait no, 10 is one, 9 is two (the two 9s). So 10, 9, 9: three values. Wait 10, 9, 9: three. So frequency for 6 - 10 is 3? Wait no, wait 10 is 10, 9, 9: three? Wait 10, 9, 9: three. Wait maybe I miscounted. Let's list all data points:

1. 11 (11 - 15)
2. 15 (11 - 15)
3. 10 (6 - 10)
4. 3 (1 - 5)
5. 18 (16 - 20)
6. 14 (11 - 15)
7. 9 (6 - 10)
8. 17 (16 - 20)
9. 14 (11 - 15)
10. 20 (16 - 20)
11. 17 (16 - 20)
12. 12 (11 - 15)
13. 13 (11 - 15)
14. 9 (6 - 10)
15. 14 (11 - 15)

So 6 - 10: points 3 (10), 7 (9), 14 (9). So three values. So frequency 3.

Step3: Count 11 to 15

Values: 11,15,14,14,12,13,14. Let's list:

11 (11 - 15), 15 (11 - 15), 14 (11 - 15), 14 (11 - 15), 12 (11 - 15), 13 (11 - 15), 14 (11 - 15). Let's count: 11,15,14,14,12,13,14: that's 7 values. Let's check:

Data points in 11 - 15:

1. 11
2. 15
3. 14
4. 14
5. 12
6. 13
7. 14

That's 7 values.

Step4: Count 16 to 20

Values: 18,17,20,17. Let's list:

1. 18
2. 17
3. 20
4. 17. So four values.

So frequencies:

1 - 5: 1

6 - 10: 3

11 - 15: 7

16 - 20: 4

Answer:

For part (a), the frequencies are:

1 to 5: 1

6 to 10: 3

11 to 15: 7

16 to 20: 4

(For part (b), the histogram would have bars with heights 1, 3, 7, 4 for the respective classes.)