Question

in a survey, 18 people reported the number of hours they spent on the internet last week. their responses are given below. complete the grouped relative frequency distribution for the data. (note that we are using a class width of 5.) write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage.
number of hours
10
1
12
17
19
6
13
5
5
9
8
2
16
3
1
11
8
12

number of hours
1 to 5
6 to 10
11 to 15
16 to 20
relative frequency
□
□
□
□

Explanation:

Step1: Count data in each class

- 1 to 5: Values are 1, 2, 3, 1 (wait, let's list all data: 10,1,12,17,19,6,13,5,5,9,8,2,16,3,1,11,8,12. Wait, no, original data: first column (number of hours) is 10,1,12,17,19; second:6,13,5,5,9; third:8,2,16,3,1; fourth:11,8,12. Wait, total 5+5+5+3? No, total people are 18. Let's list all 18 data points: 10,1,12,17,19,6,13,5,5,9,8,2,16,3,1,11,8,12. Now categorize:
- 1 to 5: 1,5,5,2,3,1 → Wait, 1,2,3,1,5,5 → that's 6 values? Wait no, let's check each number:
1: 1 (1-5), 2:2 (1-5), 3:3 (1-5), 1:1 (1-5), 5:5 (1-5), 5:5 (1-5) → that's 6? Wait no, data points: 10,1,12,17,19,6,13,5,5,9,8,2,16,3,1,11,8,12. Let's count each:
1-5: 1,2,3,1,5,5 → numbers: 1,2,3,1,5,5 → 6 values? Wait 1 (1), 2 (2), 3 (3), 1 (1), 5 (5), 5 (5) → 6.
6-10: 10,6,9,8,8,5? No, 6-10: 10 (10), 6 (6), 9 (9), 8 (8), 8 (8), 5? No, 5 is 1-5. Wait 10,6,9,8,8,5? No, 5 is 1-5. Wait 10 (6-10? 10 is ≤10, so 6-10 includes 6,7,8,9,10. So 10,6,9,8,8,5? No, 5 is 1-5. So 10,6,9,8,8, and 5? No, 5 is 1-5. Wait 10 (6-10), 6 (6-10), 9 (6-10), 8 (6-10), 8 (6-10), and what else? 5 is 1-5, 13 is 11-15, etc. Wait 6-10: 10,6,9,8,8, and 5? No, 5 is 1-5. Wait maybe I messed up. Let's do it properly:
- 1 to 5: numbers between 1 and 5 (inclusive): 1,2,3,1,5,5 → that's 6 numbers (1,2,3,1,5,5). Wait 1,2,3,1,5,5: count is 6.
- 6 to 10: numbers between 6 and 10 (inclusive): 10,6,9,8,8,5? No, 5 is 1-5. Wait 10 (10), 6 (6), 9 (9), 8 (8), 8 (8), and 5? No, 5 is 1-5. Wait 10,6,9,8,8, and 5? No, 5 is 1-5. Wait maybe 6-10: 10,6,9,8,8, and 5? No, 5 is 1-5. Wait 6-10: 10,6,9,8,8, and 5? No, 5 is 1-5. Wait 6-10: 10,6,9,8,8, and 5? No, 5 is 1-5. Wait maybe I made a mistake. Let's list all 18 numbers:
1. 10
2. 1
3. 12
4. 17
5. 19
6. 6
7. 13
8. 5
9. 5
10. 9
11. 8
12. 2
13. 16
14. 3
15. 1
16. 11
17. 8
18. 12

Now categorize each:
- 1-5: numbers 2 (1), 12 (no), 15 (1), 14 (3), 12 (no), 8 (no), 9 (no), 11 (no), 17 (no), 19 (no), 6 (no), 7 (13 no), 8 (5: yes), 9 (5: yes), 10 (9: yes), 11 (8: yes), 12 (2: yes), 13 (16: no), 14 (3: yes), 15 (1: yes), 16 (11: no), 17 (8: yes), 18 (12: no). Wait no, each number:
1:1 (1-5) → yes
2:2 (1-5) → yes
3:3 (1-5) → yes
4:17 (16-20) → no
5:19 (16-20) → no
6:6 (6-10) → yes
7:13 (11-15) → yes
8:5 (1-5) → yes
9:5 (1-5) → yes
10:9 (6-10) → yes
11:8 (6-10) → yes
12:2 (1-5) → yes
13:16 (16-20) → yes
14:3 (1-5) → yes
15:1 (1-5) → yes
16:11 (11-15) → yes
17:8 (6-10) → yes
18:12 (11-15) → yes

Now count 1-5: numbers 1,2,8,9,12,14,15 → that's 1 (1), 2 (2), 8 (5), 9 (5), 12 (2), 14 (3), 15 (1) → wait no, each number is a data point:
Data point 1:10 (6-10)
Data point 2:1 (1-5)
Data point 3:12 (11-15)
Data point 4:17 (16-20)
Data point 5:19 (16-20)
Data point 6:6 (6-10)
Data point 7:13 (11-15)
Data point 8:5 (1-5)
Data point 9:5 (1-5)
Data point 10:9 (6-10)
Data point 11:8 (6-10)
Data point 12:2 (1-5)
Data point 13:16 (16-20)
Data point 14:3 (1-5)
Data point 15:1 (1-5)
Data point 16:11 (11-15)
Data point 17:8 (6-10)
Data point 18:12 (11-15)

Now count each class:
- 1-5: data points 2 (1), 8 (5), 9 (5), 12 (2), 14 (3), 15 (1) → that's 6 data points (2,8,9,12,14,15)
- 6-10: data points 1 (10), 6 (6), 10 (9), 11 (8), 17 (8) → that's 5 data points? Wait 1,6,10,11,17 → 5? Wait 1:10, 6:6, 10:9, 11:8, 17:8 → 5? Wait 1 (10), 6 (6), 10 (9), 11 (8), 17 (8) → 5. Wait but 10,6,9,8,8 → 5.
- 11-15: data points 3 (12), 7 (13), 16 (11), 18 (12) → that's 4 data points? Wait 3:12, 7:13, 16:11, 18:12 → 4? Wait 12,13,11,12 → 4.
- 16-20: data points 4 (17), 5 (19), 13 (16) → that's 3 data points? 17,19,16 → 3.

Wait but total should be 18: 6+5+4+3=18? 6+5=11, 11+4=15, 15+3=18. Yes.

Step2: Calculate relative frequency (frequency / total)

- 1-5: frequency=6, relative frequency=6/18=0.333...≈0.33
- 6-10: frequency=5, relative frequency=5/18≈0.28
- 11-15: frequency=4, relative frequency=4/18≈0.22
- 16-20: frequency=3, relative frequency=3/18≈0.17

Wait but let's recheck the data points:

1-5: data points 2 (1), 8 (5), 9 (5), 12 (2), 14 (3), 15 (1) → 6 (correct: 1,5,5,2,3,1 → 6 numbers)
6-10: 1 (10), 6 (6), 10 (9), 11 (8), 17 (8) → 5 (10,6,9,8,8 → 5)
11-15: 3 (12), 7 (13), 16 (11), 18 (12) → 4 (12,13,11,12 → 4)
16-20: 4 (17), 5 (19), 13 (16) → 3 (17,19,16 → 3)

Now calculate each:
- 1-5: 6/18 = 1/3 ≈0.33 (rounded to nearest hundredth: 0.33)
- 6-10: 5/18 ≈0.28 (5÷18≈0.277...≈0.28)
- 11-15: 4/18 ≈0.22 (4÷18≈0.222...≈0.22)
- 16-20: 3/18 = 1/6 ≈0.17 (3÷18≈0.166...≈0.17)

Wait but maybe I made a mistake in counting. Let's re-express the data:

List of numbers:

1,2,3,1,5,5 (1-5: 6 numbers)

10,6,9,8,8 (6-10: 5 numbers)

12,13,11,12 (11-15: 4 numbers)

17,19,16 (16-20: 3 numbers)

Yes, that's correct.

So relative frequencies:

- 1 to 5: 6/18 = 0.333... ≈0.33
- 6 to 10: 5/18 ≈0.28
- 11 to 15: 4/18 ≈0.22
- 16 to 20: 3/18 ≈0.17

Answer:

1 to 5: 0.33
6 to 10: 0.28
11 to 15: 0.22
16 to 20: 0.17

(Note: If the problem expects filling the table, these are the relative frequencies rounded to the nearest hundredth.)