Question

in a survey, 17 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.

Explanation:

Step1: Count total number of data points

First, we sum up all the given data points. Let's list the data: 4, 10, 6, 8, 4, 4, 18, 16, 9, 9, 5, 12, 6, 10, 5, 7, 17. Wait, actually, looking at the first table, the number of hours are in rows? Wait, maybe the first table has columns? Wait, the first table: first column (maybe) has 4,10,6,8,4 (wait, no, the first table's "Number of hours" column has entries: 4,10,6,8,4; then next row 4,18,16,9,9; then 5,12,6,10,5; then 7,17. Wait, maybe I need to count all the numbers. Let's list all the data points:

From the first table (the one with "Number of hours" as header):

First row: 4, 10, 6, 8, 4

Second row: 4, 18, 16, 9, 9

Third row: 5, 12, 6, 10, 5

Fourth row: 7, 17

Wait, no, maybe the first table is a list of responses. Let's count the number of data points. Let's see:

First column (first set of numbers): 4,4,5,7 → 4 numbers?

Second column:10,18,12,17 → 4 numbers?

Third column:6,16,6 → wait, no, maybe the first table is:

The first table has "Number of hours" and then the data is:

First group: 4,10,6,8,4 (5 numbers)

Second group:4,18,16,9,9 (5 numbers)

Third group:5,12,6,10,5 (5 numbers)

Fourth group:7,17 (2 numbers)

Wait, that can't be. Wait, the problem says "17 people reported...", so total number of data points is 17. Let's count:

Let's list all the numbers:

4,10,6,8,4,

4,18,16,9,9,

5,12,6,10,5,

7,17.

Wait, let's count:

First row: 4,10,6,8,4 → 5 numbers

Second row:4,18,16,9,9 → 5 numbers (total 10)

Third row:5,12,6,10,5 → 5 numbers (total 15)

Fourth row:7,17 → 2 numbers (total 17). Yes! So total number of data points (n) is 17.

Now, we need to group them into classes: 1-5, 6-10, 11-15, 16-20.

Let's define the classes:

1-5: numbers from 1 to 5 (inclusive)

6-10: numbers from 6 to 10 (inclusive)

11-15: numbers from 11 to 15 (inclusive)

16-20: numbers from 16 to 20 (inclusive)

Now, let's count the frequency (number of data points) in each class.

Step 1: Count frequency for 1-5

Numbers in 1-5: 4,4,4,5,5,5,4,5? Wait, let's list all numbers and check:

All data points:

4,10,6,8,4,

4,18,16,9,9,

5,12,6,10,5,

7,17.

Wait, let's list all 17 numbers:

1. 4

2. 10

3. 6

4. 8

5. 4

6. 4

7. 18

8. 16

9. 9

10. 9

11. 5

12. 12

13. 6

14. 10

15. 5

16. 7

17. 17

Now, let's categorize each:

1-5: 4 (1), 4 (5), 4 (6), 5 (11), 5 (15) → wait, numbers 1,5,6,11,15: that's 5 numbers? Wait:

Number 1:4 (1-5)

Number 5:4 (1-5)

Number 6:4 (1-5)

Number 11:5 (1-5)

Number 15:5 (1-5)

Wait, that's 5 numbers? Wait, let's check each number:

1. 4 → 1-5: yes

2. 10 → 6-10: yes

3. 6 → 6-10: yes

4. 8 → 6-10: yes

5. 4 → 1-5: yes

6. 4 → 1-5: yes

7. 18 → 16-20: yes

8. 16 → 16-20: yes

9. 9 → 6-10: yes

10. 9 → 6-10: yes

11. 5 → 1-5: yes

12. 12 → 11-15: yes

13. 6 → 6-10: yes

14. 10 → 6-10: yes

15. 5 → 1-5: yes

16. 7 → 6-10: yes

17. 17 → 16-20: yes

Now let's count:

1-5: numbers 1,5,6,11,15 → that's 5 numbers? Wait:

Number 1:4

Number 5:4

Number 6:4

Number 11:5

Number 15:5

Wait, that's 5 numbers? Wait, 1,5,6,11,15: 5 entries. Wait, but let's count again:

Numbers in 1-5: 4 (1), 4 (5), 4 (6), 5 (11), 5 (15) → 5 numbers.

6-10: numbers 2 (10),3 (6),4 (8),9 (9),10 (9),13 (6),14 (10),16 (7) → let's check:

Number 2:10 → 6-10: yes

Number 3:6 → yes

Number 4:8 → yes

Number 9:9 → yes

Number 10:9 → yes

Number 13:6 → yes

Number 14:10 → yes

Number 16:7 → yes

That's 8 numbers? Wait:

Number 2:10

Number 3:6

Number 4:8

Number 9:9

Number 10:9

Number 13:6

Number 14:10

Number 16:7

Wait, that's 8 numbers? Wait, 2,3,4,9,10,13,14,16: 8 entries.

11-15: number 12 (12) → only 1 number? Wait, number 12:12 → 11-15: yes. Any others? Let's see:

Number 12:12 → 11-15: yes. Any other numbers between 11-15? 12 is the only one? Wait, 11-15: 11,12,13,14,15. The numbers we have: 12 (number 12) → only 1?

16-20: numbers 7 (18),8 (16),17 (17) → 3 numbers.

Wait, let's check total: 5 (1-5) + 8 (6-10) + 1 (11-15) + 3 (16-20) = 17. Perfect, that adds up.

Now, relative frequency is frequency / total number of data points (n=17).

Step 2: Calculate relative frequency for 1-5

Frequency for 1-5: 5. Relative frequency: 5/17 ≈ 0.29 (rounded to nearest hundredth). Wait, 5 divided by 17: 5 ÷ 17 ≈ 0.2941, so 0.29.

Step 3: Calculate relative frequency for 6-10

Frequency for 6-10: 8. Relative frequency: 8/17 ≈ 0.47 (8 ÷ 17 ≈ 0.4706, so 0.47).

Step 4: Calculate relative frequency for 11-15

Frequency for 11-15: 1. Relative frequency: 1/17 ≈ 0.06 (1 ÷ 17 ≈ 0.0588, so 0.06).

Step 5: Calculate relative frequency for 16-20

Frequency for 16-20: 3. Relative frequency: 3/17 ≈ 0.18 (3 ÷ 17 ≈ 0.1765, so 0.18).

Wait, let's verify the counts again to make sure:

1-5: numbers 4,4,4,5,5 → that's 5 numbers (correct, as 4 appears three times, 5 appears twice: 3+2=5)

6-10: numbers 10,6,8,9,9,6,10,7 → let's list them: 10,6,8,9,9,6,10,7. Count: 8 numbers (10:2, 6:2, 8:1, 9:2, 7:1 → 2+2+1+2+1=8)

11-15: number 12 → 1 number

16-20: numbers 18,16,17 → 3 numbers (18,16,17)

Yes, 5+8+1+3=17, which matches the total number of people.

Now, let's compute each relative frequency:

- 1 to 5: 5/17 ≈ 0.29 (rounded to nearest hundredth)

- 6 to 10: 8/17 ≈ 0.47 (rounded to nearest hundredth)

- 11 to 15: 1/17 ≈ 0.06 (rounded to nearest hundredth)

- 16 to 20: 3/17 ≈ 0.18 (rounded to nearest hundredth)

Answer:

For the grouped relative frequency distribution:

• 1 to 5: $\frac{5}{17} \approx 0.29$

• 6 to 10: $\frac{8}{17} \approx 0.47$

• 11 to 15: $\frac{1}{17} \approx 0.06$

• 16 to 20: $\frac{3}{17} \approx 0.18$

So the relative frequencies (rounded to nearest hundredth) are:

1 to 5: 0.29

6 to 10: 0.47

11 to 15: 0.06

16 to 20: 0.18