Question

complete the frequency table for the following set of data. you may optionally cl shade it out.
3, 9, 6, 2, 7, 8, 11, 0, 6, 8,
5, 8, 7, 6, 0
*click the tally box to count up. the minus counts down.
interval tally frequency
0 — 2
3 — 5
6 — 8
9 — 11

Explanation:

Step1: Analyze Interval 0–2

Identify data points in \(0 \leq x \leq 2\): 0, 2, 0. Count them: \(3\) values.

Step2: Analyze Interval 3–5

Identify data points in \(3 \leq x \leq 5\): 3, 5. Count them: \(2\) values.

Step3: Analyze Interval 6–8

Identify data points in \(6 \leq x \leq 8\): 6, 7, 8, 6, 8, 5 (wait, 5 is not, correct: 6,7,8,6,8,7,6,8. Wait, data: 6,7,8,6,8,7,6,8, and 6,7,8. Wait original data: 3,9,6,2,7,8,11,0,6,8,5,8,7,6,0. So 6: three times (6,6,6), 7: two times (7,7), 8: three times (8,8,8). So total \(3 + 2 + 3 = 8\)? Wait no: 6,7,8,6,8,7,6,8, and 6 (wait data has 6,6,6? Let's list all in 6–8: 6,7,8,6,8,7,6,8, and 6? Wait data points: 6,7,8,6,8,7,6,8, and 6? Wait original data: 3,9,6,2,7,8,11,0,6,8,5,8,7,6,0. So 6 appears at positions 3,9,14: three times. 7: positions 5,13: two times. 8: positions 6,10,12: three times. So total \(3 + 2 + 3 = 8\) values.

Step4: Analyze Interval 9–11

Identify data points in \(9 \leq x \leq 11\): 9,11. Count them: \(2\) values (9,11). Wait, data has 9,11, and is 9–11, so 9,11, and is there another? 9,11: two values? Wait data: 9,11, and 9 is once, 11 is once, and any others? 9,11: so two values? Wait no, data: 3,9,6,2,7,8,11,0,6,8,5,8,7,6,0. So 9: 1, 11:1, and is there another? No. Wait 9–11: 9,11, so two values? Wait 9 and 11: that's two? Wait 9 is one, 11 is one, so frequency 2? Wait no, wait 9 is in 9–11, 11 is in 9–11, and is there another? No. So frequency 2? Wait no, wait data has 9,11, and is 9–11, so 9 and 11: two values. Wait but let's recount:

Data points:

0–2: 0,2,0 → 3 (0,0,2)

3–5: 3,5 → 2 (3,5)

6–8: 6,7,8,6,8,7,6,8 → let's count: 6 (3 times), 7 (2 times), 8 (3 times) → 3+2+3=8

9–11: 9,11 → 2 (9,11)

Wait but let's list all data points:

3,9,6,2,7,8,11,0,6,8,5,8,7,6,0

So:

0–2: 0,2,0 → 3

3–5: 3,5 → 2

6–8: 6,7,8,6,8,7,6,8 → 6 (3),7(2),8(3) → 8

9–11: 9,11 → 2

Wait but let's check again:

Data points:

0: two times (0,0)

2: one time (2)

So 0–2: 0,0,2 → 3

3: one time (3)

5: one time (5)

So 3–5: 3,5 → 2

6: three times (6,6,6)

7: two times (7,7)

8: three times (8,8,8)

So 6+7+8: 3+2+3=8

9: one time (9)

11: one time (11)

So 9–11: 9,11 → 2

So frequencies:

0–2: 3

3–5: 2

6–8: 8

9–11: 2

Wait but let's confirm:

Total data points: 15 (3,9,6,2,7,8,11,0,6,8,5,8,7,6,0 → count: 1 (3),1(9),1(6),1(2),1(7),1(8),1(11),1(0),1(6),1(8),1(5),1(8),1(7),1(6),1(0) → 15 points.

3 (0–2) + 2 (3–5) + 8 (6–8) + 2 (9–11) = 15. Correct.

Answer:

For Interval 0–2: 3
For Interval 3–5: 2
For Interval 6–8: 8
For Interval 9–11: 2

(Assuming the table needs each frequency filled. If only one was asked, but the problem says "complete the frequency table", so all. But the initial question's table has 0–2 as first, so the first box (0–2) is 3, 3–5 is 2, 6–8 is 8, 9–11 is 2.)