Question

8, 2, 4, 5, 9, 10, 7, 0, 3, 9, 4, 4, 3, 8, 8, 11, 8, 10, 5, 10, 11, 2 *click the tally box to count up. the minus counts down. interval tally frequency 0 - 2 3 - 5 i 6 - 8 9 - 11

Explanation:

Step1: Count numbers in 0–2

Numbers: 0, 2, 2. So count is 3.

Step2: Count numbers in 3–5

Numbers: 3, 3, 4, 4, 4, 5, 5. Wait, original data: 3,9,4,4,3,8,8,11, 8,10,5,10,11,2 (wait full data: 8,2,4,5,9,10,7,0, 3,9,4,4,3,8,8,11, 8,10,5,10,11,2. Let's list all: 0,2,2,3,3,4,4,4,5,5,7,8,8,8,8,9,9,10,10,10,11,11,11? Wait no, let's count each interval:

0–2: 0,2,2 (wait 0, 2, 2? Wait original data: 8,2,4,5,9,10,7,0, 3,9,4,4,3,8,8,11, 8,10,5,10,11,2. So numbers: 0,2,2 (wait 0, 2, 2? Wait 0, 2 (first), 2 (last), and maybe another? Wait no, let's list all numbers:

First row: 8,2,4,5,9,10,7,0 → 8,2,4,5,9,10,7,0 (8 numbers)
Second row: 3,9,4,4,3,8,8,11 → 3,9,4,4,3,8,8,11 (8 numbers)
Third row: 8,10,5,10,11,2 → 8,10,5,10,11,2 (6 numbers)
Total numbers: 8+8+6=22.

Now 0–2: numbers ≥0 and ≤2. So 0,2,2 (wait 0, 2 (first row), 2 (third row), and is there another? Wait first row: 0,2; third row: 2. So 0,2,2? Wait no, first row: 8,2,4,5,9,10,7,0 → 0,2. Second row: no. Third row: 2. So 0,2,2? Wait 0, 2, 2: that's 3 numbers? Wait 0, 2 (from first row), 2 (from third row), and is there another 2? Wait first row: 2; third row: 2. So two 2s and one 0: total 3.

3–5: numbers ≥3 and ≤5. So 3,3,4,4,4,5,5. Let's check: first row: 4,5; second row: 3,3,4,4; third row: 5. So 4,5 (first row) + 3,3,4,4 (second row) + 5 (third row) = 4,5,3,3,4,4,5 → that's 7 numbers? Wait 4 (first row), 5 (first row), 3 (second), 3 (second), 4 (second), 4 (second), 5 (third). So 7 numbers? Wait but the tally for 3–5 has "I" which is 1, but maybe we need to count correctly. Wait no, let's do it properly:

List all numbers:

0,2,4,5,9,10,7,8, 3,9,4,4,3,8,8,11, 8,10,5,10,11,2. Wait no, let's sort them:

0,2,2,3,3,4,4,4,5,5,7,8,8,8,8,9,9,10,10,10,11,11,11? Wait no, let's count each:

0: 1

2: 2 (from first row 2, third row 2)

3: 2 (second row 3,3)

4: 3 (second row 4,4,4? Wait second row: 3,9,4,4,3,8,8,11 → 4,4 → two 4s? Wait no, second row: 3,9,4,4,3,8,8,11 → 3,3,4,4,9,8,8,11. So 3:2, 4:2. First row: 4,5 → 4:1, 5:1. Third row: 5 → 5:1. So 4: 1 (first) + 2 (second) = 3; 5: 1 (first) +1 (third) =2. So 3:2, 4:3, 5:2. Total for 3–5: 2+3+2=7.

6–8: numbers ≥6 and ≤8. So 7,8,8,8,8. First row:7,8; second row:8,8; third row:8. So 7,8,8,8,8 → 5 numbers? Wait first row:7,8; second row:8,8; third row:8. So 7 (1), 8 (1+2+1=4? Wait first row 8:1, second row 8:2, third row 8:1 → total 4? Wait first row:8 (1), second row:8,8 (2), third row:8 (1) → 1+2+1=4. Plus 7:1. So 5 numbers (7,8,8,8,8).

9–11: numbers ≥9 and ≤11. So 9,9,10,10,10,11,11,11. First row:9,10; second row:9,11; third row:10,10,11. So 9:2 (first 9, second 9), 10:3 (first 10, third 10,10), 11:3 (second 11, third 11,11? Wait no, first row:9,10 → 9:1, 10:1. Second row:9,11 → 9:1, 11:1. Third row:10,10,11 → 10:2, 11:1. So 9:1+1=2; 10:1+2=3; 11:1+1=2. Total:2+3+2=7? Wait 9:2, 10:3, 11:2 → 7 numbers.

Wait but the problem is to fill the frequency for each interval. Let's do each interval:

1. Interval 0–2: numbers 0,2,2 → count=3 (0:1, 2:2 → 1+2=3)
2. Interval 3–5: 3,3,4,4,4,5,5 → count=7 (3:2, 4:3, 5:2 → 2+3+2=7)
3. Interval 6–8: 7,8,8,8,8 → count=5 (7:1, 8:4 → 1+4=5)
4. Interval 9–11: 9,9,10,10,10,11,11 → wait no, earlier count was 9:2, 10:3, 11:2 → 2+3+2=7.

But the tally for 3–5 has "I" which is 1, but maybe the initial tally was 1, but we need to count correctly. Wait maybe I made a mistake. Let's start over:

List all numbers (22 numbers):

From the data:

First line: 8, 2, 4, 5, 9, 10, 7, 0 → 8 numbers: [0,2,4,5,7,8,9,10]

Second line: 3, 9, 4, 4, 3, 8, 8, 11 → 8 numbers: [3,3,4,4,8,8,9,11]

Third line: 8, 10, 5, 10, 11, 2 → 6 numbers: [2,5,8,10,10,11]

Now combine all:

[0,2,4,5,7,8,9,10, 3,3,4,4,8,8,9,11, 2,5,8,10,10,11]

Now sort them:

0, 2, 2, 3, 3, 4, 4, 4, 5, 5, 7, 8, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11? Wait no, let's count each:

0: 1

2: 2 (from first line 2, third line 2)

3: 2 (second line 3,3)

4: 3 (first line 4, second line 4,4)

5: 2 (first line 5, third line 5)

7: 1 (first line 7)

8: 4 (first line 8, second line 8,8, third line 8)

9: 2 (first line 9, second line 9)

10: 3 (first line 10, third line 10,10)

11: 3 (second line 11, third line 11,11)

Now count intervals:

0–2 (inclusive): 0,2,2 → count=3

3–5 (inclusive): 3,3,4,4,4,5,5 → count=7 (2+3+2)

6–8 (inclusive): 7,8,8,8,8 → count=5 (1+4)

9–11 (inclusive): 9,9,10,10,10,11,11,11 → count=8 (2+3+3)

Wait but the table has four intervals: 0–2, 3–5, 6–8, 9–11.

So:

0–2: 3

3–5: 7

6–8: 5

9–11: 8

But the tally for 3–5 has "I" (1), so maybe the initial frequency was 1, but we need to set it to 7. Wait the problem says "Click the tally box to count up. The minus counts down." So maybe we need to calculate the correct frequency for each.

But the question is probably to fill the frequency for each interval. Let's confirm:

Step1: 0–2

Numbers: 0,2,2 → count=3. So frequency=3.

Step2: 3–5

Numbers: 3,3,4,4,4,5,5 → count=7. So frequency=7.

Step3: 6–8

Numbers: 7,8,8,8,8 → count=5. So frequency=5.

Step4: 9–11

Numbers: 9,9,10,10,10,11,11,11 → count=8. So frequency=8.

But the table shows:

0–2: frequency box empty

3–5: tally has "I" (1) and frequency box empty (but maybe the initial is 1, but we need to set to 7)

6–8: frequency box empty

9–11: frequency box empty

But the problem might be to find the frequency for each. Let's assume the question is to find the frequency for each interval.

Answer:

For interval 0–2: 3
For interval 3–5: 7
For interval 6–8: 5
For interval 9–11: 8

(If the question is to fill the frequency boxes, these are the counts.)