Question

number of televisions per household
the center is 2.
the center is 1.5.
there are no gaps.
it has a cluster at 0, 1, and 2.
it is skewed left.
the spread from 1 to 5
mark this and return
save and exi

Explanation:

Step1: Analyze "The center is 2"

To find the center (median), we first count the number of dots. Let's count:
- At 0: 3 dots
- At 1: 8 dots (let's check the vertical dots: 8)
- At 2: 7 dots
- At 3: 0 dots
- At 4: 4 dots
- At 5: 1 dot

Total dots: \(3 + 8 + 7 + 0 + 4 + 1 = 24\). The median is the average of the 12th and 13th values. Let's order the data:
- 0: 3 values (positions 1 - 3)
- 1: 8 values (positions 4 - 11)
- 2: 7 values (positions 12 - 18)

So the 12th value is 2, 13th value is 2. Median is 2? Wait, no, wait: 3 (0s) + 8 (1s) = 11. So the 12th value is the first 2, 13th is the second 2. So median is 2? But let's check the other options. Wait, maybe I made a mistake. Wait, the center (median) calculation: for 24 data points, median is the average of the 12th and 13th. Let's list the cumulative counts:
- 0: 3 (cumulative: 3)
- 1: 8 (cumulative: 3 + 8 = 11)
- 2: 7 (cumulative: 11 + 7 = 18)
- 4: 4 (cumulative: 18 + 4 = 22)
- 5: 1 (cumulative: 22 + 1 = 23? Wait, maybe I miscounted the dots. Let's re - count the dots:

At 0: 3 dots (vertical: 3)
At 1: Let's count the vertical dots: from the graph, at 1, there are 8 dots (let's see: the dots at 1 are more than at 0, 2, 4, 5). At 2: 7 dots. At 4: 4 dots. At 5: 1 dot. At 3: 0. So total: 3 + 8 + 7 + 0 + 4 + 1 = 23? Wait, maybe the original count is 23. Then the median is the 12th value. Cumulative: 0 (3) → 1 (3 + 8 = 11) → 2 (11 + 7 = 18). So the 12th value is in the 2s. So median is 2? But let's check the option "The center is 2" – maybe that's correct? Wait, no, wait the other option "The center is 1.5" – let's see. Wait, maybe I made a mistake. Alternatively, maybe the center (mean) is different, but the question says "center" which is usually median. Wait, let's check the cluster option: "It has a cluster at 0, 1, and 2" – because most of the dots are at 0, 1, 2 (3 + 8 + 7 = 18 out of 24), so that's a cluster. "There are no gaps" – there is a gap at 3 (no dots at 3), so "There are no gaps" is false. "It is skewed left" – skewed left means tail on the left, but here the tail is on the right (more dots on the left, fewer on the right), so it's skewed right, so "It is skewed left" is false. "The center is 1.5" – let's see, if median is 2, then this is false. Wait, maybe my dot count is wrong. Let's re - examine the graph:

- At 0: 3 dots (three vertical dots)
- At 1: Let's count the vertical dots: from the top, 8 dots (let's count: the first dot at 1 is the top, then 7 more? Wait, the graph shows at 1, there are 8 dots (let's see: the dots at 1 are more than at 2. At 2, there are 7 dots (since at 2, the number of dots is less than at 1). At 4, there are 4 dots (four vertical dots). At 5, 1 dot. At 3, 0. So total dots: 3 + 8 + 7 + 0 + 4 + 1 = 23. So median is the 12th value. Cumulative:

0: 3 (positions 1 - 3)

1: 8 (positions 4 - 11)

2: 7 (positions 12 - 18)

So the 12th value is 2, so median is 2. So "The center is 2" – maybe correct? But also "It has a cluster at 0, 1, and 2" – because 0, 1, 2 have most of the data (18 out of 23), so that's a cluster. Wait, but let's check the options again. The options are checkboxes, so we need to find which are correct. Wait, the question is to identify the correct statements. Let's go through each:

1. "The center is 2": As per median calculation, median is 2 (for 23 data points, median is the 12th value, which is 2). So this could be correct.

2. "The center is 1.5": Median is 2, so this is false.

3. "There are no gaps": There is a gap at 3 (no dots at 3), so false.

4. "It has a cluster at 0, 1, and 2": Most of the data (18 out of 23) is at 0, 1, 2, so this is a cluster. So this is correct.

5. "It is skewed left": Skewed left means the tail is on the left (low values have few data points, high values have more). But here, low values (0, 1, 2) have more data, high values (4, 5) have less, so it's skewed right, so false.

6. "The spread is from 1 to 5": The spread (range) is max - min = 5 - 0 = 5, so spread from 0 to 5, not 1 to 5, so false.

Wait, but the problem is to choose the correct options. Wait, maybe I made a mistake in median. Let's calculate the mean: sum of (x * frequency) / total. x = 0: 0 * 3 = 0; x = 1: 1 * 8 = 8; x = 2: 2 * 7 = 14; x = 3: 0 * 0 = 0; x = 4: 4 * 4 = 16; x = 5: 5 * 1 = 5. Total sum: 0 + 8 + 14 + 0 + 16 + 5 = 43. Mean: 43 / 23 ≈ 1.87, which is close to 1.5? No, 1.87 is close to 2. Wait, maybe the "center" here is median. So median is 2, so "The center is 2" is correct? But also "It has a cluster at 0, 1, and 2" is correct. Wait, but let's check the gap: at 3, there are no dots, so "There are no gaps" is false. So the correct options are "The center is 2", "It has a cluster at 0, 1, and 2". But maybe the question is a multiple - choice where we have to pick the correct one. Wait, the original question is not clear, but assuming we have to pick the correct statement. Let's re - evaluate:

- "The center is 2": Median is 2 (as per 24 data points? Wait, maybe I miscounted the dots. Let's count again:

At 0: 3 dots

At 1: Let's count the vertical dots: the first dot at 1 is the top, then 7 more? Wait, the graph shows at 1, there are 8 dots (let's see: the dots at 1 are more than at 2. At 2, there are 7 dots (since the column at 2 is one less than at 1). At 4, 4 dots. At 5, 1 dot. At 3, 0. So 3 + 8 + 7 + 0 + 4 + 1 = 23. So median is the 12th value. Cumulative:

0: 3 (1 - 3)

1: 8 (4 - 11)

2: 7 (12 - 18)

So 12th value is 2, 13th is 2. Median is 2. So "The center is 2" is correct.

- "It has a cluster at 0, 1, and 2": Since most of the data (18 out of 23) is at 0, 1, 2, this is a cluster. So this is correct.

- "There are no gaps": There is a gap at 3, so false.

- "It is skewed left": Skewed left means tail on the left, but here the tail is on the right (more data on the left), so it's skewed right, false.

- "The spread is from 1 to 5": Range is 5 - 0 = 5, so spread from 0 to 5, false.

- "The center is 1.5": Median is 2, mean is ~1.87, so false.

So the correct statements are "The center is 2" and "It has a cluster at 0, 1, and 2". But maybe the question is to pick one. Assuming the most probable correct statement is "It has a cluster at 0, 1, and 2" because a cluster is a group of data points close together, and 0, 1, 2 have most of the dots.

Answer:

It has a cluster at 0, 1, and 2.