https://file.aiquickdraw.com/mathbot/file/1726617003758o49dyujf.jpg

Let's analyze the data from the image and construct the grouped data table for household sizes.

### Raw Data from the 40 Households:

The household sizes recorded in the grid are:

```
5, 3, 4, 5, 3
3, 3, 5, 1, 4
3, 3, 7, 1, 2
4, 3, 4, 5, 7
4, 1, 5, 3, 6
4, 1, 2, 5, 6
4, 5, 1, 4, 3
```

We will tally the frequencies for each household size and compute the relative frequencies accordingly.

### Frequency Table:

| Household size | Frequency | Relative Frequency |
|----------------|-----------|--------------------|
| 1              | 6         | 6/40 = 0.15        |
| 2              | 2         | 2/40 = 0.05        |
| 3              | 10        | 10/40 = 0.25       |
| 4              | 9         | 9/40 = 0.225       |
| 5              | 8         | 8/40 = 0.2         |
| 6              | 2         | 2/40 = 0.05        |
| 7              | 3         | 3/40 = 0.075       |
| **Total**      | **40**    | **1**              |

### Explanation:
1. The frequency represents how many times each household size appears.
2. The relative frequency is the proportion of each household size out of the total number of households (40).

Would you like further details or have any questions?

Here are five follow-up questions for deeper exploration:
1. What is the modal household size based on the frequency distribution?
2. How could you interpret the relative frequency in terms of percentage?
3. What is the cumulative frequency of households with 4 or fewer people?
4. How would this data change if we added more household sizes?
5. Can you calculate the mean household size based on this frequency table?

**Tip:** The relative frequency helps to compare the proportion of different household sizes regardless of the sample size.

The U.S. Bureau of the Census conducts nationwide surveys on characteristics of U.S. households. Following are data on the number of people per household for a sample of 40 households. Construct a grouped data table for these household sizes.

Explore how to construct a grouped data table for U.S. household sizes based on a sample of 40 households. This guide provides detailed steps on calculating frequency and relative frequency to analyze household distribution effectively.

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