To find the five-number summary (Min, Q1, Median, Q3, Max) for this dataset, we'll go through the following steps:

1. Organize the data by listing each number of people with its corresponding frequency.
2. Find the five-number summary, including the minimum, the quartiles (Q1, Median, Q3), and the maximum.

Step 1: Organizing the Data

The frequency table gives us the number of households corresponding to each number of people. We'll list the numbers accordingly:

• 1 person: 4 households → $1, 1, 1, 1$
• 2 people: 7 households → $2, 2, 2, 2, 2, 2, 2$
• 3 people: 4 households → $3, 3, 3, 3$
• 4 people: 2 households → $4, 4$
• 5 people: 1 household → $5$
• 6 people: 1 household → $6$
• 7 people: 1 household → $7$

Now, combining them into one ordered list: $1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6, 7$

Step 2: Finding the Five-Number Summary

• Minimum (Min): The smallest number in the dataset is $\mathbf{1}$.

• Maximum (Max): The largest number in the dataset is $\mathbf{7}$.

• Median (Q2): Since we have 20 data points, the median is the average of the 10th and 11th values in the ordered list: $Q2 = \frac{2 + 2}{2} = 2$

• First Quartile (Q1): The first quartile is the median of the lower half of the data (the first 10 values). The 5th and 6th values are both 2, so: $Q1 = \frac{2 + 2}{2} = 2$

• Third Quartile (Q3): The third quartile is the median of the upper half of the data (the last 10 values). The 15th and 16th values are 3 and 4, so: $Q3 = \frac{3 + 4}{2} = 3.5$

Final Five-Number Summary

• Min: 1
• Q1: 2
• Median (Q2): 2
• Q3: 3.5
• Max: 7

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. How do you calculate the interquartile range (IQR) using the five-number summary?
2. If the dataset had an extra household with 8 people, how would the five-number summary change?
3. How would you interpret the third quartile (Q3) in this context?
4. What does the five-number summary tell us about the spread of household sizes in this sample?
5. How could you use this five-number summary to identify potential outliers?

Tip: Quartiles divide your data into four equal parts. Q1 is the 25th percentile, the median (Q2) is the 50th percentile, and Q3 is the 75th percentile.