https://file.aiquickdraw.com/mathbot/file/1727958863783a7d7huj8.jpg

Let's break down the questions from the image:

1. **First Question:**
   - It asks for the **average number of household members** in "Mansion X" (マンションX). The table provides the distribution of household members (世帯人数) for Mansion X and Mansion Y. We need to compute the average for Mansion X.
   
   The formula for the average is:
   \[
   \text{Average} = \frac{\sum (\text{number of households} \times \text{household size})}{\text{total number of households}}
   \]

   For Mansion X:
   - 1 person: 9 households
   - 2 persons: 21 households
   - 3 persons: 27 households
   - 4 persons: 35 households
   - 5 persons: 8 households
   - Total: 100 households

   So the average is calculated as:
   \[
   \text{Average} = \frac{(1 \times 9) + (2 \times 21) + (3 \times 27) + (4 \times 35) + (5 \times 8)}{100}
   \]
   \[
   = \frac{9 + 42 + 81 + 140 + 40}{100} = \frac{312}{100} = 3.12
   \]

   Therefore, the average number of household members for Mansion X is **3.12**, rounded to **3.12** as instructed.

2. **Second Question:**
   - This asks which of the three statements (ア, イ, ウ) are correct:
     - ア: "The average household size in Mansion Y is 1.17 people."
     - イ: "In Mansion X, households with 3 or more people make up 70%."
     - ウ: "In Mansion Y, households with 2 or fewer people make up 58%."

   Let's analyze each statement:

   - **Statement ア (Mansion Y's average is 1.17):**
     - Using the same method as above, compute the average for Mansion Y:
       \[
       \text{Average for Y} = \frac{(1 \times 14) + (2 \times 15) + (3 \times 13) + (4 \times 6) + (5 \times 2)}{50}
       \]
       \[
       = \frac{14 + 30 + 39 + 24 + 10}{50} = \frac{117}{50} = 2.34
       \]
       So, **ア is incorrect** because the average is 2.34, not 1.17.

   - **Statement イ (Households with 3 or more people in Mansion X make up 70%):**
     - Households with 3 or more people in Mansion X = 27 (3 people) + 35 (4 people) + 8 (5 people) = 70 households.
     - Percentage = \( \frac{70}{100} \times 100 = 70\% \).
     - So, **イ is correct**.

   - **Statement ウ (Households with 2 or fewer people in Mansion Y make up 58%):**
     - Households with 2 or fewer people in Mansion Y = 14 (1 person) + 15 (2 people) = 29 households.
     - Percentage = \( \frac{29}{50} \times 100 = 58\% \).
     - So, **ウ is correct**.

Thus, both **イ and ウ are correct**, making the answer **F (イ and ウ are both correct)**.

---

Would you like further details or clarifications? Here are some follow-up questions for you:

1. How would you calculate the median household size for Mansion Y?
2. What is the percentage of households with exactly 4 members in Mansion X?
3. How does the distribution of households in Mansion X compare to Mansion Y in terms of skewness?
4. What are the possible effects on the average household size if the number of 5-member households in Mansion X were doubled?
5. How would you compute the mode of the household size for both Mansion X and Y?

**Tip:** Always double-check rounding requirements in exam problems; they often specify the precision needed for averages.

Calculate the average number of household members for Mansion X and determine which of the statements (ア, イ, ウ) are correct.

Learn how to calculate the average household size for Mansion X and determine the correctness of related statistical statements regarding Mansion X and Mansion Y. This problem covers average and percentage calculations, perfect for high school students in Grades 10-12.

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