The following values represent the number of cars owned by the 20 families on Pearl Street.
1,1,2,3,2,5,4,3,2,4,5,2,6,2,1,2,4,2,1,1
This can be expressed in frequency distribution format as follows :
`{:(x,"The number of families having x number of cars"),(1,5),(2,7),(3,a),(4,3),(5,b),(6,1):}`
What are the value of a and b, resepectively?

Options

A. 1 and 1
B. 1 and 2
C. 2 and 1
D. 2 and 2

Answer

To solve the problem, we need to determine the values of \( a \) and \( b \) in the frequency distribution table based on the given data of the number of cars owned by 20 families.

The data provided is:
1, 1, 2, 3, 2, 5, 4, 3, 2, 4, 5, 2, 6, 2, 1, 2, 4, 2, 1, 1

We will count the occurrences of each number of cars to fill in the frequency distribution table.

### Step-by-Step Solution:

1. **Count the occurrences of each number of cars:**
- For \( 1 \): Count how many times \( 1 \) appears in the data.
- Occurrences: 1, 1, 1, 1, 1 (Total: 5)
- For \( 2 \): Count how many times \( 2 \) appears in the data.
- Occurrences: 2, 2, 2, 2, 2, 2, 2 (Total: 7)
- For \( 3 \): Count how many times \( 3 \) appears in the data.
- Occurrences: 3, 3 (Total: 2) → This gives us \( a = 2 \)
- For \( 4 \): Count how many times \( 4 \) appears in the data.
- Occurrences: 4, 4, 4 (Total: 3)
- For \( 5 \): Count how many times \( 5 \) appears in the data.
- Occurrences: 5, 5 (Total: 2) → This gives us \( b = 2 \)
- For \( 6 \): Count how many times \( 6 \) appears in the data.
- Occurrences: 6 (Total: 1)

2. **Compile the frequency distribution:**
- The frequency distribution can now be summarized as follows:
- \( 1 \): 5 families
- \( 2 \): 7 families
- \( 3 \): 2 families (a = 2)
- \( 4 \): 3 families
- \( 5 \): 2 families (b = 2)
- \( 6 \): 1 family

3. **Final Values:**
- The values of \( a \) and \( b \) are both \( 2 \).

### Conclusion:
The values of \( a \) and \( b \) are \( 2 \) and \( 2 \) respectively.