To solve this problem, we need to calculate the percentage of respondents in each rating category (1, 2, 3, 4) and then compare these percentages to the bar graphs provided.

Step 1: Total number of respondents

The total number of respondents is: $18 + 27 + 63 + 42 = 150$

Step 2: Calculate percentages for each rating

For each rating, the percentage is calculated as: $\text{Percentage} = \left(\frac{\text{Number of people}}{\text{Total number of respondents}}\right) \times 100$

1. For rating 1: $\frac{18}{150} \times 100 = 12\%$

2. For rating 2: $\frac{27}{150} \times 100 = 18\%$

3. For rating 3: $\frac{63}{150} \times 100 = 42\%$

4. For rating 4: $\frac{42}{150} \times 100 = 28\%$

Step 3: Match percentages to the bar graphs

Now compare the calculated percentages (12%, 18%, 42%, 28%) to the percentage distributions in the provided bar graphs:

• Option A: Does not match (incorrect percentages).
• Option B: Matches 12%, 18%, 42%, 28% exactly.
• Option C: Incorrect order of percentages.
• Option D: Incorrect percentages.

Final Answer:

The correct bar graph is B.

Do you have any questions or would you like further clarification?

Related Questions:

1. How can you verify percentages using a different method?
2. What are some other examples where percentages are used to represent data?
3. How can pie charts represent the same data, and how would they look?
4. What is the importance of normalizing data using percentages?
5. Can percentages be misleading when interpreting data, and why?

Tip: Always double-check total percentages add up to 100% to ensure your calculations are correct!