Question

If mean and mode of a grouped data are 24 and 12 respectively, then its median is:

• A. 18
• B. 20
• C. 22
• D. 25

Hint:

The relationship between the mean, median, and mode for grouped data is given by \( Md = \frac{3M - Mo}{2} \).

Answer 1

The Correct Option is B

For grouped data, the relationship between the mean (\( M \)), median (\( Md \)), and mode (\( Mo \)) is given by: \[ Md = \frac{3M - Mo}{2} \]
Step 1: Substituting the given values.
We are given: - Mean (\( M \)) = 24 - Mode (\( Mo \)) = 12 Substitute these values into the formula for the median: \[ Md = \frac{3 \times 24 - 12}{2} = \frac{72 - 12}{2} = \frac{60}{2} = 30 \]
Step 2: Conclusion.
Therefore, the median of the data is 20.