Question

If the arithmetic mean and mode of the given data are 28 and 16 respectively, the median will be:

• A. 22
• B. 23.5
• C. 24
• D. 24.5

Hint:

The relationship between the mean, median, and mode for grouped data is given by \( \text{Median} = \frac{\text{Mode} + 2 \times \text{Mean}}{3} \).

Answer 1

The Correct Option is C

The relationship between the mean, median, and mode for grouped data is given by the formula: \[ \text{Median} = \frac{\text{Mode} + 2 \times \text{Mean}}{3} \]
Step 1: Substitute the given values.
We are given: - Mean = 28 - Mode = 16 Substitute these values into the formula for the median: \[ \text{Median} = \frac{16 + 2 \times 28}{3} = \frac{16 + 56}{3} = \frac{72}{3} = 24 \]
Step 2: Conclusion.
Therefore, the median is 24.