Question

If mode and mean of some observations are 45 and 27 respectively, then median will be:

• A. 34
• B. 33
• C. 32
• D. 40

Hint:

To find the median in a frequency distribution when mode and mean are given, use the formula: \( \text{Median} = \frac{\text{Mode} + 2 \times \text{Mean}}{3} \).

Answer 1

The Correct Option is B

In a frequency distribution, the relationship between mode, median, and mean is given by the empirical formula: \[ \text{Median} = \frac{\text{Mode} + 2 \times \text{Mean}}{3} \]
Step 1: Apply the formula.
We are given the mode is 45 and the mean is 27. Substituting these values into the formula: \[ \text{Median} = \frac{45 + 2 \times 27}{3} = \frac{45 + 54}{3} = \frac{99}{3} = 33 \]
Step 2: Conclusion.
Therefore, the median is 33. The correct answer is (B).