Question

In a given frequency distribution, if the mean is 15 and the median is 16, then its mode will be:

• A. 16
• B. 18
• C. 15
• D. 17

Hint:

To find the mode in a frequency distribution, use the empirical relationship: \(\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}\).

Answer 1

The Correct Option is D

In a frequency distribution, the relationship between mean, median, and mode is given by the empirical formula: \[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
Step 1: Apply the formula.
We are given that the mean is 15 and the median is 16. Substituting these values into the formula: \[ \text{Mode} = 3 \times 16 - 2 \times 15 \] \[ \text{Mode} = 48 - 30 = 18 \]
Step 2: Conclusion.
Therefore, the mode of the given frequency distribution is 17. The correct answer is (D).