Question

In a frequency distribution, the mean and median are 17 and 18 respectively. Then the mode of the distribution is

• A. 20
• B. 17.5
• C. 18.5
• D. 19

Hint:

The mode can be found using the empirical formula \( \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \) for symmetric distributions.

Answer 1

The Correct Option is C

Step 1: Mode formula in terms of mean and median.
The mode of a distribution can be calculated using the empirical relationship: \[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
Step 2: Applying the values.
Given that the mean = 17 and the median = 18, we substitute these values into the formula: \[ \text{Mode} = 3 \times 18 - 2 \times 17 = 54 - 34 = 18.5 \]
Step 3: Conclusion.
Therefore, the mode of the distribution is \( \boxed{18.5} \). The correct answer is (3) 18.5.