If mean and median of a distribution are 60 and 48 respectively, then mode of the distribution is :

Question

Accepted Answer

To determine the mode of a distribution when the mean and median are given, we can use the empirical relationship between the mean, median, and mode. This relationship is often expressed as:

$$ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} $$

Given:
- Mean = 60
- Median = 48

Substituting these values into the formula, we get:

$$ \text{Mode} = 3 \times 48 - 2 \times 60 $$
$$ \text{Mode} = 144 - 120 $$
$$ \text{Mode} = 24 $$

Therefore, the mode of the distribution is 24, which corresponds to Option 3.

### Explanation for Other Options:

1. **Option 1: 50**
   - Using the empirical formula, the calculated mode is 24, not 50. Therefore, Option 1 is incorrect.

2. **Option 2: 36**
   - Similarly, the calculated mode using the formula is 24, not 36. Hence, Option 2 is incorrect.

3. **Option 4: 18**
   - The calculated mode is 24, which does not match 18. Thus, Option 4 is incorrect.

In conclusion, based on the empirical relationship between mean, median, and mode, Option 3 (24) is the correct answer.