Question

If the mean and mode of a frequency distribution be 53.4 and 55.2 respectively, find the median.

Answer 1

Given: Mean = 53.4, Mode = 55.2. (Using the empirical relation Mode = 3 × Median – 2 × Mean.)

Step-wise calculation:

1. Start from Mode = 3 × Median – 2 × Mean.

2. Rearrange: 3 × Median = Mode + 2 × Mean.

3. Substitute values: 3 × Median = 55.2 + 2 × 53.4

= 55.2 + 106.8

= 162.0

4. Divide by 3: Median = `162.0/3`

= 54.0