If the mode of a data exceeds its mean by 20.1, then the mode exceeds the median by _____. (Use empirical formula)

Correct option is C

Given:

Mode exceeds Mean by 20.1

Formula Used:

Mode = 3 × Median – 2 × Mean

Solution: 

Mode = Mean + 20.1

Substituting Mode = Mean + 20.1 into the empirical formula:

Mean + 20.1 = 3 × Median − 2 × Mean

Mean + 2 × Mean + 20.1 = 3 × Median

3 × Mean + 20.1 = 3 × Median

Mean + $$\frac{20.1}3$$​ = Median 

Now, 

Mode = Mean + 20.1

Median = Mean + $$\frac{20.1}{3}$$​​

So,

Mode - Median = $$20.1 - \frac{20.1}{3} = \frac{60.3 - 20.1}{3} = \frac{40.2}{3} = 13.4$$​​