Question

If mode − median = 2, then median − mean = ______.

Answer 1

If mode − median = 2, then median − mean = 1.

Explanation:

Using the empirical relation

\[\text{Mode}=3(\text{Median})-2(\text{Mean})\], we get:

\[\text{Mode}-\text{Median}=2(\text{Median}-\text{Mean})\]

Since mode − median = 2, \[2=2(\text{Median}-\text{Mean})\].

Hence, \[\text{Median}-\text{Mean}=1\].