Question

The empirical relationship between mean, median and mode is :

• A. Mean > Median > Mode
• B. Mean = Median = Mode
• C. Mode - Mean = 3 (Median - Mean)
• D. Mean - Mode = 3 (Mean - Median)

Answer 1

Answer: (C)

Mode - Mean = 3 (Median - Mean)

Empirical relationship between mean, median and mode is:
Mode = 3 Median - 2 Mean
$\Rightarrow$ Mode - Mean = 3 Median - 2 Mean - Mean
$\Rightarrow$ Mode - Mean = 3 Median - 3 Mean
$\Rightarrow$ Mode - Mean = 3 [Median - Mean]
$\therefore$ Option C is correct.