Question

If mean and mode for a certain data are 37 and 52 respectively, then the median of the data is

• A. 37
• B. 48
• C. 42
• D. 52

Answer 1

The correct option is C 42

Mean = 37,
Mode = 52
Using empirical relationship between the three measures of central tendency:
3Median = Mode + 2 Mean
$\Rightarrow$ 3Median = 52 + 2(37)
$\Rightarrow$ 3Median = 52 + 74
$\Rightarrow$ 3Median = 126
$\Rightarrow$ Median = $\frac{126}{3}$
$\Rightarrow$ Median = 42
Hence, the correct answer is option c.