Question

If the median and mode of 4 observations is 4, 6 and the sum of squares of observations is 48. Then
standard deviation is

• A.
• B. 4
• C.
• D.

Answer 1

The correct option is C

Given that median = 4 and mode = 6. We know that
Mean - mode = 3 (Mean - Median)
Mean - 6 = 3 (Mean - 4)
$\overline{x}-6=3\overline{x}-12$
$\overline{x}=3$
${\sigma }^2=\frac{\sum x_i^2}{n}-{\left(\frac{\sum x^i}{n}\right)}^2=\frac{48}{4}-(3{)}^2=3$ $\therefore \sigma =\sqrt{3}$