Question

Let $x _ { 1 } , x _ { 2 } , \ldots , x _ { n }$ be n observations such that $\sum x _ { i } ^ { 2 } = 400$ and $\sum x _ { i } = 80$. Then a possible value of n among the following is

• A. 9
• B. 12
• C. 15
• D. 18

Answer 1

Answer: (D)

18

Answer 2

Since, root mean square ≥ arithmetic mean

∴ $\sqrt { \frac { \sum _ { i = 1 } ^ { n } x _ { i } ^ { 2 } } { n } } \geq \frac { \sum _ { i = 1 } ^ { n } x _ { i } } { n } = \sqrt { \frac { 400 } { n } } \geq \frac { 80 } { n } \Rightarrow n \geq 16$

Hence, possible value of n = 18.