Let x1, x2, ldots, xn be n observations such that Sigma xi2=400 and Sigma x i =80. Then a possible value of n among the following is

Question

Let x1, x2, ldots, xn be n observations such that Sigma xi2=400 and Sigma x i =80. Then a possible value of n among the following is (A) 9 (B) 12 (C) 15 (D) 18

Tardigrade Admin · Accepted Answer

Since root mean square ≥ arithmetic mean √( displaystyle∑i=1n xi2/n) ≥ ( displaystyle∑i=1n xi/n) =√(400/n) ≥ (80/n) ⇒ n ≥ 16 Hence, the possible value of n is 18

Q. Let $x_{1}, x_{2}, \dots, x_{n}$ be $n$ observations such that $Σ x_{i}^{2} = 400$ and $Σ x_{i} = 80$ . Then a possible value of $n$ among the following is

9

12

15

18

Since root mean square $\geq$ arithmetic mean
$\frac{i = 1 \sum n x _{i}^{2}}{n} \geq \frac{i = 1 \sum n x _{i}}{n}$
$= \frac{400}{n} \geq \frac{80}{n}$
$\Rightarrow n \geq 16$
Hence, the possible value of $n$ is $18$

Q. Let x1​,x2​,…,xn​ be n observations such that Σxi2​=400 and Σxi​=80. Then a possible value of n among the following is

9

12

15

18

Since root mean square ≥ arithmetic mean ni=1∑n​xi2​​​≥ni=1∑n​xi​​ =n400​​≥n80​ ⇒n≥16 Hence, the possible value of n is 18

Q. Let $x_{1}, x_{2}, \dots, x_{n}$ be $n$ observations such that $Σ x_{i}^{2} = 400$ and $Σ x_{i} = 80$ . Then a possible value of $n$ among the following is

Since root mean square $\geq$ arithmetic mean
$\frac{i = 1 \sum n x _{i}^{2}}{n} \geq \frac{i = 1 \sum n x _{i}}{n}$
$= \frac{400}{n} \geq \frac{80}{n}$
$\Rightarrow n \geq 16$
Hence, the possible value of $n$ is $18$