Let x_1,x_2…,x_n be n observations such that ∑xi2=300 and ∑x_i=90. Then a possible value of n among the following is

Correct answer: (C) 29. Variance =(Σx)/i2n-Σx^in2 ⇒Σx^(i2n≥Σxin2) ⇒n≥(Σx^i2)/(Σxi2)⇒n≥8100/300⇒n≥27

Q41 / 77 · NTA Abhyas (JEE Main) 2020 · Mathematics · Statistics

Let $x_{1}, x_{2} \dots, x_{n}$ be $n$ observations such that $\sum x_{i}^{2} = 300$ and $\sum x_{i} = 90 .$ Then a possible value of $n$ among the following is

Variance

= \frac{Σ x_{i}^{2}}{n} - {(\frac{Σ x_{i}}{n})}^{2}

\Rightarrow {\frac{Σ x_{i}^{2}}{n} \geq (\frac{Σ x_{i}}{n})}^{2}

\Rightarrow n \geq \frac{{(Σ x_{i})}^{2}}{Σ x_{i}^{2}} \Rightarrow n \geq \frac{8100}{300} \Rightarrow n \geq 27

Hence, the correct answer is option: 'C'.