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JEE Main 2005
Exam
JEE Main
Year
2005
Subject
Mathematics
Chapter
Statistics

JEE Main 2005 · Mathematics · Statistics

Let x_1, x_2, , x_ n be n observations such that ∑ x_ i ^2=400 and...

Let x1,x2,…,xn\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{\mathrm{n}} be n\mathrm{n} observations such that ∑xi2=400\sum \mathrm{x}_{\mathrm{i}}^2=400 and ∑xi=80\sum \mathrm{x}_{\mathrm{i}}=80. Then a possible value of n\mathrm{n} among the following is

Options

  1. A15
  2. B18
  3. C9
  4. D12

Correct answer

B. 18

Step-by-step solution

∑xi2n≥(∑xin)2⇒n≥16\begin{aligned}& \frac{\sum x_i^2}{n} \geq\left(\frac{\sum x_i}{n}\right)^2 \\ & \Rightarrow n \geq 16 \end{aligned}
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