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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Statistics

NTA Abhyas 2020 · Mathematics · Statistics

If x _ 1 , x _ 2 , x _ 3 , x _ 4 , x _ 5 ....... x _ n are n...

If x1,x2,x3,x4,x5.......xn{x}_{1}, {x}_{2}, {x}_{3}, {x}_{4}, {x}_{5}....... {x}_{n} are nn observations such that ∑i=1nxi2=400\mathop{∑}_{i = 1}^{n}{x}_i^{2} = 400 and ∑i=1nxi=100,\mathop{∑}_{i = 1}^{n}{x}_{i} = 100, then the possible value of nn among the following is

Options

  1. A1818
  2. B2020
  3. C2424
  4. D2727

Correct answer

D. 2727

Step-by-step solution

We know that,
σ2≥0{\sigma}^{2} \ge 0
⇒Σxi2n−(Σxin)2≥0⇒ \dfrac{Σ{x}_i^{2}}{n} - \left(\dfrac{Σ{x}_{i}}{n}\right)^{2} \ge 0
⇒400n−10000n2≥0⇒ \dfrac{400}{n} - \dfrac{10000}{n^{2}} \ge 0
⇒n≥25⇒ n \ge 25
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