Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Statistics

NTA Abhyas 2020 · Mathematics · Statistics

Let x _ 1 , x _ 2 ,.... , x _ n be n observations such that ∑ ( x _...

Let x1,x2,....,xn{x}_{1}, {x}_{2},.... , {x}_{n} be nn observations such that ∑(xi)2=400∑ {\left({x}_{i}\right)}^{2} = 400 and ∑xi=40∑ {x}_{i} = 40, then a possible value of nn among the following is

Options

  1. A5
  2. B1
  3. C2
  4. D3

Correct answer

A. 5

Step-by-step solution

Since, variance is always greater than or equal to zero hence x12+x22+...+xn2n≥(x1+x2+...+xnn)2\dfrac{{x}_{1}^{2} + {x}_{2}^{2} + \text{...} + {x}_n^{2}}{n} \ge {\left(\dfrac{{x }_{1} + {x}_{2} + \text{...} + {x}_{n}}{n}\right)}^{2}

⇒400n≥1600n2⇒ \dfrac{4 0 0}{n} \ge \dfrac{1 6 0 0}{n^{2}}

⇒n≥4⇒ n \ge 4
&
Practice Statistics on Quantrex Academy →

More from Statistics

Consider a data consisting of 10 observations x_1, x_2, …, x_ 10 , whose mean is 5 and… JEE Advanced 2026A set of four observations has mean 1 and variance 13 . Another set of six observations… JEE Main 2026Let the mean and the variance of seven observations 2, 4, α, 8, β, 12, 14 , α < β , be 8… JEE Main 2026A data consists of 20 observations x_1, x_2, …, x_ 20 . If ∑_ i=1 ^ 20 (x_i + 5)^2 = 2500… JEE Main 2026A variable X takes values 0, 0, 2, 6, 12, 20, …, n(n-1) with frequencies ^nC_0, ^nC_1… JEE Main 2026The mean deviation about the mean for the data x_i 5 7 9 10 12 15 f_i 8 6 2 2 2 6 is… JEE Main 2026For 10 observations x_1, x_2, …, x_ 10 , if ∑_ i=1 ^ 10 (x_i+2)^2=180 and ∑_ i=1 ^ 10… JEE Main 2026Suppose that the mean and median of the non-negative numbers 21, 8, 17, a, 51, 103, b… JEE Main 2026The mean and variance of n observations are 8 and 16 , respectively. If the sum of the… JEE Main 2026If the mean of the data Class 5-10 10-15 15-20 20-25 25-30 30-35 Frequency 2 k 28 54 k+1… JEE Main 2026The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these… JEE Main 2026Let X=\ x ∈ ~N: 1 ≤ x ≤ 19\ and for some a, b ∈ ℝ, Y=\ a x+b: x ∈ X\ . If the mean and… JEE Main 2026The mean and variance of a data of 10 observations are 10 and 2, respectively. If an… JEE Main 2026If the mean and the variance of the data Class 4-8 8-12 12-16 16-20 Frequency 3 λ 4 7 are… JEE Main 2026Let the mean and variance of 8 numbers -10,-7,-1, x, y, 9,2,16 be (7)/(2) and (293)/(4)… JEE Main 2026If the mean deviation about the median of the numbers k, 2 k, 3 k, …. ., 1000 k is 500… JEE Main 2026 Full Statistics list Statistics JEE Maths PYQsJEE Mathematics PYQs All NTA Abhyas JEE Main PYQs