JEE Main 2020 · 3 September · evening · Single correct · +4 / −1

Let xᵢ (1 ≤ i ≤ 10) be ten observations of a random variable X. If
Σᵢ₌₁¹⁰ ( xᵢ - p ) = 3 and Σᵢ₌₁¹⁰ ( xᵢ - p )² = 9
where 0 ≠ p ∈ R, then the standard deviation of these observations is :

  1. (a) 7/10
  2. (b) 9/10
  3. (c) 4/5
  4. (d) √(3/5)
Answer and solution

Answer (b) 9/10

Solution

Maths sir · 3 steps

Shifting every observation by p does not change the spread, so find the SD of xᵢ - p instead.

  1. Shift the data. Let dᵢ = xᵢ - p. Subtracting the same number from every observation moves the data but does not change its spread. So σₓ = σ_d.
  2. Read the sums. With n = 10, we have Σ dᵢ = 3, so d̄ = 3/10. We also have Σ dᵢ² = 9.

    σ² = (Σ dᵢ²)/n - ((Σ dᵢ)/n)² = 9/10 - (3/10)² = (90 - 9)/100 = 81/100

  3. So. σ = √(81/100) = 9/10, which is option (b). The value of p never mattered.

The idea to keep. Variance and SD do not change when you add or subtract a constant from every observation. If sums of (xᵢ - p) are given, treat xᵢ - p as the data and use mean of squares minus square of mean.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Statistics

Asked about 100 times in JEE Main since 2020. This question is from 2020.