Question

The mean of 5 observations is 3 and variance is 2. If three of the five observations are 1, 3, 5, find the other two.

(a) 2, 6

(b) 3, 3

(c) 1, 5

(d) 2, 4

I had been asked this question in unit test.

My query is from Statistics in section Statistics of Mathematics – Class 11

Answer 1

Correct answer is (d) 2, 4

To explain I would say: \(\frac{1}{5}\) (Σ xi) = 3 = 1 + 3 + 5 + x4 + x5

⇒ x4 + x5 = 15 ———— (i)

Now, \(\frac{1}{5}\) Σ (xi)^2 – \([\frac{1}{5}\) Σ xi]^2 = 4

⇒ (x4)^2 + (x5)^2 = 30 —————-(ii)

Solving equation i and ii, x4 = 2 and x5 = 4.