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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, 4I had been asked this question in unit test.My query is from Statistics in section Statistics of Mathematics – Class 11

Answer»

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.


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