The mean of five observations is 5 and their variance is 9.20 . If three of the given five observations are 1, 3 and 8 , then a ratio of other two observations is

Step-by-step solution

Let, the two unknown terms are x   &   y . The mean is defined as μ = ∑ x i N ⇒ 5 = 1 + 3 + 8 + x + y 5 ⇒ 25 = 12 + x + y ⇒ x + y = 13         . . . 1 And, the variance is defined as σ 2 = ∑ x i - μ 2 N = ∑ x i 2 N - μ 2 ⇒ 9.2 = 1 + 9 + 64 + x 2 + y 2 5 - 25 ⇒ 34.2 × 5 = 74 + x 2 + y 2 ⇒ 171 = 74 + x 2 + y 2 ⇒ 97 = x 2 + y 2           . . . 2 Put the value of y from equatio