Question

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:
(A) 10 : 3 (B) 4 : 9
(C) 5 : 8 (D) 6 : 7

Answer 1

Let 5 observation are 1,3,8,a and b

mean given = 5

so, (1+3+8+a+b)/5 = 5

→ (12+a+b) = 25

→ (a + b) = 13 ---------- Equation(1)

now, given variance = 9.2

So,

→ (sum of xi²)/5 - (25) = 9.2

→ (sum of xi²)/5 = 25+9.2 = 34.2

→ (sum of xi²) = 34.2*5 = 171

So,

→ 1² + 3² + 8² + a² + b² = 171

→ a² + b² = 171 - (1 +9 + 64) = 97 ------- equation (2)

Now,

using a²+b² = (a + b)² - 2ab and putting both value of Equations we get

→ 97 = 13² - 2ab

→ 2ab = 169-97

→ 2ab = 72

→ ab = 36

so, we can say that, a:b = 9:4 or 4:9..

B is the answer hope it helps you mark as brainliest please