Statistics · Question 19

Let the Mean and Variance of five observations x1 = 1, x2 = 3, x3 = a, x4 = 7 and x5 = b, a > b, be 5 and 10 respectively. Then the Variance of the observations n + xn, n = 1, 2, , 5 is

1. 17
2. 16
3. 16.4
4. 17.4

Answer

(2) 16

Solution

Mean = 5: 1 + 3 + a + 7 + b = 25 a + b = 14

Variance = 10: xi25 - 52 = 10 xi2 = 175

1 + 9 + a2 + 49 + b2 = 175 a2 + b2 = 116

2ab = 142 - 116 = 80 ab = 40

a = 10, b = 4 (as a > b)

New observations n + xn: 2, 5, 13, 11, 9

Mean = 405 = 8

y2 = 4 + 25 + 169 + 121 + 81 = 400

Variance = 4005 - 82 = 80 - 64 = 16

Answer: (2)