Statistics · Question 18

Let the mean and the standard deviation of the observations 2, 3, 3, 4, 5, 7, a, b be 4 and 2 respectively. Then the mean deviation about the mode of these observations is :

1. 12
2. 34
3. 1
4. 2

Answer

(3) 1

Solution

Mean = 4 2 + 3 + 3 + 4 + 5 + 7 + a + b = 8 4 = 32

24 + a + b = 32 a + b = 8

Variance = xi28 - (mean)2 = 2

xi2 = 8(2 + 16) = 144

4 + 9 + 9 + 16 + 25 + 49 + a2 + b2 = 144 a2 + b2 = 32

2ab = (a + b)2 - (a2 + b2) = 64 - 32 = 32 ab = 16

(a - b)2 = 64 - 64 = 0 a = b = 4

Observations: 2, 3, 3, 4, 4, 4, 5, 7 mode = 4

|xi - 4| = 2 + 1 + 1 + 0 + 0 + 0 + 1 + 3 = 8

Mean deviation about mode = 88 = 1

Answer: (3)