Question

Consider three observations a, band c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?

विकल्प

• b² = a² + c² + 3d²

• b² = 3(a² + c²) – 9d²

• b² = 3(a² + c²) + 9d²

• b² = 3(a² + c² + d²)

Answer 1

`bb(b^2 = 3(a^2 + c^2) - 9d^2)`

Explanation:

For three observations a, b and c,

Mean `(barx) = (a + b + c)/3`

Also given that b = a + c

`(barx) = (2b)/3`  ...(i)

Also given that standard deviation of (a + 2), (b + 2) and (c + 2) is d.

S.D. (a + 2, b + 2, c + 2) = d

S.D. (a, b, c) = d

d² = `(a^2 + b^2 + c^2)/3 - (barx)^2`; S.D. = `sqrt((sumx^2)/n - (barx)^2`

d² = `(a^2 + b^2 + c^2)/3 - ((2b)/3)^2`

d² = `(3(a^2 + b^2 + c^2) - 4b^2)/9`

9d² = 3(a² + b² + c²) – 4b²

9d² = 3(a² + c²) + 3b² – 4b²

9d² = 3(a² + c²) – b²

b² = 3(a² + c²) – 9d²