JEE MAIN - Mathematics (2021 - 16th March Morning Shift - No. 10)
Consider three observations a, b, and 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?
b2 = 3(a2 + c2) + 9d2
b2 = 3(a2 + c2) $$-$$ 9d2
b2 = 3(a2 + c2 + d2)
b2 = a2 + c2 + 3d2
Explanation
For a, b, c
mean = $$\overline x = {{a + b + c} \over 3}$$
$$\overline x = {{2b} \over 3}$$
We know, S.D. of a + 2, b + 2, c + 2 = S.D. of a, b, c = d
$${d^2} = {{{a^2} + {b^2} + {c^2}} \over 3} - {{4{b^2}} \over 9}$$
$${b^2} = 3{a^2} + 3{c^2} - 9{d^2}$$
mean = $$\overline x = {{a + b + c} \over 3}$$
$$\overline x = {{2b} \over 3}$$
We know, S.D. of a + 2, b + 2, c + 2 = S.D. of a, b, c = d
$${d^2} = {{{a^2} + {b^2} + {c^2}} \over 3} - {{4{b^2}} \over 9}$$
$${b^2} = 3{a^2} + 3{c^2} - 9{d^2}$$
Comments (0)
