If mean of observations x1, x2, x3 and x4 is x and difference of first three observations with respect to x is respectively – 1, – 3, – 5 then difference of fourth observation with respect to x is ___
(a) 8
(b) 9
(c) 10
(d) 11
The correct option (b) 9
Explanation:
x = [(x1 + x2 + x3 + x4)/4]
also (x1 – x) = – 1, (x2 – x) = – 3, (x3 – x) = – 5,
Now ∑(xi – x) = 0
∴ (x1 – x) + (x2 – x) + (x3 – x) + (x4 – x) = 0
∴ – 1 – 3 – 5 = – (x4 – x)
∴ 9 = x4 – x
∴ x4 – x = 9.
