Question

In a series of 2m observations half of them equal to b and remaining half equal to – b. If the standard deviation of the observations is 3 then |b| = ________

(a) 3

(b) √3

(c) (√3/n)

(d) (1/n)

Answer 1

The correct option (a) 3   

Explanation:

m observation have value = b and m have value = – b.

∴ Mean = [{bm + (– b)m}/2m] = 0  

i.e. x = 0

Standard deviation = √[{∑(xi – x)²}/2n]

∴ 3 = √[{(b – 0)² + (b – 0)² + ----- (0 – b)² + (0 – b)² + -----}/2n]

∴ 3 = √[{b² ∙ (2n)}/2n]

∴ |b| = 3.