Question

Find the mean deviation from mean of the observations: a, a+d, …., (a+2nd).

(a) n(n + 1)d^2/3

(b) n(n + 1)d^2/2

(c) a + n(n + 1)d^2/2

(d) n(n + 1)d/(2n + 1)

I have been asked this question in an interview for job.

This interesting question is from Statistics in division Statistics of Mathematics – Class 11

Answer 1

Right answer is (d) n(n + 1)d/(2n + 1)

To elaborate: Mean = \(\frac{1}{n}\) Σ xi = \(\frac{1}{2n+1}\) [a + (a + d) + … + (a + 2nd)] = a + nd

⇒ Mean Deviation = \(\frac{1}{2n+1}\) [2 × d × (1 + 2 + … + n)] = [n (n + 1) (d)]/(2n + 1).