Question

The mean deviation of an ungrouped data is 150. If each observation is increased by 3.5%, then what is the new mean deviation?

(a) 153.5

(b) 3.5

(c) 155.25

(d) 150

I had been asked this question in homework.

My doubt stems from Statistics in section Statistics of Mathematics – Class 11

Answer 1

Right choice is (c) 155.25

Explanation: If x1, x2, …, xn are the observations, then the new observations are (1.035) x1, (1.035) x2, ……, (1.035) xn.

Therefore, the new mean is (1.035) x̄

Now, Mean deviation = \(\frac{1}{n}\)[Σi = n |xI – mean|]

⇒ New mean deviation = \(\frac{1}{n}\)[Σi = n|(1.035)xI – (1.035) x̄|] = (1.035) × \(\frac{1}{n}\)[Σi = n |xI – mean|] = 1.035 x 150 = 155.25.