First slide

Introduction to statistics

Question

The mean deviation of an ungrouped data is 50. If each observation is increased by 2%, then the new mean deviation is

Easy

A

50
B

51
C

49
D

50.5

Solution

If $x_{1} \dots x_{n}$ are the observations then the new
observations are $(1.02) x_{1}, (1.02) x_{2} . ., (1.02) x_{n}$
Therefore the new mean $= (1.02) \bar{x}$
New mean deviation $= \frac{1}{n} \sum |(1.02) x_{i} - (1.02) \bar{x}|$
$\begin{array}{l} = (1.02) \frac{1}{n} \sum |x_{i} - \bar{x}| \\ = (1.02) \times 50 = 51 \end{array}$

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