First slide

Introduction to statistics

Question

If the mean deviations about the median of the numbers a, 2a, . . . ,50a is 50, then $| a |$ is equal to

Easy

A

3
B

4
C

5
D

2

Solution

Median a, 2a, . . . , 50 is $\frac{25 a + 26 a}{2} = (25 .5) a$
Mean deviation about median $= \frac{\sum_{i = 1}^{50} ∣ x_{i} - median ∣}{n}$
$\begin{array}{l} \Rightarrow 50 = \frac{1}{50} {2 | a | \cdot (0 .5 + 1 .5 + 2 .5 + \dots + 24 .5)} \\ \Rightarrow 2500 = 2 | a | \frac{25}{2} (2 \times 0 .5 + 24 \times 1) = 2 | a | \cdot \frac{25}{2} (25) \\ \Rightarrow | a | = 4 \end{array}$

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