First slide

Introduction to statistics

Question

Let the data $4, 10, x, y, 27$ be in increasing order. If the median of the data is $18$ and its mean deviation about mean is $7.6,$ then the mean of this data, is

Moderate

A

$7$
B

$16$
C

$16.5$
D

$15.5$

Solution

The median of the given data is $x$ and it is given that the median is $18 .$ Therefore, $x = 18 .$ Let $X$ be the mean. It is given that the mean deviation about mean is $7.6$ and mean is less than the median i.e. $X < 18 .$
$∴ \bar{X} = \frac{4 + 10 + 18 + y + 27}{5}$
and $\frac{(\bar{X} - 4) + (\bar{X} - 10) + (18 - \bar{X}) + (y - \bar{X}) + (27 - \bar{X})}{5} = 7.6$
$\begin{array}{l} \Rightarrow 5 \bar{X} - y = 59 and, y - \bar{X} = 7 \\ \Rightarrow \bar{X} = 16.5 \end{array}$

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