Q77 / 160 · TS EAMCET 2021 (04 Aug Shift 1) · Mathematics

If $10$ is the mean of the data $2, 3, 5, 18, 17, 15, 13, x, 9$ and $7,$ then the mean deviation of this data about its mean is

A
$4.7$
Correct answer
B
$4.8$
C
$4.9$
D
$5.0$

Solution

Mean $= \bar{x} = 10 = \frac{2 + 3 + 5 + 18 + 17 + 15 + 13 + x + 9 + 7}{10}$

$\Rightarrow x = 11$

$\begin{matrix} \end{matrix}$ $\begin{matrix} x_{i} & |x_{i} - \bar{x}| \\ 2 & 8 \\ 3 & 7 \\ 5 & 5 \\ 18 & 8 \\ 17 & 7 \\ 15 & 5 \\ 13 & 3 \\ 11 & 1 \\ 9 & 1 \\ 7 & 3 \end{matrix}$

Mean Deviation $= \frac{\sum_{i = 1}^{10} |x_{i} - \bar{x}|}{10} = \frac{48}{10} = 4.8$

Hence, the correct answer is option: 'B'.

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Solution

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