$x_{i}$ $3$ $5$ $7$ $9$ $11$ $13$
$f_{i}$ $6$ $8$ $15$ $3$ $8$ $4$
Find the Mean Deviation (M.D) about the median.

2.32

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2.12

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2.65

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2.73

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Solution

The correct option is A $2.32$
Total Frequency, $N = \sum f_{i} = 44$ .
Mean, $u = \frac{(\sum f_{i} \times x_{i})}{N} = \frac{330}{44} = 7.5$
$x_{i}$ $3$ $5$ $7$ $9$ $11$ $13$
$f_{i}$ $6$ $8$ $15$ $3$ $8$ $4$
$C . F$ $6$ $14$ $29$ $32$ $40$ $44$

Thus $N = 44$ , even.
$M = \frac{22^{n d} + 23^{r d}}{2}$ observations.
$∴ M = \frac{7 + 7}{2} = 7$
Now deviations $f_{i} \times | x_{i} - M |$ are,
$| x_{i} - M |$ $4$ $2$ $0$ $2$ $4$ $6$
$f_{i}$ $6$ $8$ $15$ $3$ $8$ $4$
$f_{i} \times | x_{i} - M |$
$24$ $16$ $0$ $6$ $32$ $24$

$∴ M D (M) = \frac{(\sum f_{i} \times | x_{i} - M |)}{N} = \frac{102}{44} = 2.32$
Thus, $M D (M) = 2.32$
Ans-Option $A$ .

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