Question

Find the mean deviation about the median for the data in the following:-
$x_i$ 5 7 9 10 12 15
$f_i$ 8 6 2 2 2 6

Answer 1

$xi$ $fi$ $fixi$ $\left|xi-\overline{x}\right|$ $fi\left|xi-\overline{x}\right|$

5 8 40 $\left|5-9\right|=4$ 32

7 6 42 2 12

9 2 18 0 0

10 2 20 1 2

11 2 24 3 6

12 6 90 6 36

$\overline{26}$ $\overline{254}$ $\overline{\sum =88}$

$Mean\left(x\right)=\frac{\sum fixi}{\sum fi}=\frac{234}{26}=9$

Mean Deviation about mean $=\frac{\sum fi\left|xi-\overline{x}\right|}{\sum fi}=\frac{88}{26}=3.384$