Question

Find the mean deviation about the median for the following continuous distribution:

Marks obtained	0-10	10-20	20-30	30-40	40-50	50-60
No. of body	6	8	14	16	4	2

Answer 1

Class $(fi-hi)$	frequency $fi$	cumulative frequency $cfi$	Midpoint $(l+h)/2$	$fi|xi-M|$
$0-10$	6	6	5	137.16
$10-20$	8	6+8=14	15	102.88
$\to 20-30$	14	14+14=28	25	40.04
$30-40$	16	28+16=44	35	114.24
$40-50$	4	44+4=48	45	68.56
$50-60$	2	48+2=50	55	54.28

$N=\sum fi=50$ $\sum fi|xi-M|=517.16$

Here, $\frac{N}{2}=\frac{50}{2}=25$, which lies in the class 20-30

Therefore the median class is 20-30.

$\therefore$ Median, $M=l+\frac{\frac{N}{2}-cf}{f}\times h$

where $l$ is the lower limit of the median class.

$cf$ is the cumulative frequency of the class interval proceeding the median class.

$f$ is the frequency of median class.

$h$ is the width of the median class.

$\therefore M=20+\frac{25-14}{14}\times 10$

$=20+\frac{11}{14}\times 10$

$=20+\frac{55}{7}$

$\Rightarrow M=27.86$ (approx)

mean deviation about median = $\frac{\sum fi|xi-M|}{\sum fi}$

$=\frac{517.16}{50}$

$=10.343$ (approx)