Question

The number of telephone calls received at an exchange in 245 successive one-minute intervals are shown in the following frequency distribution:

Number of calls	0	1	2	3	4	5	6	7
Frequency	14	21	25	43	51	40	39	12

Compute the mean deviation about median.

Answer 1

We will first calculate the median.

$x_i$	fi	Cumulative Frequency	$\left|d_i\right|=\left|x_i-4\right|$	$f_i\left|d_i\right|$
0	14	14	4	56
1	21	35	3	63
2	25	60	2	50
3	43	103	1	43
4	51	154	0	0
5	40	194	1	40
6	39	233	2	78
7	12	245	3	36
	$N=\Sigma f_i=245$			$\sum _{i=1}^n{f}_i\left|d_i\right|=366$

Here,
$\frac{N}{2}=\frac{245}{2}=122.5$

The cumulative frequency just greater than 122.5 is 154 and the corresponding value of x is 4.

∴ $Median,M=4$

$MD=\frac{1}{N}\sum _{i=1}^n{f}_i\left|d_i\right|=\frac{1}{245}\times 366=1.493$