Question

The number of telephone calls received at an exchange in 245 successive on2-minute intervals is 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 the median.

Answer 1

To find the mean deviation from the median, firstly let us calculate the median.

We know, Median is the even term, (3 + 5)/2 = 4

So, Median = 8

Let x_i =Number of calls

And, f_i = Frequency

xi	fi	Cumulative Frequency	|di| = |xi – M| = |xi – 61|	fi |di|
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
				Total = 366
	Total = 245

N = 245

MD = 1/n ∑ⁿ_i=1|d_i|

= 1/245 × 336

= 1.49

∴ The mean deviation is 1.49.