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
	\[N = \Sigma f_i = 245\]			\[\sum^n_{i = 1} f_i \left| d_i \right| = 366\]

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.

∴  \[\text{Median,} M = 4\]

\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| d_i \right| = \frac{1}{245} \times 366 = 1 . 493\]