Question

Calculate mean deviation from the median of the following data: 

Class interval:	0–6	6–12	12–18	18–24	24–30
Frequency	4	5	3	6	2

Answer 1

Calculation of mean deviation about the median. 

Class Interval	Mid-Values (xi)	Frequency (fi)	Cummulative Frequency (c.f.)	\[\left| x_i - 14 \right|\]	\[f_i \left| x_i - 14 \right|\]
0–6	3	4	4	11	44
6–12	9	5	9	5	25
12–18	15	3	12	1	3
18–24	21	6	18	7	42
24–30	27	2	20	13	26
		N = 20			\[\sum f_i| x_i - 14 | = 140\]

Here, N = 20. So,

\[\frac{N}{2} = 10\] The cummulative frequency just greater than \[\frac{N}{2}\]  is 12. Thus, 12–18 is the median class.

 

Now, l = 12, h = 6, f = 3 and F = 9

\[\therefore \text{ Median } = l + \frac{\frac{N}{2} - F}{f} \times h = 12 + \left( \frac{10 - 9}{3} \right) \times 6 = 14\]

Now,

Mean deviation about median = \[\frac{1}{N}$\sum_{} f_i \left| x_i - 14 \right| = \frac{1}{20} \times 140 = 7\]