Question

Calculate the mean deviation about the median of the following frequency distribution:

xi	5	7	9	11	13	15	17
fi	2	4	6	8	10	12	8

Answer 1

We will first calculate the median for the data. 

 

\[x_i\]	fi	Cumulative Frequency	\[\left| d_i \right| = \left| x_i - 13 \right|\]	\[f_i \left| d_i \right|\]
5	2	2	8	16
7	4	6	6	24
9	6	12	4	24
11	8	20	2	16
13	10	30	0	0
15	12	42	2	24
17	8	50	4	32
	\[N = \Sigma f_i = 50\]			\[\sum^n_{i = 1} f_i \left| d_i \right| = 136\]

Here,

\[\frac{N}{2} = \frac{50}{2} = 25\]

The cumulative frequency just greater than 25 is 30 and the corresponding value of x is 13.

\[\therefore \text{ Median }, M = 13\]

\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| d_i \right|\]
\[ = \frac{1}{50} \times 136\]
\[ = 2 . 72\]