Question

Find the mean deviation from the median for the following data:

$$x_i$$	$$15$$	$$21$$	$$27$$	$$30$$
$$f_i$$	$$3$$	$$5$$	$$6$$	$$7$$

Answer 1

Correct option is A. $$5.93$$

$$x_i$$	$$f_i$$	$$C.F$$	$$X_i-30$$	$$f_i|Xi-30|$$
15	3	3	15	45
21	5	8	9	45
27	6	14	7	42
30	7	21	0	0
35	8	29	5	40
	$$\displaystyle \sum f_i=29$$			$$\sum f_i|X_i-30|=172$$

We have $$N=29$$

$$\Rightarrow \dfrac{N}{2}=29$$

$$\Rightarrow N=14.5$$

The cumulative frequency just greater than $$\dfrac{N}{2}$$ i.e, $$14.5$$ is

$$21$$. The corresponding value ob variable is $$30$$. So median $$=30$$

Mean deviation $$\displaystyle =\dfrac{1}{N}\sum f_i|x_i-30|$$

$$=\dfrac{172}{29}$$

$$=5.93$$

$$\therefore$$ The given answer is correct.