Question

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

$$x_i$$	$$5$$	$$7$$	$$9$$	$$10$$	$$12$$	$$15$$
$$f_i$$	$$8$$	$$6$$	$$2$$	$$2$$	$$2$$	$$6$$

Answer 1

Correct option is A. $$3.38$$
Computation of mean deviation about mean

$$x_i$$	$$f_i$$	$$x_i\ f_i$$	$$|x_i -9|$$	$$\displaystyle \sum f_i |x_i -9|$$
$$5$$	$$8$$	$$40$$	$$4$$	$$32$$
$$7$$	$$6$$	$$42$$	$$2$$	$$12$$
$$9$$	$$2$$	$$18$$	$$0$$	$$0$$
$$10$$	$$2$$	$$20$$	$$1$$	$$2$$
$$12$$	$$2$$	$$24$$	$$3$$	$$6$$
$$15$$	$$6$$	$$90$$	$$6$$	$$3$$
	$$N=\displaystyle \sum f_i =26$$	$$\displaystyle \sum f_i x_i =234$$		$$=\displaystyle \sum f_i |x_i -9| =88$$

We have, $$N=\displaystyle \sum f_i=26$$, and $$\displaystyle \sum f_i\ x_i=234$$

$$\therefore \ $$ Mean $$=\bar X=\dfrac {1}{N}\displaystyle \sum f_i \ x_i =\dfrac {234}{26}=9$$

Mean deviation $$=\dfrac {1}{N}\displaystyle \sum f_i |x_i -9|=\dfrac {234}{26}=9$$

Mean deviation $$=\dfrac {1}{N}=\displaystyle \sum f_i |x_i -9 =|\dfrac {88}{26}=3.38$$