Find the mean deviation and its coefficient about from the following data: | Statistics | SciPiPupil

Question: Find the mean deviation and its coefficient about from the following data:

Class Interval	Above 2	Above 4	Above 6	Above 8
Frequency	12	8	3	1

Solution:

Here,

Interval between two classes (i) = 2. 

Arranging data in a table,

C.I.	Frequency (f)	Mid Value(x)	fx	|x-x̄|	f|x-x̄|
0>2 (2-4)	4	3	12	2	8
>4 (4-6)	5	5	25	0	0
>6 (6-8)	2	7	14	2	4
>8 (8-10)	1	9	9	4	4
	N= 12		$\sum$fx = 60		$\sum$f|x-x̄| = 16

Now,

Mean (x̄) =$\dfrac{\sum fx}{N}$

$= \dfrac{60}{12}$

$= 5$

And,

Mean Deviation from Mean (M.D.) = $\dfrac{\sum f|x-x̄|}{N}$

$= \dfrac{16}{12}$

$= 1.33$

Also,

Coefficient of M.D. = $\dfrac{M.D.}{x̄}$

$= \dfrac{1.33}{5}$

$= 0.266$

$= 0.267$

Hence, the required mean deviation about the mean of the given data is 1.33 and coefficient of mean deviation is 0.267.

Explanation

Here in this question, we have the class interval of 2. The data says 'above' so, we will add add the class interval to the given data. This means, we know the data is above 2 so, it becomes (2+2) = 4. So, this class contains the values (2 - 4). 

And, we have been given cumulative frequency that is in decreasing order. So, this question becomes a little different than the other in which we used to solve with c.f. in ascending order.

Here, to find the frequency of a respective class Interval, we need to subtract the c.f. of the just next class interval from the c.f. of the respective class interval.

For example: to find the frequency of (2-4) in the above data, we subtract the c.f. of the just next class interval i.e. (4-6) which is 8 from the c.f. of the respective class interval i.e. (0-2) which is 12. This mean, frequency of (2-4) is 12-8 = 4.

Similarly, you can find the frequency of the rest of the class interval(s) as well.

Related Notes and Solutions:

Here is the website link to the notes of Statistics of Class 10.

#SciPiPupil