Question

Calculate the mean and median for the folllowing data:

Marks	:	10	11	12	13	14	16	19	20
Number of students	:	3	5	4	5	2	3	2	1

Using empirical formula, find its mode.

Answer 1

Calculation of Mean

Marks (xi)	10	11	12	13	14	16	19	20	Total
Number of Students (fi)	3	5	4	5	2	3	2	1	$\sum _{}{f}_i$ = 25
fixi	30	55	48	65	28	48	38	20	$\sum _{}{f}_i{x}_i$ = 332

Mean = $\frac{\sum _{}{f}_i{x}_i}{\sum _{}{f}_i}=\frac{332}{25}=13.28$
Here, n = 25, which is an odd number. Therefore,
Median = Value of ${\left(\frac{n+1}{2}\right)}^{th}$ observation = the 13^th observation = 13.
Now,
Mode = 3 Median - 2 Mean

$\Rightarrow$Mode = 3 x 13 - 2 x (13.28)
$\Rightarrow$Mode = 39 - 26.56
$\Rightarrow$Mode = 12.44.