Question

The following table shows the ages of the patients admitted in a hospital during a year:

Age (in years)	5-15	15-25	25-35	35-45	45-55	55-65
No. of patients	6	11	21	23	14	5

Find the mean of the data given above.

• A. $33.42$ years
• B. $35.37$ years
• C. $37.15$ years
• D. None of these

Answer 1

The correct option is B $35.37$ years

Let us find the mean of the data:

Age (in years)	Number of patients $f_i$	Class mark $x_i$	$u_i=\frac{x_i-30}{10}$	$f_i\times u_i$
5-15	6	10	-2	-12
15-25	11	20	-1	-11
25-35	21	$30-a$	0	0
35-45	23	40	1	23
45-55	14	50	2	28
55-65	5	60	3	15
Total	$n=80$			43

$a=30,h=10,n=80$ and $\sum f_i{u}_i=43$
Mean $=a+h\times \frac{1}{n}\times \sum f_i{u}_i=30+10\times \frac{1}{80}\times 43$
$=30+5.37=35.37$ years
Thus mean $=35.37$ years.