Question

The following table shows the age distribution of cases of a certain disease reported during a year in a particular city.

Age in years	$5-14$	$15-24$	$25-34$	$35-44$	$45-54$	$55-64$
No. of cases	$6$	$11$	$12$	$10$	$7$	$4$

Obtain the mean, median and mode of the above data.

Answer 1

Convert closed intervals to open intervals.

Age	Mid Point ($x_i$)	Cases ($f_i$)	Cumulative Frequency (c.f.)
4.5-14.5	9.5	6	6
14.5-24.5	19.5	11	17
24.5-34.5	29.5	12	29
34.5-44.5	39.5	10	39
44.5-54.5	49.5	7	46
54.5-64.5	59.5	4	50=n

$N=50;h=10$

mean$=\frac{\sum f_i{x}_i}{\sum f_i}$

$=\frac{9.5\left(6\right)+19.5\left(11\right)+29.5\left(12\right)+39.5\left(10\right)+49.5\left(7\right)+59.5\left(4\right)}{50}=32.1$

$\frac{N}{2}=25,l=24.5,c=17,f=12$

median$=l+\frac{h}{f}\times (\frac{n}{2}-c)$

$=24.5+\frac{10}{12}\times 8$

$=31.167$

$\approx 31.2$ years

mode$=L+\frac{f_m-f_{m-1}}{2f_m-f_{m-1}-f_{m+1}}\times n$

$l=24.5;h=10;f_m=12;f_{m-1}=11;f_{m+1}=10$

mode$=24.5+\frac{1}{3}\times 10$

$=27.83$ years