The following table shows the number of employees in a company and their ages. Find the mode of the ages.
Age (Years) $35 - 40$ $40 - 45$ $45 - 50$ $50 - 55$ $55 - 60$
No. of Employees $7$ $6$ $9$ $5$ $3$

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Solution

Modal class will be $45 - 50$ due to its highest frequency.
$l_{1} = 45$
$f_{o} = 6$
$f_{1} = 9$
$f_{2} = 5$
$c = 5$
Mode $= l_{1} + \frac{f_{1} - f_{o}}{2 f_{1} - f_{o} - f_{2}} \times c$
$= 45 + \frac{9 - 6}{(18 - 6 - 5)} \times 5 = 45 + \frac{3}{7} \times 5$
$= 45 + \frac{15}{7} = 47.1$ .

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Age in years	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$	$50 - 55$	$55 - 60$
Number of employees	$4$	$16$	$19$	$28$	$22$	$8$	$3$

Age (Years)	36 - 40	41 - 45	46 - 50	51 - 55	56 - 60
No. of Employees	7	6	9	5	3

C.I	$35 - 40$	$40 - 45$	$45 - 50$	$50 - 55$	$55 - 60$
F	$7$	$6$	$9$	$5$	$3$

Age in years	25-30	30-35	35-40	40-45	45-50	50-55	55-60
Number of employees	4	16	19	28	22	8	3

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

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