An SBI health insurance agent found the following data for distribution of ages of $\displaystyle 100$ policy holders. The health insurance policies are given to persons of age $\displaystyle 15$ years and onwards, but less than $\displaystyle 60$ years.

Age (in yrs)	Number of policy holders
$\displaystyle 15$-$\displaystyle 20$	$\displaystyle 2$
$\displaystyle 20$-$\displaystyle 25$	$\displaystyle 4$
$\displaystyle 25$-$\displaystyle 30$	$\displaystyle 18$
$\displaystyle 30$-$\displaystyle 35$	$\displaystyle 21$
$\displaystyle 35$-$\displaystyle 40$	$\displaystyle 33$
$\displaystyle 40$-$\displaystyle 45$	$\displaystyle 11$
$\displaystyle 45$-$\displaystyle 50$	$\displaystyle 3$
$\displaystyle 50$-$\displaystyle 55$	$\displaystyle 6$
$\displaystyle 55$-$\displaystyle 60$	$\displaystyle 2$

Find the modal age and median age of the policy holders.

Age (in years) & f & cf $\displaystyle 15$-$\displaystyle 20$ & $\displaystyle 2$ & $\displaystyle 2$ $\displaystyle 20$-$\displaystyle 25$ & $\displaystyle 4$ & $\displaystyle 6$ $\displaystyle 25$-$\displaystyle 30$ & $\displaystyle 18$ & $\displaystyle 24$ $\displaystyle 30$-$\displaystyle 35$ & $\displaystyle 21$ & $\displaystyle 45$ $\displaystyle 35$-$\displaystyle 40$ & $\displaystyle 33$ & $\displaystyle 78$ $\displaystyle 40$-$\displaystyle 45$ & $\displaystyle 11$ & $\displaystyle 89$ $\displaystyle 45$-$\displaystyle 50$ & $\displaystyle 3$ & $\displaystyle 92$ $\displaystyle 50$-$\displaystyle 55$ & $\displaystyle 6$ & $\displaystyle 98$ $\displaystyle 55$-$\displaystyle 60$ & $\displaystyle 2$ & $\displaystyle 100$ Total & $\displaystyle 100$ &Modal class = $\displaystyle 35$- $\displaystyle 40$ Mode \(\displaystyle =35+\frac{33-21}{2(33)-21-11} \times 5\) \(\displaystyle =\frac{625}{17}=36.7(\) approx.\(\displaystyle )\) ∴ Modal age \(\displaystyle =36.7\) years (approx.) \(\displaystyle \frac{\mathrm{n}}{2}=50\), Median class \(\displaystyle =35-40\) Median \(\displaystyle =35+\frac{50-45}{33} \times 5\)