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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 2 · Set 1 · Q35
An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. The health insurance policies are given to…
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.
Find the modal age and median age of the policy holders.
| Age (in yrs) | Number of policy holders |
| $\displaystyle 15$-$\displaystyle 20$ | $\displaystyle 2$ |
| $\displaystyle 20$-$\displaystyle 25$ | $\displaystyle 4$ |
| $\displaystyle 25$-$\displaystyle 30$ | $\displaystyle 18$ |
| $\displaystyle 30$-$\displaystyle 35$ | $\displaystyle 21$ |
| $\displaystyle 35$-$\displaystyle 40$ | $\displaystyle 33$ |
| $\displaystyle 40$-$\displaystyle 45$ | $\displaystyle 11$ |
| $\displaystyle 45$-$\displaystyle 50$ | $\displaystyle 3$ |
| $\displaystyle 50$-$\displaystyle 55$ | $\displaystyle 6$ |
| $\displaystyle 55$-$\displaystyle 60$ | $\displaystyle 2$ |
Marking-scheme solution
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 \(\displaystyle =35+\frac{50-45}{33} \times 5\)
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CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.