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Mathematics · 2024 · 5 marks
CBSE 2024 · Region 4 · Set 1 · Q35
The following table shows the ages of the patients admitted in a hospital during a year : Age (in years) $\displaystyle 5$-$\displaystyle 15$ $\displaystyle 15$-$\displaystyle 25$ $\displaystyle 25$-$\displaystyle 35$ $\displaystyle 35$-$\displaystyle 45$ $\displaystyle 45$-$\displaystyle 55$ $\displaystyle 55$-$\displaystyle 65$ Number of patients $\displaystyle 6$ $\displaystyle 11$ $\displaystyle 21$ $\displaystyle 23$ $\displaystyle 14$ $\displaystyle 5$
Find the mode and mean of the data given above.
| Age (in years) | $\displaystyle 5$-$\displaystyle 15$ | $\displaystyle 15$-$\displaystyle 25$ | $\displaystyle 25$-$\displaystyle 35$ | $\displaystyle 35$-$\displaystyle 45$ | $\displaystyle 45$-$\displaystyle 55$ | $\displaystyle 55$-$\displaystyle 65$ |
| Number of patients | $\displaystyle 6$ | $\displaystyle 11$ | $\displaystyle 21$ | $\displaystyle 23$ | $\displaystyle 14$ | $\displaystyle 5$ |
Marking-scheme solution
| Age (in years) | No. of patients \(\displaystyle \left(\boldsymbol{f}_{\boldsymbol{i}}\right)\) | Mid point \(\displaystyle \left(\boldsymbol{x}_{\boldsymbol{i}}\right)\) | \(\displaystyle \boldsymbol{x}_{\boldsymbol{i}} \boldsymbol{f}_{\boldsymbol{i}}\) |
| $\displaystyle 5$-$\displaystyle 15$ | $\displaystyle 6$ | $\displaystyle 10$ | $\displaystyle 60$ |
| $\displaystyle 15$-$\displaystyle 25$ | $\displaystyle 11$ | $\displaystyle 20$ | $\displaystyle 220$ |
| $\displaystyle 25$-$\displaystyle 35$ | $\displaystyle 21$ | $\displaystyle 30$ | $\displaystyle 630$ |
| $\displaystyle 35$-$\displaystyle 45$ | $\displaystyle 23$ | $\displaystyle 40$ | $\displaystyle 920$ |
| $\displaystyle 45$-$\displaystyle 55$ | $\displaystyle 14$ | $\displaystyle 50$ | $\displaystyle 700$ |
| $\displaystyle 55$-$\displaystyle 65$ | $\displaystyle 5$ | $\displaystyle 60$ | $\displaystyle 300$ |
| Total | $\displaystyle 80$ | $\displaystyle 2830$ |
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CBSE Class 10 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.