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Mathematics · 2024 · 4 marks
CBSE 2024 · Region 5 · Set 1 · Q38
Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop…
Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run $\displaystyle 100$ m , was noted as follows :
| Time (in seconds) | $\displaystyle 0$-$\displaystyle 20$ | $\displaystyle 20$-$\displaystyle 40$ | $\displaystyle 40$-$\displaystyle 60$ | $\displaystyle 60$-$\displaystyle 80$ | $\displaystyle 80$-$\displaystyle 100$ |
| Number of students | $\displaystyle 8$ | $\displaystyle 10$ | $\displaystyle 13$ | $\displaystyle 6$ | $\displaystyle 3$ |
(i)
What is the median class of the above given data ?
(ii)
(a)
Find the mean time taken by the students to finish the race.
OR
(b)
Find the mode of the above given data.
(iii)
How many students took time less than $\displaystyle 60$ seconds?
Marking-scheme solution
(i)
Correct Cummulative Frequency
Median class $\displaystyle =40-60$
(ii)(a)
Correct table for $\displaystyle \mathrm{x}_{\mathrm{i}}$ and $\displaystyle \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}$
\[\text { Mean }=\frac{1720}{40}=43
\]
OR
(b)
Modal class = $\displaystyle 40$-$\displaystyle 60$
\[\begin{aligned}
\text { Mode } & =40+\frac{(13-10)}{(26-10-6)} \times 20 \\
& =46
\end{aligned}
\]
(iii)
$\displaystyle 31$ students took time less than $\displaystyle 60$ seconds
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CBSE Class 10 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.