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Mathematics · 2024 · 4 marks
CBSE 2024 · Region 3 · Set 1 · Q37
Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with…
Vocational training complements traditional education by providing practical skills and hands-on experience. While education equips individuals with a broad knowledge base, vocational training focuses on job-specific skills, enhancing employability thus making the student self- reliant. Keeping this in view, a teacher made the following table giving the frequency distribution of students/adults undergoing vocational training from the training institute.
| Age (in years) | $\displaystyle 15$-$\displaystyle 19$ | $\displaystyle 20$-$\displaystyle 24$ | $\displaystyle 25$-$\displaystyle 29$ | $\displaystyle 30$-$\displaystyle 34$ | $\displaystyle 35$-$\displaystyle 39$ | $\displaystyle 40$-$\displaystyle 44$ | $\displaystyle 45$-$\displaystyle 49$ | $\displaystyle 50$-$\displaystyle 54$ |
| Number of participants | $\displaystyle 62$ | $\displaystyle 132$ | $\displaystyle 96$ | $\displaystyle 37$ | $\displaystyle 13$ | $\displaystyle 11$ | $\displaystyle 10$ | $\displaystyle 4$ |
(i)
What is the lower limit of the modal class of the above data ?
(ii)
(a)
Find the median class of the above data.
OR
(b)
Find the number of participants of age less than $\displaystyle 50$ years who undergo vocational training.
(iii)
Give the empirical relationship between mean, median and mode.
Marking-scheme solution
(i)
Modal class is $\displaystyle 19.5$-$\displaystyle 24.5$ Lowe limit =$\displaystyle 19.5$
(ii)(a)
| Age (in years) | $\displaystyle 14.519.5$ | $\displaystyle 19.524.5$ | $\displaystyle 24.529.5$ | $\displaystyle 29.534.5$ | $\displaystyle 34.539.5$ | $\displaystyle 39.544.5$ | $\displaystyle 44.549.5$ | $\displaystyle 49.554.5$ |
| Number of participa nts | $\displaystyle 62$ | $\displaystyle 132$ | $\displaystyle 96$ | $\displaystyle 37$ | $\displaystyle 13$ | $\displaystyle 11$ | $\displaystyle 10$ | $\displaystyle 4$ |
| \(\displaystyle c f\) | $\displaystyle 62$ | $\displaystyle 194$ | $\displaystyle 290$ | $\displaystyle 327$ | $\displaystyle 340$ | $\displaystyle 351$ | $\displaystyle 361$ | $\displaystyle 365$ |
\[\frac{n}{2}=\frac{365}{2}=182.5
\]
median class \(\displaystyle =19.5-24.5\)
OR
(ii) (b) \(\displaystyle 62+132+96+37+13+11+10=361\)
(iii) $\displaystyle 3$ median = mode +$\displaystyle 2$ mean
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