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Mathematics · 2023 · 5 marks
CBSE 2023 · Region 2 · Set 3 · Q32
The mode of the following frequency distribution is 55. Find the missing frequencies 'a' and 'b'.
The mode of the following frequency distribution is 55. Find the missing frequencies 'a' and 'b'.
| Class Interval | $\displaystyle 0$-$\displaystyle 15$ | $\displaystyle 15$-$\displaystyle 30$ | $\displaystyle 30$-$\displaystyle 45$ | $\displaystyle 45$-$\displaystyle 60$ | $\displaystyle 60$-$\displaystyle 75$ | $\displaystyle 75$-$\displaystyle 90$ | Total |
| Frequency | $\displaystyle 6$ | $\displaystyle 7$ | a | $\displaystyle 15$ | $\displaystyle 10$ | b | $\displaystyle 51$ |
Marking-scheme solution
Modal Class: $\displaystyle 45$-$\displaystyle 60$
Mode = $\displaystyle 55$
\(\displaystyle 55=45+\frac{15-\mathrm{a}}{30-(\mathrm{a}+10)} \times 15\)
\(\displaystyle \Rightarrow \mathrm{a}=5\)
\(\displaystyle 6+7+\mathrm{a}+15+10+\mathrm{b}=51\)
\(\displaystyle \Rightarrow \mathrm{a}+\mathrm{b}=13\)
\(\displaystyle \Rightarrow \mathrm{b}=13-5=8\)
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