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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 3 · Set 1 · Q3
Find the mode of the given frequency distribution : Class Frequency $\displaystyle 15$-$\displaystyle 25$ $\displaystyle 6$ $\displaystyle 25$-$\displaystyle 35$ $\displaystyle 11$ $\displaystyle 35$-$\displaystyle 45$ $\displaystyle 22$ $\displaystyle 45$-$\displaystyle 55$ $\displaystyle 23$ $\displaystyle 55$-$\displaystyle 65$ $\displaystyle 14$ $\displaystyle 65$-$\displaystyle 75$ $\displaystyle 5$
| Class | Frequency |
| $\displaystyle 15$-$\displaystyle 25$ | $\displaystyle 6$ |
| $\displaystyle 25$-$\displaystyle 35$ | $\displaystyle 11$ |
| $\displaystyle 35$-$\displaystyle 45$ | $\displaystyle 22$ |
| $\displaystyle 45$-$\displaystyle 55$ | $\displaystyle 23$ |
| $\displaystyle 55$-$\displaystyle 65$ | $\displaystyle 14$ |
| $\displaystyle 65$-$\displaystyle 75$ | $\displaystyle 5$ |
Marking-scheme solution
Modal class is $\displaystyle 45$-$\displaystyle 55$
\[\begin{array}{l}
\text { Mode }=45+10 \times \frac{23-22}{46-22-14} \\
=46
\end{array}
\]
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