An age-wise list of number of literate people in a block is prepared in the following table. There are total…

Question

An age-wise list of number of literate people in a block is prepared in the following table. There are total $100$ people and their median age is $41.5$ years. Information about two groups are missing, which are denoted by $x$ and $y$. Find the value of $x$ and $y$.
Age (in years) Number of literate people
$10-20$ $15$
$20-30$ $x$
$30-40$ $12$
$40-50$ $20$
$50-60$ $y$
$60-70$ $8$
$70-80$ $10$

Accepted Answer

Age (in years) Number of literate people ($f_i$) Cumulative frequency
$10-20$ $15$ $15$
$20-30$ $x$ $15 + x$
$30-40$ $12$ $27 + x$
$40-50$ $20$ $47 + x$
$50-60$ $y$ $47 + x + y$
$60-70$ $8$ $55 + x + y$
$70-80$ $10$ $65 + x + y$
$65 + x + y = 100$
$\Rightarrow x + y = 35$ ...(i)
Median $= 41.5$
$40-50$ is the median class.
$\Rightarrow 41.5 = 40 + \frac{\frac{100}{2}-27-x}{20} \times 10$
Solving, we get $x = 20$
From (i), $y = 15$

An age-wise list of number of literate people in a block is prepared in the following table. There are total 100…

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