In the following table, the median age of 200 spectators of a football match is 32 . Find the missing…

Question

In the following table, the median age of $200$ spectators of a football match is $32$. Find the missing frequencies $p$ and $q$.
Age (in years) Number of Spectators
$0-10$ $20$
$10-20$ $p$
$20-30$ $50$
$30-40$ $60$
$40-50$ $32$
$50-60$ $q$

Accepted Answer

Age (in years) Number of consumers Cumulative frequency
$0-10$ $20$ $20$
$10-20$ $p$ $20 + p$
$20-30$ $50$ $70+ p$
$30-40$ $60$ $130 + P$
$40-50$ $32$ $162 + p$
$50-60$ $q$ $162 + p + q$
Total $162 + p + q$
$1$ mark for correct table
$162 + p + q = 200$
$\Rightarrow p + q = 38$ (i)
Median $= 32 \Rightarrow 30-40$ is the median class.
$\Rightarrow 32 = 30 + \frac{(100-70-p)}{60} \times 10$
Solving, we get $p = 18$
From (i), $q = 20$

In the following table, the median age of 200 spectators of a football match is 32 . Find the missing frequencies p…

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