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The median of the following data is $50$ and sum of all frequencies is $90$ :
Class: $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$
Frequency: $p$ $15$ $25$ $20$ $q$ $8$ $10$
Find the values of $p$ and $q$.
Class: $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$
Frequency: $p$ $15$ $25$ $20$ $q$ $8$ $10$
Find the values of $p$ and $q$.
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Correct table (1.5 Marks)
Median Class = $50 – 60$ (1/2 Mark)
$\therefore 50 = 50 + \frac{10}{20} (\frac{90}{2} - p - 40)$ (1 Mark)
$\Rightarrow p = 5$ (1/2 Mark)
As, $p + q + 78 = 90$ (1 Mark)
$\Rightarrow 5 + q = 12$
$\therefore q = 7$ (1/2 Mark)
Median Class = $50 – 60$ (1/2 Mark)
$\therefore 50 = 50 + \frac{10}{20} (\frac{90}{2} - p - 40)$ (1 Mark)
$\Rightarrow p = 5$ (1/2 Mark)
As, $p + q + 78 = 90$ (1 Mark)
$\Rightarrow 5 + q = 12$
$\therefore q = 7$ (1/2 Mark)