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#### The median of the following data is 50. Find the values of p and q, if the sum of all the frequencies is 90. Marks Frequency 20-30 30-40 40-50 50-60 60-70 70-80 80-90 p 15 25 20 q 8 10

Solution.

 marks Frequency Cummulative frequency 20-30 1 p 30-40 15 15+p 40-50 25 40+p = cf 50-60 20=f 60+p 60-70 q 68+p+q 70-80 8 68+p+q 80-90 10 78+p+q

n = 90, $\frac{n}{2}= 45$
l = 50, f = 20, cf = 40 + p, h = 10
median = $l+\frac{\left ( \frac{n}{2}-cf \right )}{f}\times h$

$50= 50+\frac{\left ( 45-40-p \right )}{20}\times 10$

$0= \frac{5-p}{2}$
5 – p = 0
p = 5
78 + 5 + q = 90
q = 90 – 83
q = 7