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

 

Answers (1)

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

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