Question

●The median of the following data is 50.find the value of pand q , if the sum of all the frequency is 90​

Answer 1

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Given :The median of the data is 50 and sum of all the frequencies is 90.

To Find :Find the values of p and q.

Solution :

Marks Frequency cf

20-30 p p

30-40 15 15+p

40-50 25 40+p

50-60 20 60+p

60-70 q 60+p+q

70-80 8 68+p+q

80-90 10 78+p+q

Median = 50

Sum of all frequency = p + 15 + 25 + 20 + q + 8 + 10 = 90

p + q = 90 - 78

p + q = 12

Now we will find the value of p and q by using the formula,

Median=L+\frac{\frac{n}{2}-cf }{f}\times cMedian=L+

f

2

n

−cf

×c

50=40+\frac{\frac{90}{2}-(15+p) }{25}\times 1050=40+ 25290−(15+p) ×10

50=40+\frac{45-(15+p)}{25}\times 1050=40+ 2545−(15+p)×10

50=40+(\frac{-2}{5}p) +5250=40+( 5−2p+52

50=\frac{-2}{5}p +5250= 5−2 p+52\frac{-2}{5}p=-25−2

p=−2

p = 5

∵ p + q = 12

put the value of p

5 + q = 12

q = 12 - 5

q = 7

value of p = 5 and q = 7

Step-by-step explanation:

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