Question

The median of the following data is 50. Find the values of p and q,if the sum of all the frequencies is 90.

Answer 1

Hope this helps

Mark Brainliest if useful

Answer 2

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,

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

$50=40+\frac{\frac{90}{2}-(15+p) }{25}\times 10$

$50=40+\frac{45-(15+p)}{25}\times 10$

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

$50=\frac{-2}{5}p +52$

$\frac{-2}{5}p=-2$

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