Question

find the values of f1 and f2​

Answer 1

Step-by-step explanation:

Median 49.2 lies in the class 40 - 50

Hence, 40 - 50 is the median class.

$\therefore \: L = 40, f = 25, c.f. =f_1 + 15, \: h = 10 \\ N = f_1 +f_2 + 78 \\ Also, \: N = \Sigma f_i = 90 \\ \therefore \: f_1 +f_2 + 78 = 90 \\ \therefore \: f_1 +f_2 = 90 - 78 \\ \therefore \: f_1 +f_2 = 12 \\ median = L + ( \frac{ \frac{N}{2} - cf}{f} ) \times h \\ \therefore \: 49.2 = 40 + \frac{ \frac{90}{2} - (f_1 + 15)}{25} ) \times 10 \\ \therefore49.2 - 40 = \frac{45 -f_1 - 15 }{25} \times 10 \\ \therefore \: 9.2 \times 25 = (30 -f_1 ) \times 10 \\ \therefore \: 230 = (30 -f_1 ) \times 10 \\ \therefore \: 23 = (30 -f_1 ) \\ \therefore \:f_1 = 30 - 23 \\ \huge \red{ \boxed{\therefore \:f_1 = 7}} \\ \implies \: 7 + f_2 =12 \\ \implies \: f_2 =12 - 7 \\ \huge \red{ \boxed{\implies \: f_2 =5}}$