Question

mean of following distribution is 50. find the value of 'b' & hence find the frequency of 30 &70
x- 10 30 50 70 90
f- 17 (5b+3) 32 (7b-11) 19

Answer 1

Dear student

x :	10	30	50	70	90
f :	17	5b + 3	32	7b – 11	19

Calculation of Arithmetic mean

x	f	xf
10	17	170
30	5b + 3	150b + 90
50	32	1600
70	7b – 11	990b – 770
90	19	1710
	N=Σy = 12b + 60	Σxy = 640b + 2800

Given mean = 50

$$\begin{gathered} \mathrm{Therefore},\mathrm{Mean}=50=\frac{{\displaystyle \sum _{}}\mathrm{xf}}{{\displaystyle \sum _{}}\mathrm{f}} \\ \Rightarrow \frac{640\mathrm{b}+2800}{12\mathrm{b}+60}=50 \end{gathered}$$

640b + 2800 = 600b + 3000

⇒ 40b = 200

⇒ b = 5

∴ The frequency of 30 = 5b + 3 = 5(5) + 3 = 28

and the frequency of 70 = 7b – 11 = 7(5) – 11 = 24
Regards