if the arithmetic mean of the following distribution is 56, find the missing frequencies f1 and f2 - Maths - Statistics

Question

if the arithmetic mean of the following distribution is 56, find
the missing frequencies f1 and f2

Gursheen kaur. · Accepted Answer

Let assumed mean , A= 50

h= 20

Class interval	class mark $x_{i}$	frequency $f_{i}$	$u_{i} = \frac{x_{i} - A}{h} = \frac{x_{i} - 50}{20}$	$f_{i} u_{i}$
0-20	10	16	-2	-32
20-40	30	f1	-1	-f1
40-60	50	25	0	0
60-80	70	16	1	16
80-100	90	f2	2	2f2
100-120	110	10	3	30
	$\sum f_{i} = 67 + f_{1} + f_{1}$			$\sum f_{i} u_{i} = 14 - f_{1} + 2 f_{2}$

$\sum f_{i} = 90 = 67 + 2 f_{1} f_{1} + f_{2} = 23............ (1) n o w, m e a n = A + h * \frac{\sum f_{i} u_{i}}{\sum f_{i}} \Rightarrow 56 = 50 + 20 (\frac{14 - f_{1} + 2 f_{2}}{90}) \Rightarrow 56 - 50 = 20 (\frac{14 - f_{1} + 2 f_{2}}{90}) \Rightarrow 6 = 20 (\frac{14 - f_{1} + 2 f_{2}}{90}) \Rightarrow 6 = 2 (\frac{14 - f_{1} + 2 f_{2}}{9}) \Rightarrow 54 = 28 - 2 f_{1} + 4 f_{2} \Rightarrow 26 = - 2 f_{1} + 4 f_{2} \Rightarrow 13 = - f_{1} + 2 f_{2} ..... (2) o n s o l v i n g (1) & (2), w e g e t, f_{2} = 12 p u t i n (1), w e g e t, f_{1} + 12 = 23 f_{1} = 23 - 12 = 11$