Find the missing frequencies in the following frequency distribution, whose mean is $50$ .

Open in App

Solution

We will prepare the following table:

From the table, $68 + f_{1} + f_{2} = 120$
$\Rightarrow f_{1} + f_{2} = 120 - 68$
$\Rightarrow f_{1} + f_{2} = 52$ ---(1)
Given: Mean $¯ ¯ ¯ x = 50$
We know that,
Mean, $¯ ¯ ¯ x = \frac{\sum f x}{\sum f}$
$\Rightarrow \frac{3480 + 30 f_{1} + 70 f_{2}}{120} = 50$
$\Rightarrow 3480 + 30 f_{1} + 70 f_{2} = 6000$
$\Rightarrow 30 f_{1} + 70 f_{2} = 6000 - 3480$
$\Rightarrow 30 f_{1} + 70 f_{2} = 2520$
$\Rightarrow 3 f_{1} + 7 f_{2} = 252$ ----(2)
Lets multiply equation (1) by 3
$f_{1} + f_{2} = 52$
$\Rightarrow 3 (f_{1} + f_{2}) = 3 \times 52$
$\Rightarrow 3 f_{1} + 3 f_{2} = 156$ ---(3)
Lets do (2)-(3)
$\Rightarrow 3 f_{1} + 7 f_{2} - 3 f_{1} - 3 f_{2} = 252 - 156$
$\Rightarrow 4 f_{2} = 96$
$\Rightarrow f_{2} = \frac{96}{4}$
$\Rightarrow f_{2} = 24$
Lets substitute, $f_{2} = 24$ in $f_{1} + f_{2} = 52$
$f_{1} + f_{2} = 52$
$\Rightarrow f_{1} + 24 = 52$
$\Rightarrow f_{1} = 52 - 24$
$\Rightarrow f_{1} = 28$
$∴ f_{1} = 28, f_{2} = 24$

Suggest Corrections

Similar questions

x	10	20	30	40	50	60	Total
f	4	f₁	8	f₂	3	4	35

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

Class	0-20	20-40	40-60	60-80	80-100	Total
Frequency	17	f₁	32	f₂	19	120

Find the missing frequency p for the following frequency distribution whose mean is $28.25$ .

50

150

$x$	$10$	$30$	$50$	$70$	$90$	$T o t a l$
$f$	$17$	$f_{1}$	$32$	$f_{2}$	$19$	$120$

Join BYJU'S Learning Program