The mean of the following frequency distribution is $62.8$ and the sum of the observation is $50$ . Find the missing frequencies $F_{1}$ and $F_{2}$ .
Class 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 Total
Frequency 5 $F_{1}$ 10 $F_{2}$ 7 8 50

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Solution

Given mean of frequency distribution is $62.8$
& the sum of all frequencies is $50$
Class mid point of class $(x_{i})$
frequency $(f_{i})$ $f_{i} x_{i}$
$0 - 20$
$20 - 40$
$40 - 60$
$60 - 80$
$80 - 100$
$100 - 120$ $10$
$30$
$50$
$70$
$90$
$110$ $5$
$f_{1}$
$10$
$f_{2}$
$7$
$8$ $50$
$30 f_{1}$
$500$
$70 f_{2}$
$630$
$880$
$50$ $2060 + 30 f_{1} + 70 f_{2}$
$∴ \sum f_{i} = 50$

$30 + f_{1} + f_{2} = 50 \Rightarrow f_{1} + f_{2} = 50 - 30 = 20$

$f_{1} + f_{2} = 20$ ___(1)

mean $¯ x = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{2060 + 30 f_{1} + 70 f_{2}}{50}$

$62.8 \times 50 = 2060 + 30 f_{1} + 70 f_{2}$

$30 f_{1} + 70 f_{2} = 3140 - 2060 = 1080$

$10 (3 f_{1} + 7 f_{2}) = 1080$

$3 f_{1} + 7 f_{2} = 108$ __(2)

$f_{1} = 9 \Rightarrow (1) \Rightarrow f_{2} = 20 - f_{1} = 20 - 9$

$f_{2} = 11$

$∴ f_{1} = 9, f_{2} = 11$

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Class	mid point of class $(x_{i})$	frequency $(f_{i})$	$f_{i} x_{i}$
$0 - 20$ $20 - 40$ $40 - 60$ $60 - 80$ $80 - 100$ $100 - 120$	$10$ $30$ $50$ $70$ $90$ $110$	$5$ $f_{1}$ $10$ $f_{2}$ $7$ $8$	$50$ $30 f_{1}$ $500$ $70 f_{2}$ $630$ $880$
		$50$	$2060 + 30 f_{1} + 70 f_{2}$

The mean of the following frequency distribution is 62.8 and the sum of the observation is 50. Find the missing frequencies F1 and F2.Class0 - 2020 - 4040 - 6060 - 8080 - 100100 - 120TotalFrequency5F110F27850

The mean of the following frequency distribution is $62.8$ and the sum of the observation is $50$ . Find the missing frequencies $F_{1}$ and $F_{2}$ .
Class 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 Total
Frequency 5 $F_{1}$ 10 $F_{2}$ 7 8 50