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Direct Method of Finding Mean

Marks 10-20 2...

Question

Marks 10-20 20-30 30-40 40-50 50-60
Frequency 4 10 20 40 50
The following frequency distribution showing the marks obtained by $124$ students in Economy at a certain school. Find the arithmetic mean using direct method.

50

marks

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80

marks

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30

marks

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45

marks

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Solution

The correct option is D $45$ marks
Answer:- Direct Method:
Marks Frequency $x_{i}$ $f_{i} x_{i}$
$10 - 20$ $4$ $15$ $60$
$20 - 30$ $10$ $25$ $250$
$30 - 40$ $20$ $35$ $700$
$40 - 50$ $40$ $45$ $1800$
$50 - 60$ $50$ $55$ $2750$

$Σ f_{i} = 124$ $Σ f_{i} x_{i} = 5560$
$M e a n = \frac{Σ f_{i} x_{i}}{Σ f_{i}} = \frac{5560}{124} = 44.83 ≃ 45 m a r k s .$

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Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$10$	$15$	$25$	$50$

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80, 10, 30, 70, 60, 50, 50, 40, 40, 20, 40, 90, 50, 30, 70, 10, 60, 50, 20, 70, 70, 30, 80, 40, 20, 80, 90,

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Marks obtained	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
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