Find the mean of the following frequency distribution using direct method.

16.20

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14.16

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16.17

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14.28

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Solution

The correct option is C $14.16$
Answer:- Using direct method
Representing the data into frequency distribution table
$x_{i} = mid point of each class interval$

Class interval No. of workers
$(f_{i})$ $x_{i}$ $f_{i} x_{i}$
0-5 4 2.5 10
5-10 5 7.5 37.5
10-15 6 12.5 75
15-20 7 17.5 122.5
20-25 8 22.5 180
$Σ f_{i} = 30$ $Σ f_{i} x_{i} = 425$
$∴ m e a n = \frac{Σ f_{i} x_{i}}{Σ f_{i}} = \frac{425}{30} = 14.16$

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Class interval	No. of workers $(f_{i})$	$x_{i}$	$f_{i} x_{i}$
0-5	4	2.5	10
5-10	5	7.5	37.5
10-15	6	12.5	75
15-20	7	17.5	122.5
20-25	8	22.5	180
	$Σ f_{i} = 30$		$Σ f_{i} x_{i} = 425$