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What is the mean of the following frequency distribution?

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16.20

14.16

16.17

14.28

answer is B.

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Detailed Solution

It is given the frequency distribution table.
Question Image

We convert the data in terms of the following expression.

x_{i} = \frac{lower limit + upper limit}{2}

Class interval	$x_{i}$	$(f_{i})$	${(x}_{i}) \times (f_{i}) = (x_{i} f_{i})$
0 - 5	2.5	4	10
5 - 10	7.5	5	37.5
10 - 15	12.5	6	75
15 - 20	17.5	7	122.5
20 - 25	22.5	8	180
		$Σ f_{i} = 30$	$Σ f_{i} x_{i} = 425$

From the table, we get

Σ f_{i} = 30

Σ f_{i} x_{i} = 425

We know that,
Mean=

\frac{Σ f_{i} x_{i}}{Σ f_{i}}

\Rightarrow Mean = \frac{425}{30}

\Rightarrow Mean = 14.16

Thus, the average of the data is 14.16.
Hence, the correct option is 2.

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