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The arithmetic mean of the following frequency distribution will be:

Age (in years)
Number of workers
18-24
6
24-30
8
30-36
12
36-42
8
42-48
4
48-54
2

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33.2 years

33.3 years

33.4 years

33.5 years

answer is B.

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Detailed Solution

The given frequency distribution table is:

Age (in years)	Number of workers
18-24	6
24-30	8
30-36	12
36-42	8
42-48	4
48-54	2

Formula:
Mean

= ∑ f i x i ∑ f i

where

f_{i}

is the frequency and

x_{i}

is the mid-value of the class.
The frequency distribution table will be:

Age (in years)	Number of workers, $f_{i}$	Mid-value, $x_{i}$	$f_{i} x_{i}$
18-24	6	21	126
24-30	8	27	216
30-36	12	33	396
36-42	8	39	312
42-48	4	45	180
48-54	2	51	102
	Σ $f_{i}$ =40		Σ $f_{i} x_{i}$ =1332

M e a n = 133240 = 33.3

Thus, the mean of the given data is 33.3 years.

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