Find the mode of the ages of 181 workers of a factory from the following frequency distribution:

Age (in years) 20-30 30-40 40-50 50-60 60-70

Number of workers 25 47 62 37 10

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Solution

As the class 40-50 has the maximum frequency, it is the modal class.

$Now, x_{k} = 40, h = 10, f_{k} = 62, f_{k - 1} = 47 and f_{k + 1} = 37 ∴ Mode, M_{0} = x_{k} + \{h \times \frac{(f_{k} - f_{k - 1})}{(2 f_{k} - f_{k - 1} - f_{k + 1})}\} = 40 + \{10 \times \frac{(62 - 47)}{(2 \times 62 - 47 - 37)}\} = 40 + \{10 \times \frac{15}{40}\} = (40 + \frac{15}{4}) = (40 + 3.75) = 43.75$

Hence, mode = 43.75 years

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Age (in years)	20-30	30-40	40-50	50-60	60-70
Number of workers	25	47	62	37	10