The median value for the following frequency distribution is 35 and the sum of the all frequencies is 170. Using the formula for median, find the missing frequencies.

Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70

Frequency 10 20 ? 40 ? 25 15

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Solution

Let, $f_{1} and f_{2}$ be the frequencies of the class intervals 20-30 and 40-50, respectively.
$Then 10 + 20 + f_{1} + 40 + f_{2} + 25 + 15 = 170 \Rightarrow f_{1} + f_{2} = 60$
The median is 35 which lies in the class of 30-40. So, the median class is 30-40.
$Now, l = 30, h = 10, f = 40, N = 170 and c f = 10 + 20 + f_{1} = f_{1} + 30 ∴ Median, M = l + \{h \times \frac{(\frac{N}{2} - c f)}{f}\} \Rightarrow 30 + [10 \times \frac{85 - (f_{1} + 30)}{40}] = 35 \Rightarrow 30 + \frac{55 - f_{1}}{4} = 35 \Rightarrow 55 - f_{1} = 20 \Rightarrow f_{1} = 35 Now, f_{2} = (60 - 35) = 25 Hence, f_{1} = 35 a n d f_{2} = 25$

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Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	10	20	?	40	?	25	15