Given the following frequency distribution
with some missing frequencies
Class Frequency
10-20 180
20-30 --
30-40 34
40-50 180
50-60 136
60-70 --
70-80 50
If the total frequency is 685 and median is 42.6 then the
missing frequencies are

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80, 25

832, 22

81, 24

82, 23

answer is C.

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Detailed Solution

Let the missing frequencies be $f 1 a n d f 2$ , respectively.

Class	Frequency ( $f$ )	Cum. Freq. $(c . f .$ )
10-20	180	180
20-30	$f_{1}$	180+ $f_{1}$
30-40	34	214 + $f_{1}$
40-50	180	394 + $f_{1}$
50-60	136	530+ $f_{1}$
60-70	$f_{2}$	530+ $f_{1}$ + $f_{2}$
70-80	50	580+ $f_{1}$ + $f_{2}$
Total	685

We have $580 + f_{1} + f_{2} = 685 \Rightarrow f_{1} + f_{2} = 105$

As median $42.6$ lies in the class $40 - 50$ , median class is
$40 - 50 .$ We have that $l = 40, f = 180, C = 214 + f_{1}$ and $h = 10$ .

Now, $Median =∣ l + \frac{h}{f} (\frac{N}{2} - C)$

$\begin{array}{l} \Rightarrow 42.6 = 40 + \frac{10}{180} (\frac{685}{2} - 214 - f_{1}) \\ \Rightarrow 2.6 \times 18 = 342.5 - 214 - f_{1} \Rightarrow f_{1} = 81.7 \end{array}$