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

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

80, 25

832, 22

81, 24

82, 23

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

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

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