Book Online Demo

Check Your IQ

Try Test

Courses

The mode of the following data is $85.7$ . What is the missing frequency?

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

33

31

30

32

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

It is given the following frequency distribution table.
Question Image

We know that, mode is given as:

Mode = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h

Given

Mode = 85.7

So, from the table, we get

\Rightarrow

Modal class

= 85 - 95

Lower limit of modal class

l = 85

Class size

h = 10

Frequency of modal class

f_{1} = 32

Preceding frequency of modal class

f_{0} = f

Succeeding frequency of modal class

f_{2} = 6

Putting the values in the formula, we get

85.7 = 85 + (\frac{32 - f}{64 - f - 6}) \times 10

\Rightarrow 85.7 = 85 + (\frac{320 - 10 f}{58 - f})

\Rightarrow 85.7 \times (58 - f) = 85 (58 - f) + (320 - 10 f)

\Rightarrow 4970.6 - 85.7 f = 4930 - 85 f + 320 - 10 f

\Rightarrow - 279.4 = - 9.3 f

\Rightarrow f = 30.04 \approx 30

Thus, the approximate value of missing frequency is 30.
Hence, the correct option is 3.

Watch 3-min video & get full concept clarity