# If the Mean of the Following Frequency Distribution is 18 , Find the Missing Frequency . - Mathematics

If the mean of the following frequency distribution is 18 , find the missing frequency .

 Class interval : 11-13 13-15 15-17 17-19 19-21 21-23 23-25 Frequency : 3 6 9 13 f 5 4

#### Solution

It is given that mean of the data is 18.
Let the assumed mean A = 18 and h = 2.

 Marks Mid-Value(xi) Frequency $u_i = \frac{x_i - 18}{2}$ $f_i u_i$ 11–13 12 3 -3 -9 13–15 14 6 -2 -12 15–17 16 9 -1 -9 17–19 18 13 0 0 19–21 20 f 1 f 21–23 22 5 2 10 23–25 24 4 3 12 N = 40 + f sumf_iu_i = -8 +f

We know that mean,  overlineX = A +h (1/N sum f_1u_i)

Now, we have $N = \sum_{} f_i = 40 + f, h = 2, A = 18, \sum_{} f_i u_i = - 8 + f$

$18 = 18 + 2\left[ \frac{1}{\left( 40 + f \right)} \times \left( - 8 + f \right) \right]$

$\Rightarrow 0 = \frac{- 16 + 2f}{40 + f}$

$\Rightarrow - 16 + 2f = 0$

$\Rightarrow f = 8$

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 15 Statistics
Exercise 15.3 | Q 27 | Page 25