Answer the given question with proper steps.

Q.  The mean of the following distribution is 18. Find the frequency f of the class 19 — 21. 

 

Dear Student,

To solve this question, we first need to find the midpoints of each class and the product of midpoint and frequency.
 

Class	Frequency	Midpoint	Midpoint x Frequency
11-13	3	12	36
13-15	6	14	84
15-17	9	16	144
17-19	13	18	234
19-21	f	20	20f
21-23	5	22	110
23-25	4	24	96

Now, the formula for calculating the mean is:

$$\begin{gathered} Mean = \frac{Sum of (Frequency\times Mid point)}{Total frequency} \\ It is given that mean = 18 \\ So, \\ 18 = \frac{36+84+144+234+20f+110+96}{3+6+9+13+f+5+4} \\ 18 = \frac{704+20f}{40+f} \\ 720+18f = 704 +20f \\ 20f-18f = 720 - 704 \\ 2f = 16 \\ f = 8 \end{gathered}$$

Thus, the frequency of the class 19-21 is 8.

Hope it helps.

Regards