Question

The arithmetic mean of the following series is 18, find out the missing frequency.

Class Interval	11−13	13−15	15−17	17−19	19−21	21−23	23−25
Frequency	3	6	9	13	?	5	4

Answer 1

Class interval	Mid value (m)	Frequency (f)	Multiple of mid value and frequency (fm)
11 − 13 13 − 15 15 − 17 17 − 19 19 − 21 21 − 23 23 − 25	12 14 16 18 20 22 24	3 6 9 13 f 5 4	36 84 144 234 20f 110 96
		Σf = 40 + f	Σfm = 704 + 20f

$$\begin{gathered} \overline{X}\mathit{=}\frac{\Sigma fm}{\Sigma f} \\ \mathrm{or},18=\frac{704+20f}{40+f} \\ \mathrm{or},\mathrm{18\; (40\; +}\mathit{f})\; =\; 704\; +\; 20f \\ \mathrm{or},\mathit{}\mathit{720\; +\; 18f\; =\; 704\; +\; 20f} \\ \mathrm{or},\mathit{}\mathit{720\; -\; 704\; =\; 20f\; -\; 18f} \\ \mathrm{or}\mathit{,}\mathit{}\mathit{16\; =\; 2f} \\ \mathrm{or},\mathit{}\mathit{2f\; =\; 16} \\ \mathrm{or},\mathit{}f\mathit{=}\frac{\mathit{16}}{\mathit{2}} \\ \mathit{\Rightarrow }\mathit{}f\mathit{=}\mathit{}\mathit{8} \end{gathered}$$

Hence, the missing frequency is 8.