Question

The following series gives the weekly wages. The mean wages are ₹ 50.75. Find out the missing value.

Weekly Wages	40−43	43−46	46−49	49−52	52−55
Frequency	3	6	9	13	?

Answer 1

Weekly wages	Mid value (m)	Frequency (f)	Multiple of mid value and frequency (fm)
40 − 43 43 − 46 46 − 49 49 − 52 52 − 55	41.5 44.5 47.5 50.5 53.5	3 6 9 13 f	124.5 267 427.5 656.5 53.5f
		Σf = 31 + f	Σfm = 1475.5 + 53.5f

$$\begin{gathered} \overline{X}\mathit{=}\frac{\mathrm{\Sigma }fm}{\mathrm{\Sigma }f} \\ \mathrm{or},50.75=\frac{147.5+53.5f}{31+f} \\ \mathrm{or},\mathrm{50.75(31\; +}f)=\; 1475.5\; +\; 53.5f \\ \mathrm{or},\mathrm{1573.25\; +\; 50.75}f=\; 1475.5\; +\; 53.5f \\ \mathrm{or},\mathrm{1573.25\; -\; 1475.5\; =}53.5f-\; 50.75f \\ \mathrm{or},97.75=2.75f \\ \mathrm{or},2.75f=97.75 \\ \mathrm{or},f=\frac{97.75}{2.75} \\ \Rightarrow f=35.54\mathrm{or}36approx. \end{gathered}$$

Hence, the missing frequency or value is 36.