Question

In the following frequency distribution, ifthe arithmetic mean is 45.6, find out missing frequency.

Wages (₹)	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of Workers	5	6	7	X	4	3	9

Answer 1

Wages (X)	Mid Value (m)	No. of worker (f)	fm
10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80	15 25 35 45 55 65 75	5 6 7 X 4 3 9	75 150 245 45 220 195 675
		∑f = 34 + X	∑fm = 1560 + 45X

Substituting the values in the formula for mean.
$$\begin{gathered} \overline{X}=\frac{\Sigma fm}{\Sigma f} \\ 45.6=\frac{1560+45X}{34+X} \\ \mathrm{or},\mathrm{45.6\; (34\; +\; X)}=\; 1560+45\; X \\ \mathrm{or},1550.4+45.6\; X=\; 1560+45\; X \\ \mathrm{or},\mathrm{45.6\; X\; -\; 45\; X\; =\; 1560}-1550.4 \\ \mathrm{or},0.6X=9.6 \\ \mathrm{or},\mathrm{X}=16 \end{gathered}$$

$X=\frac{9.6}{.6}$
X = 16
Hence, the missing frequency is 16.