Question

The mean weight of six boys in a groups is 48 kg. The individual weights of five of them are 51 kg, 45 kg, 49 kg, 46 kg and 44 kg. The weight of the 6th boy is
(a) 52 kg
(b) 52.8 kg
(c) 53 kg
(d) 47 kg

Answer 1

(c) 53 kg

Mean weight of six boys = 48 kg
Let the weight of the 6th boy be x kg.

$$\begin{gathered} \mathrm{We}\mathrm{know}: \\ \mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{all}\mathrm{observations}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{observations}} \\ =\frac{51+45+49+46+44+x}{6} \\ =\frac{235+x}{6} \\ \mathrm{Given}: \\ \mathrm{Mean}=48\mathrm{kg} \\ \Rightarrow \frac{235+x}{6}=48 \\ \Rightarrow 235+x=288 \\ \Rightarrow x=53 \\ \mathrm{Hence},\mathrm{the}\mathrm{weight}\mathrm{of}\mathrm{the}6\mathrm{th}\mathrm{boy}\mathrm{is}53\mathrm{kg}. \end{gathered}$$