Question

The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6 of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.

Answer 1

We have:

Mean = $\frac{\mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{weight}s\mathrm{of}the\mathrm{students}}{\mathrm{Number}\mathrm{of}\mathrm{students}}$

Let the weight of the seventh student be x kg.

$$\begin{gathered} \mathrm{Mean}=\frac{52+54+55+53+56+54+x}{7}=55 \\ \Rightarrow \frac{324+x}{7}=55 \\ \Rightarrow 324+x=385 \\ \Rightarrow x=385-324 \\ \Rightarrow x=61\mathrm{kg}. \end{gathered}$$
Thus, the weight of the seventh student is 61 kg.