# The mean weight of 25 students in a class is 58 kg. The mean weight of a second class of 29 students is 62 kg. How do you find the mean weight of all the students?

Dec 15, 2016

The mean or average weight of all the students is 60.1 kg rounded to the nearest tenth.

#### Explanation:

This is a weighted average problem.

The formula for determining a weighted average is:

$\textcolor{red}{w = \frac{\left({n}_{1} \times {a}_{1}\right) + \left({n}_{2} \times {a}_{2}\right)}{{n}_{1} + {n}_{2}}}$

Where $w$ is the weighted average,

${n}_{1}$ is the number of objects in the first group and ${a}_{1}$ is the average of the first group of objects.

${n}_{2}$ is the number of objects in the second group and ${a}_{2}$ is the average of the second group of objects.

We were given ${n}_{1}$ as 25 students, ${a}_{1}$ as 58 kg, ${n}_{2}$ as 29 students and ${a}_{2}$ as 62 kg. Substituting these into the formula we can calculate $w$.

$w = \frac{\left(25 \times 58\right) + \left(29 \times 62\right)}{25 + 29}$

$w = \frac{1450 + 1798}{54}$

$w = \frac{3248}{54}$

$w = 60.1$