How is an average mass different from a weighted mass

In an average mass, each entry has equal weight. In a weighted average, we multiply each entry by a number representing its relative importance.

Assume that your class consists of 15 girls and 5 boys. Each girl has a mass of 54 kg, and each boy has a mass of 62 kg.

Average mass = (girl + boy) / 2 = (54 kg + 62 kg) / 2 = 58 kg

Weighted average (Method 1)

Use the numbers of each gender (15 girls + 5 boys),

Weighted average = (15*54 kg + 5*62 kg) / 20 = (810 kg + 310 kg) / 20

= 1120 kg/20 = 56 kg.

If you put all the students on one giant balance, their total mass would be

1120 kg and the average mass of a student would be 56 kg.

Weighted average (Method 2)

Use the relative percentages of each gender (75 % girls and 25 % boys).

Weighted average = 0.75*54 kg + 0.25*62 kg = 40.5 kg + 15.5 kg = 56 kg

Each girl contributes 40.5 kg and each boy contributes 15.5 kg to the weighted average mass of a student.