Average Calculator

Weighted averages and common mistakes

A plain average treats every value equally, but many real situations need a weighted average. If a course grade is 40% exams and 60% assignments, and you scored 70 on exams and 85 on assignments, the weighted average is 0.4 × 70 + 0.6 × 85 = 28 + 51 = 79, not the simple average of 77.5.

A common mistake is averaging averages. If one class of 20 students averaged 60 and another class of 30 averaged 80, the combined average is (20 × 60 + 30 × 80) ÷ 50 = 3,600 ÷ 50 = 72, not 70. Always go back to the totals and counts when combining groups of different sizes.

Mean, median and mode

The arithmetic mean is the sum of all values divided by how many there are. The median is the middle value when the data are sorted (or the average of the two middle values for an even count). The mode is the value that appears most often. Each answers a different question.

The mean uses every value, so it is the best summary when data are evenly spread. The median is better when a few extreme values would distort the mean, which is why incomes and house prices are usually reported as medians.

Worked example

Monthly expenses of 12,000, 15,000, 11,000, 14,000 and 48,000 (a month with a big repair) have a mean of 1,00,000 ÷ 5 = 20,000. The median is 14,000. Here the median better represents a typical month, while the mean is right for working out yearly totals.

Weighted averages

If some values count more than others — exam components, credit hours or quantities bought at different prices — use the weighted average calculator, which multiplies each value by its weight before dividing by the total weight.