An average summarises several numbers in one reference value. The simple arithmetic mean gives every value equal importance. A weighted average accounts for values that contribute differently, such as exams with different point totals or products purchased in different quantities.
Formulas
Arithmetic mean = sum of all values ÷ number of values. For a weighted mean, multiply each value by its weight, add the products and divide by the sum of all weights.
Two examples
You receive scores of 2, 3 and 4 in three tests using the same scale. The mean is (2 + 3 + 4) ÷ 3 = 3. Each test has equal weight.
In two exams, the first counts for 40% and the second for 60%. You score 80 and 90 points. The weighted average is 80 × 0.4 + 90 × 0.6 = 86 points. The average calculator calculates the simple mean. For weighted school grades, use the grade calculator and follow your school’s weighting rules.
When should you use each type?
Use the simple mean when every observation is equally important. A weighted average is appropriate when quantities, time periods or exam components have different weights. If individual values vary widely, the median may also be useful because it is less affected by outliers.
Common mistakes
- Ignoring weights when they are not equal.
- Failing to check that percentage weights add up to 100%.
- Silently treating missing values as zero.
- Overlooking outliers or treating the mean as a typical individual observation.
An average is a summary, not the whole story. For important decisions, also consider the spread and distribution of the data.
Additional practical tip
For every calculation, record which observations are included and which are excluded. For grades, take weights from the assessment rules or assignment. For measurements, the minimum, maximum and median can show whether unusual values distort the mean.
Read next: Related guide and calculator.
Germany’s Federal Statistical Office also explains the arithmetic mean in an educational module (German-language resource).
Interpret the average carefully
A mean is most useful when every value matters equally and the data has been collected in a comparable way. However, a single very high or very low value can shift it noticeably. Imagine five months of household spending, with one unusually expensive repair. The average rises even though the other months remain similar. In that situation, also check the median, minimum and maximum. School grades may use different exam weights, so follow the official weighting and use the dedicated grade calculator. Record which values you included so that someone else can understand or reproduce the result later.