Why averaging two averages can give the wrong answer
Group averages need group sizes. Without weights, a small group can influence the combined result as much as a much larger one.
Average & median →Reconstruct the totals
One class has 10 students averaging 80, and another has 30 averaging 60. Their total scores are 800 and 1800. The combined mean is (800+1800)/(10+30) = 65. Averaging 80 and 60 gives 70, incorrectly treating the two classes as equal-size units. The weighted calculation preserves both the total score and the total number of students.
Use a tool that matches the inputs
The average tool treats each entered observation equally. If you have the individual scores, enter them all. If you have only group means and counts, calculate Σ(count×mean)/Σcount with the scientific calculator. For academic GPA, use the GPA tool when credits and grade conventions match the course system; do not assume every letter grade carries the same numerical value worldwide.
Avoid overlapping groups and rounded means
The formula assumes each observation is counted once and each group mean uses the same definition. Overlapping membership double-counts some observations. Rounded published means may also make the reconstructed total approximate rather than exact. If group sizes are unknown, the combined individual mean cannot generally be determined; report the limitation instead of silently giving equal weight to the published averages. Equal weighting is justified only when the intended unit of analysis really is the group rather than the individual.
Try the calculators
- Average & median
Find the mean, median and sum of a list.
- Standard deviation
Calculate population or sample standard deviation.
- GPA calculator
Calculate a credit-weighted GPA on a 4.0 scale.