The arithmetic mean is the total divided by the number of observations. When combining group averages, the group sizes matter. Averaging the averages works only under the appropriate weighting.
Reconstruct the totals
Four students average 10 points, and six students average 15 points. The first group contributes 4 × 10 = 40 points. The second contributes 6 × 15 = 90.
Together, the ten students have 130 points, so the combined mean is 13. Taking (10 + 15) ÷ 2 would give 12.5 and incorrectly assign equal weight to groups of different sizes.
Use the same idea for percentages
Suppose one practice set has five questions and you answer all five correctly. Another has fifteen questions and you answer nine correctly. The set percentages are 100% and 60%, but overall accuracy is 14 ÷ 20 = 70%, not 80%.
The denominator tells you the weight. Always ask what is being counted before averaging percentages.
Mean and median can differ
For the values 2, 3, 4, 5 and 26, the median is the middle value, 4. The mean is 40 ÷ 5 = 8. The large final value pulls the mean upward without changing the middle position.
Neither summary is automatically wrong. They describe different aspects of the dataset.
Find a missing value
Five numbers have a mean of 12, so their total must be 60. If four of them sum to 47, the missing number is 13. Working with the required total is simpler than repeatedly guessing an average.
A final reasonableness check
With positive weights, a weighted mean should lie between the smallest and largest component values. If your combined average falls outside that range, inspect the arithmetic or the interpretation of the weights. Then confirm that you included every observation exactly once.