How to Calculate Average — Mean, Weighted & Special Cases

Average is one of the first statistics most people learn, but it comes in more than one form — and using the wrong one gives a misleading answer. This guide covers the basic (arithmetic) average, weighted average, and a few commonly confused special cases: average speed and average atomic mass.

The Basic Average (Arithmetic Mean) Formula

Average = Sum of All Values ÷ Number of Values. Example: find the average of 10, 20, 30, 40, 50. Sum = 150. Count = 5. Average = 150 ÷ 5 = 30.

How to Calculate a Weighted Average

A weighted average gives more influence to some values than others — used for grades weighted by credit hours, or an investment portfolio return weighted by position size. Formula: Weighted Average = Σ(value × weight) ÷ Σ(weight). Example: grades of 85, 90, and 78 with weights 3, 2, and 1 (e.g., credit hours): (85×3 + 90×2 + 78×1) ÷ (3+2+1) = (255+180+78) ÷ 6 = 513 ÷ 6 = 85.5. Notice this differs from the simple average of (85+90+78)/3 = 84.33, because the weighted version gives more importance to the 85 grade.

How to Calculate Average Speed

Average speed is NOT simply the average of two speeds — it depends on time spent at each speed, not distance. The correct formula: Average Speed = Total Distance ÷ Total Time. Common mistake: if you drive 60 km/h for one hour and 40 km/h for one hour, the average speed IS the simple average (50 km/h) because you spent equal time at each speed. But if you drive 60 km/h for 100km and 40 km/h for 100km (equal distance, not equal time), the correct average is Total Distance ÷ Total Time = 200 ÷ (100/60 + 100/40) = 200 ÷ 4.167 = 48 km/h — not the simple average of 50.

How to Calculate Average Atomic Mass

Average atomic mass (used in chemistry) is a weighted average based on isotope abundance, not a simple average of isotope masses. Formula: Average Atomic Mass = Σ(isotope mass × fractional abundance). Example: Chlorine has two isotopes — Cl-35 (mass 35, abundance 75.77%) and Cl-37 (mass 37, abundance 24.23%). Average Atomic Mass = (35 × 0.7577) + (37 × 0.2423) = 26.52 + 8.97 = 35.49 — very close to chlorine's actual periodic table value of 35.45.

Other Common Average Calculations

• •Average of a frequency table: multiply each value by its frequency, sum them, then divide by the total count — this is itself a form of weighted average.
• •Moving average: the average of a fixed-size "window" of recent values, recalculated as new data arrives — common in finance and trend analysis.
• •Median vs average: the median (middle value) is sometimes a better representation than the average when a dataset has extreme outliers, since a few very large or small values can skew the average significantly.