weighted average

Meaning: A weighted average counts each value in proportion to its share of the sample, not equally. For atomic mass, each isotope's mass is multiplied by its fractional abundance and the products are summed. So periodic table masses are not whole numbers, and the result lies between the lightest and heaviest isotope, nearer the most abundant one. The same arithmetic gives the molar mass of a gas mixture from mole fractions.

Equation: average mass = Σ(f × m), summed over all isotopes, where f is the fractional abundance of an isotope (unitless, percent ÷ 100, all values summing to 1) and m is that isotope's mass in atomic mass units (u; 1 u = 1.66 × 10⁻²⁷ kg).

On the MCAT: Passages give isotope masses and abundances, or mass spectrometer peak heights, and ask for the average atomic mass. Often the question runs backward: chlorine isotopes are near 35 and 37 and the listed mass is 35.45, about a quarter of the way up from 35, so roughly three-quarters of the sample is the lighter isotope. Estimating by position between the two masses is faster than full arithmetic.

Common confusion: Taking a simple average, (35 + 37)/2 = 36, ignores abundance. The answer must sit nearer the more abundant isotope, and percentages must be converted to fractions first.