Averages & Ratios calculators

The median is better when the data is skewed or contains outliers, because it depends only on the middle of the sorted list. A few very large salaries can raise the mean income well above what most people earn, while the median stays representative. For symmetric data without outliers the two are close.

An unweighted GPA uses the same scale for every class, usually topping out at 4.0. A weighted GPA adds extra points for harder classes such as honors, AP or IB, so it can exceed 4.0. Colleges often recalculate GPAs using their own method.

Only average percentages directly when they are based on equal-sized groups. Otherwise, convert each to its underlying counts or weight each percentage by its group size. Two classes with 90% and 70% pass rates do not average to 80% if one class is three times larger.

They are closely related but not identical. A fraction compares a part with the whole, while a ratio can compare any two quantities, including two parts. A class with 12 girls and 18 boys has a girl-to-boy ratio of 2:3, but girls make up 2/5 of the class.

Over equal distances you spend more time at the slower speed, so it carries more weight in the true average. The harmonic mean accounts for that time, while the arithmetic mean treats each speed as if it lasted equally long. The harmonic mean is always less than or equal to the arithmetic mean for positive numbers.