Concept 2

Compute and interpret mean, median, mode, range, and weighted averages.

Use the statistic that matches the data, and weight each part correctly when the problem gives percentages or weights.

Core Idea

Mean uses every value, median is the middle value after the data are ordered or the average of the two middle values, mode is the most frequent value, and range is maximum minus minimum. For a weighted average, multiply each value by its weight before adding, so categories with larger weights affect the result more.

Understanding

Rule: ACT questions may ask you to compute a statistic or decide which statistic best describes a set of data. Mean is sensitive to extreme values because every number affects it. Median is often a better measure of center when the data are skewed or contain outliers. Mode describes the most common value, and range gives a quick measure of spread.

Weighted averages are especially common in grade, price, and mixture contexts. The key is that not all parts count equally. Multiply each value by its weight, then add the weighted parts. If the weights are percentages, they should total 100% or 1.

Question

Worked Example

A student's course grade is based on quizzes and tests. Quizzes count for 40% of the grade, and tests count for 60%. If the quiz average is 80 and the test average is 92, what is the overall course grade?

Select an answer to see the explanation