Introduction
Mean, median, and range are the foundational descriptive statistics for quantitative data on the SAT. This skill appears in the Problem-Solving and Data Analysis domain (≈15% of the section). Questions ask you to compute these measures, find a missing data value from a given mean, and reason about what happens to the mean and median when a value — especially an extreme outlier — is added, removed, or changed. This note covers exactly those tasks. (Standard deviation and the shape of distributions are covered in the sibling note Distributions and Standard Deviation.)
Core Concept
The Three Measures
Mean (arithmetic average): add all values, then divide by the count.
Median: the middle value when data are arranged in order. For an even number of values, average the two middle values.
Range: the spread from the smallest to the largest value.
Finding a Missing Value from the Mean
Rearrange the mean formula: . Compute the required total, then subtract all known values.
Quick example: If four of five numbers are and the mean is , then the required total is . Known sum . Missing value .
How Outliers Move the Mean and Median
An outlier is a value far from the rest of the data. Because the mean uses every value in its calculation, a single extreme outlier can shift the mean dramatically while barely moving the median.
| Situation | Effect on mean | Effect on median |
|---|---|---|
| Add a very large outlier | Increases substantially | Increases slightly (at most one position) |
| Remove a very large outlier | Decreases substantially | Changes slightly or not at all |
| Replace a central value with an extreme one | Large shift | Small or no shift |
Key principle: The mean is pulled toward the outlier; the median resists it.
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