Compute and interpret measures of center and spread for a data set.
Center and spread are the two most important questions to ask about any data set: where is the "middle" (mean, median), and how spread out are the values around it (range, variance, standard deviation)? Mean is the familiar average; median is the middle value when the data is sorted (or the average of the two middle values, for an even count) -- median resists being dragged around by one extreme outlier the way the mean can be.
Standard deviation measures the typical distance a data point sits from the mean. To compute it: find each value's deviation from the mean, square every deviation (so negatives do not cancel positives), average those squares (that average is the variance), then take the square root to return to the original units. A small standard deviation means the data huddles close to the mean; a large one means it is spread wide.
Mastery looks like: They compute mean, median, range, variance, and standard deviation for a data set and can explain what a large or small standard deviation indicates.
Common stumbles: Forgetting to square the deviations (letting negatives cancel positives and wrongly getting an average deviation of 0); taking the square root too early, before averaging the squared deviations.