Descriptive Statistics: Summarizing Data

Descriptive statistics summarize a data set with a small number of values so we can understand its key features quickly. The three measures of center each answer 'what is a typical value?' differently. The mean (arithmetic average) is calculated by summing all values and dividing by the count: mean = Σx / n. For the data set {4, 7, 7, 9, 13}, the mean is (4+7+7+9+13)/5 = 40/5 = 8. The mean is sensitive to outliers — a single extreme value can pull it far from where most data sits. The median is the middle value when data is sorted in order. For an odd count, it is the middle number; for an even count, it is the average of the two middle numbers. For {4, 7, 7, 9, 13}, the median is 7 (the 3rd of 5 values). The median is resistant to outliers — it represents the midpoint regardless of extreme values. The mode is the most frequently occurring value — in {4, 7, 7, 9, 13} it is 7, because 7 appears twice. A data set can have no mode, one mode (unimodal), or multiple modes (bimodal, multimodal). When data is symmetric (bell-shaped), mean ≈ median ≈ mode. When data is skewed, mean and median diverge — and the median is usually the better measure of center.