Algebra 2 · Unit 12 · Topic 12.1
Describing Data with Center and Spread
Mean and median summarize center, while range and standard deviation describe spread in different ways.
Definition and explanation
Mean and median summarize center, while range and standard deviation describe spread in different ways. For a population of N observations, variance is the average squared deviation from its mean; standard deviation is its square root.
Worked example
For the population data 2, 4, 4, 6, the mean and median are 4 and the range is 4. Squared deviations total 4 + 0 + 0 + 4 = 8. Population variance is 8/4 = 2, so population standard deviation is √2.
Common mistake
A sample variance usually divides by n − 1, not n; label whether the data are treated as a population or a sample.
Key takeaway
Mean and median summarize center, while range and standard deviation describe spread in different ways.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.