Statistics

Standard deviation, regression lines, correlation

Standard Deviation, Regression and Correlation

Standard deviation measures how spread out data is from the mean. A small SD means data clusters near the mean; a large SD means data is widely spread. Regression lines show the trend in bivariate data, and correlation measures the strength of a linear relationship.

Example

Calculating Standard Deviation

Data: 4, 7, 8, 9, 12 Mean = 40/5 = 8 Deviations: −4, −1, 0, 1, 4 Squares: 16, 1, 0, 1, 16 Variance = 34/5 = 6.8 SD = √6.8 ≈ 2.61

Correlation

Correlation coefficient (r) ranges from −1 to 1: • r close to 1: strong positive correlation • r close to −1: strong negative correlation • r close to 0: weak or no linear correlation The regression line (line of best fit) is used to make predictions.

Note

Remember

SD is always positive. About 68% of data falls within 1 SD of the mean in a normal distribution. Correlation does not imply causation. Use your calculator's STAT mode for regression equations.

Key Vocabulary

Standard deviationA measure of how spread out data is from the mean

VarianceThe average of the squared deviations from the mean

CorrelationThe strength and direction of a linear relationship between variables

Regression lineThe line of best fit through data points

Bivariate dataData involving two variables

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Standard deviation

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