Statistics: Variability, Variance, and Standard Deviation

Vocabulary flashcards covering core concepts of variance, standard deviation, mean, and related terms as discussed in the notes.

Population variance (σ^2)

The average of squared deviations from the population mean; symbol σ^2; formula: (1/N) Σ (X_i − μ)^2.

Sample variance (s^2)

The average of squared deviations from the sample mean using the denominator (n−1) to produce an unbiased estimator of σ^2; formula: (1/(n−1)) Σ (X_i − x̄)^2.

Standard deviation (σ)

The square root of the variance; a measure of dispersion in the same units as the data.

Sample standard deviation (s)

The square root of the sample variance; s = sqrt(s^2).

Mean (population mean, μ)

The average of all observations in the population.

Sample mean (x̄)

The average of observations in a sample; used to estimate μ.

Deviation (X − μ, X − x̄)

Difference between an observation and the mean; X − μ for population, X − x̄ for sample.

Variance (general)

A measure of dispersion; the average squared distance from the mean.

Degrees of freedom (n−1)

The number of values free to vary when estimating a parameter from a sample; n−1 is used in variance estimation.

Unbiased estimator

A statistic whose expected value equals the true population parameter (e.g., s^2 is an unbiased estimator of σ^2).

Biased estimator

A statistic that systematically over- or underestimates a population parameter.

Range

The difference between the maximum and minimum values in a data set; a simple measure of spread.

Relationship: standard deviation and variance

Standard deviation is the square root of the variance; variance is the average of squared deviations.

Population vs. Sample

Population is the entire group of interest; a sample is a subset drawn from the population.