APEX AP Stats Lesson 1.3.7 Study: Measuring Variation Studyguide

Standard Deviation (SD)

Used when we use the mean as the measure of center; measures/determines variation.

Sample Standard Deviation (s)

Using a sample to estimate standard deviation of a population.

Population Standard Deviation (sigma; aka σ)

Uses a population to find the standard deviation.

Degrees of Freedom

n-1 is used to not underestimate the value for a population parameter when using a sample.

Measure of Variation

One number that describes the spread of the data set or of the entire population.

Population Standard Deviation Formula

σ = radical{[(x1 - population mean)^2 +(x2 - population mean)^2 … (x_N - population mean)^2]/N}

N

Population size/total number of observations.

X-1 and X-2

The observations used in the population standard deviation formula.

Mu (μ)

The population mean.

Sample Standard Deviation Formula

s = radical{[(x1 - x-hat)^2 + (x2 - x-hat)^2 + … (x_n - x-hat)^2]/n-1}

X-hat

Sample mean.

Example: Calculating the Sample Standard Deviation

Given: (4, 4, 10, 10), n=4, sample standard deviation is ~3.46.

Purpose of Sample Standard Deviation

To give an unbiased estimate of sigma (σ).