Chapter 4 Variability

Sample variance

Average squared distance from the sample mean

Population standard deviation

Square root of the average squared distance from μ

Sample standard deviation

Standard distance from M

Population variance

σ²

unbiased

A sample mean (that is, M = ∑X/n) is a _____________ estimator of the population mean. biased or unbiased?

biased

A sample statistic is _______________ if it consistently underestimates or overestimates the corresponding population parameter. biased or unbiased?

unbiased

A sample statistic is_____________ if the average value of the sample statistic, obtained over all possible samples, is equal to the population parameter. biased or unbiased?

unbiased

A sample variance that is computed as s² = SS / (n - 1) is a _____________ estimator of the population variance. unbiased or biased?

Population variance

Average squared distance from μ

Memorize

Variance is defined as the mean squared deviation, and, for a population, is computed as the sum of squared deviations divided by N. Without some adjustment, the sample variance will be biased and will consistently underestimate the corresponding population value.

multimodal

a distribution with more than two scores with greatest frequency

bimodal

distribution with two scores with the greatest frequency

sample variance

s²

major mode

taller peak when two scores with greatest frequency have unequal frequencies

Population standard deviation

the square root of the population variance

sample standard deviation

the square root of the sample variance