AP Statistics Day 5 Objective: Students will be able to understand and calculate variances and standard deviations.

Variance The variance ( ) of a set of observations is the average of the squares of the deviations of the observations from their mean. The equation is: OR

Standard Deviation The standard deviation (s) is the square root of the variance. The standard deviation measures the spread by looking at how far the observations are from their mean.

Properties of Standard Deviation “s” measures spread about the mean and should be used only when the mean is chosen as the measure of center. “s” = 0 only when there is no spread. This happens when all observations have the same value. Otherwise s > 0. As the observations become more spread out about their mean, “s” gets larger. “s”, like the mean , is strongly influenced by extreme observations. A few outliers can make “s” very large.

Read Pages 51 – 53 Chapter Review Homework Page 46 #’s 1.35 and 1.36 Read Pages 51 – 53 Chapter Review

STUDY (Test Wednesday) Mean, Median, IQR (Middle 50%) Types of Variables (Categorical, Quantitative) Center & Spread Standard Deviation (High, Low, Zero) Resistant and Nonresistant Measures Modified Boxplot Finding Outliers Skewed Charts and Plots