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Honors Statistics. Day 4 Objective: Students will be able to understand and calculate variances and standard deviations. As well as determine how to describe the spread and center of a distribution based on a graph. Describing Distributions with Numbers: Center/Mean. The Mean The Average
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Honors Statistics Day 4 Objective: Students will be able to understand and calculate variances and standard deviations. As well as determine how to describe the spread and center of a distribution based on a graph.
Describing Distributions with Numbers: Center/Mean • The Mean • The Average • The Arithmetical Mean • The mean is not a resistance measure of center
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.
Linear Transformations • Adding “a” to each data point does not change the shape or spread • Adding “a” to each data point does change the center by “a”
Linear Transformations • Multiplying each data point by “b” does change the shape or spread by a factor of “b”. • Multiplying each data point by “b” does change the center by a factor of “b”.
Comparing Distributions • We have already seen the usefulness of comparing two distribution in the answering difficult questions like: • “Who was a better home run hitter, Barry Bonds or Hank Aaron?” • We used side-by-side boxplots to answer that question.
Reminders • If there are outliers, don’t use mean or standard deviation to compare distributions. • You can’t compare a standard deviation of one distribution to the IQR of a different distribution. • You can’t compare a mean of one distribution to the median of a different distribution.
Homework Complete Practice Test 1B
STUDY Test 9/11(A) or 9/12(B) • Mean, Median, IQR (Middle 50%) • Types of Variables (Categorical, Quantitative) • Center & Spread • Standard Deviation (High, Low, Zero) • Resistant and Nonresistant Measures • Modified Boxplots • Finding Outliers • Skewed Charts and Plots • Linear Transformations