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Honors Statistics

Learn to calculate variances and standard deviations, describe spread and center of distributions, and compare data using mean and standard deviation. Explore linear transformations and distribution comparisons with real-world examples.

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Honors Statistics

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  1. 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.

  2. Describing Distributions with Numbers: Center/Mean • The Mean • The Average • The Arithmetical Mean • The mean is not a resistance measure of center

  3. 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

  4. 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.

  5. 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.

  6. Calculating “s” by hand

  7. Calculating “s” by hand

  8. Calculating “s” by hand

  9. Calculating “s” by hand

  10. Calculating “s” using TI-83

  11. Calculating “s” using TI-83

  12. Calculating s using TI-83

  13. 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”

  14. 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”.

  15. 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.

  16. 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.

  17. Homework Complete Practice Test 1B

  18. 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

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