© 2008 Pearson Addison-Wesley. All rights reserved Chapter 6 Putting Statistics to Work

Copyright © 2008 Pearson Education, Inc. Slide 6-2 Chapter 6 Putting Statistics to Work 6ACharacterizing Data 6BMeasures of Variation 6CThe Normal Distribution 6DStatistical Inference

Copyright © 2008 Pearson Education, Inc. Slide 6-3 Unit 6A Characterizing Data

Copyright © 2008 Pearson Education, Inc. Slide 6-4 The mean is what we most commonly call the average value. It is defined as follows: The median is the middle value in the sorted data set (or halfway between the two middle values if the number of values is even). The mode is the most common value (or group of values) in a distribution. Measures of Center in a Distribution 6-A

Copyright © 2008 Pearson Education, Inc. Slide A Mean vs. Average

Copyright © 2008 Pearson Education, Inc. Slide 6-6 Finding the Median for an Odd Number of Values 6-A (sorted list) (odd number of values) median is 6.44 exact middle

Copyright © 2008 Pearson Education, Inc. Slide 6-7 Finding the Median for an Even Number of Values 6-A (sorted list) (even number of values) median is 5.02

Copyright © 2008 Pearson Education, Inc. Slide 6-8 Mode Examples 6-A a b c Mode is 5 Bimodal (2 and 6) No Mode

Copyright © 2008 Pearson Education, Inc. Slide 6-9 Shapes of Distributions 6-A Two single-peaked (unimodal) distributions. A double-peaked (bimodal) distribution.

Copyright © 2008 Pearson Education, Inc. Slide 6-10 Symmetric and Skewed Distributions 6-A

Copyright © 2008 Pearson Education, Inc. Slide 6-11 Variation 6-A From left to right, these three distributions have increasing variation. Variation describes how widely data values are spread out about the center of a distribution.

Copyright © 2008 Pearson Education, Inc. Slide 6-12 Unit 6B Measures of Variation

Copyright © 2008 Pearson Education, Inc. Slide 6-13 Why Variation Matters 6-B Big Bank (three line wait times): Best Bank (one line wait times):

Copyright © 2008 Pearson Education, Inc. Slide 6-14 Five Number Summaries & Box Plots 6-B lower quartile = 5.6 high value (max) = 7.8 upper quartile = 7.7 median = 7.2 lower quartile = 6.7 low value (min) = 6.6 Best BankBig Bank high value (max) = 11.0 low value (min) = 4.1 upper quartile = 8.5 median = 7.2

Copyright © 2008 Pearson Education, Inc. Slide 6-15 Standard Deviation 6-B Let A = {2, 8, 9, 12, 19} with a mean of 10. Use the data set A above to find the sample standard deviation.

Copyright © 2008 Pearson Education, Inc. Slide 6-16 Range Rule of Thumb for Standard Deviation 6-B Estimate standard deviation by taking an approximate range, (usual high – usual low), and dividing by 4. If we know the standard deviation, we can estimate: low value  mean – 2 x standard deviation high value  mean + 2 x standard deviation

Copyright © 2008 Pearson Education, Inc. Slide 6-17 Unit 6C The Normal Distribution

Copyright © 2008 Pearson Education, Inc. Slide 6-18 The Rule for a Normal Distribution 6-C

Copyright © 2008 Pearson Education, Inc. Slide 6-19 Z-Score Formula 6-C Example: If the nationwide ACT mean were 21 with a standard deviation of 4.7, find the z-score for a 30. What does this mean? This means that an ACT score of 30 would be about 1.91 standard deviations above the mean of 21.

Copyright © 2008 Pearson Education, Inc. Slide 6-20 Standard Scores and Percentiles 6-C

Copyright © 2008 Pearson Education, Inc. Slide 6-21 Unit 6D Statistical Inference

Copyright © 2008 Pearson Education, Inc. Slide 6-22 A set of measurements or observations in a statistical study is said to be statistically significant if it is unlikely to have occurred by chance (1 out of 20) or 0.01 (1 out of 100) are two very common levels of significance that indicate the probability that an observed difference is simply due to chance. Inferential Statistics Definitions 6-D

Copyright © 2008 Pearson Education, Inc. Slide 6-23 Margin of Error and Confidence Interval The margin of error for 95% confidence is 6-D The 95% confidence interval is found by subtracting and adding the margin of error from the sample proportion.

Copyright © 2008 Pearson Education, Inc. Slide 6-24 Null and Alternative Hypotheses The null hypothesis claims a specific value for a population parameter. It takes the form null hypothesis: population parameter = claimed value The alternative hypothesis is the claim that is accepted if the null hypothesis is rejected. 6-D

Copyright © 2008 Pearson Education, Inc. Slide 6-25 Outcomes of a Hypothesis Test Rejecting the null hypothesis, in which case we have evidence that supports the alternative hypothesis. Not rejecting the null hypothesis, in which case we lack sufficient evidence to support the alternative hypothesis. 6-D