2. Copyright © 2011 Pearson Education, Inc. Putting Statistics to Work

3. Copyright © 2011 Pearson Education, Inc. Slide 6-3 Unit 6A Characterizing Data

4. 6-A Copyright © 2011 Pearson Education, Inc. Slide 6-4 The distribution of a variable (or data set) describes the values taken on by the variable and the frequency (or relative frequency) of these values. Definition

5. 6-A Copyright © 2011 Pearson Education, Inc. Slide 6-5 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. 6-A You try it! Copyright © 2011 Pearson Education, Inc. Slide 6-6 The lengths (in minutes) of a sample of cell phone calls are shown: 61936128 Find the mean. A. 54 B. 9 C. 6 D. 7

7. 6-A Copyright © 2011 Pearson Education, Inc. Slide 6-7 Mean vs. Average

8. 6-A Copyright © 2011 Pearson Education, Inc. Slide 6-8 6.72 3.46 3.60 6.44 26.70 (data set) 3.46 3.60 6.44 6.72 26.70 (sorted list) (odd number of values) median is 6.44 exact middle Example: Find the median of the data set below. Finding the Median for an Odd Number of Values

9. 6-A Copyright © 2011 Pearson Education, Inc. Slide 6-9 6.72 3.46 3.60 6.44 (data set) 3.46 3.60 6.44 6.72 (sorted list) (even number of values) 3.60 + 6.44 2 median is 5.02 Example: Find the median of the data set below. Finding the Median for an Even Number of Values

10. 6-A Copyright © 2011 Pearson Education, Inc. Slide 6-10 Finding the Mode a. 5 5 5 3 1 5 1 4 3 5 b. 1 2 2 2 3 4 5 6 6 6 7 9 c. 1 2 3 6 7 8 9 10 Mode is 5 Bimodal (2 and 6) No Mode Example: Find the mode of each data set below.

11. 6-A Copyright © 2011 Pearson Education, Inc. Slide 6-11 Effects of Outliers An outlier is a data value that is much higher or much lower than almost all other values. Consider the following data set of contract offers: $0 $0 $0 $0 $2,500,000 The mean contract offer is As displayed, outliers can pull the mean upward (or downward). The median and mode of the data are not affected.

12. 6-A Copyright © 2011 Pearson Education, Inc. Slide 6-12 Two single-peaked (unimodal) distributions A double-peaked (bimodal) distribution Shapes of Distributions

13. 6-A Copyright © 2011 Pearson Education, Inc. Slide 6-13 Symmetry A distribution is symmetric if its left half is a mirror image of its right half.

14. 6-A Copyright © 2011 Pearson Education, Inc. Slide 6-14 A distribution is left- skewed if its values are more spread out on the left side. A distribution is right- skewed if its values are more spread out on the right side. Skewness

15. 6-A Copyright © 2011 Pearson Education, Inc. Slide 6-15 Variation 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.

16. 6-A Assignment P. 379-380 7-37 odd Copyright © 2011 Pearson Education, Inc. Slide 6-16