1. Skill 18: Describing Numerical Data Please have Skill 17 IP out, ready to be checked.

2. Our Goal in Skill 18 Our goal in this skill is to describe the center and spread of sets of data by using numbers. Center: What value best describes the whole data set? Spread: How much does our data vary? Is it consistent?

3. Measuring the Center by Calculating the Mean The most common measure of center is the ____________________________, or mean. To find the mean of a set of data,

4. Measuring the Center by Calculating the Mean Example #1: Below is a set of data that describes the commute times (in minutes) for 15 workers in North Carolina. 40 20 10 10 30 5 60 40 20 10 12 15 30 25 10 a) Calculate the mean commute time for these 15 workers.

5. Measuring the Center by Calculating the Mean Example #1: Below is a set of data that describes the commute times (in minutes) for 15 workers in North Carolina. 40 20 10 10 30 5 60 40 20 10 12 15 30 25 10 b) Calculate the mean again, this time excluding the person who reported a 60-minute travel time to work. What do you notice?

6. Measuring the Center by Calculating the Mean The mean is easily influenced by “extreme” values.

7. You Try: 1.Find the mean test score for a group of Algebra II students: 78919688859331968583 2. Explain why the mean is probably not a good representation of the typical test score.

8. Measuring the Center by Calculating the Median The median M is the ___________________________________ of a set of data, the value where half the numbers are smaller and the other half are larger. To find the median of a set of data,

9. Measuring the Center by Calculating the Median Example #2: Calculate the median commute time for the 15 workers in North Carolina. 40 20 10 10 30 5 60 40 20 10 12 15 30 25 10

10. Measuring the Center by Calculating the Median Example #3: Katherine’s first 14 quiz grades were a) Calculate the median quiz grade.

11. Measuring the Center by Calculating the Median Example #3: Katherine’s first 14 quiz grades were b) Suppose Katherine has an unexcused absence for the 15th quiz, and she receives a score of zero. Recalculate the mean and the median. What property of measures of center does this illustrate?

12. You Try: 1.Find the median test score for a group of Algebra II students: 7891968885933196858397 2.The student that scored an 88 transfers to a different school. Recalculate the median, with their score removed. 3.Write 5 numbers that have a median of 20.

13. Measuring the Spread of a Set of Data by Calculating the Range The range of a set of data is the difference between the _______________________________ and ________________________________ values. Example #3: Find the range of commute times for the North Carolina workers.

14. You Try: 1.Find the range of test scores for a group of Algebra II students: 7891968885933196858397 2. Write a set of 5 numbers that have a range of 18.

15. Measuring the Spread of a Set of Data by Calculating the Interquartile Range What happens if your maximum or minimum value is an “extreme” number, that doesn’t really fit with the rest of your data? The interquartile range of a set of data measures the range of the _____________________________________________________ of the data.

16. Measuring the Spread of a Set of Data by Calculating the Interquartile Range To calculate the interquartile range of a set of data: 1) 2) 3) 4)

17. Measuring the Spread of a Set of Data by Calculating the Interquartile Range Example #4: Calculate the interquartile range of the commute times for the 15 workers in North Carolina. 40 20 10 10 30 5 60 40 20 10 12 15 30 25 10

18. Measuring the Spread of a Set of Data by Calculating the Interquartile Range Example #5: Calculate the interquartile range for the commute times of 20 NYC residents: 5 10 10 15 15 15 15 20 20 20 20 25 30 30 40 40 45 60 60 65 85

19. You Try: 1.Find the IQR of fish lengths for a group of fish in an aquarium: 2831364835232126253337 2.The fish that has a length of 48 cm dies  Recalculate the IQR, with their length removed.

20. Comparing Two Sets of Data When comparing sets of data, we should always compare their centers and spreads. Let’s collect data for our class. How many minutes does it take you to get to school each day? Males: Females: Example #6: Compare the two sets of data by calculating the statistics of center and spread.

21. Comparing Two Sets of Data Example #7: An organization recorded the study habits and attitudes of 18 first-year college women and 20 first-year college men, and gave them each a score. A high score = good study habits. Compare the sets of data.

22. Exit Quiz 46342181012192729324250 1.Mean 2.Median 3.Range 4.IQR