Main Idea and New Vocabulary Example 1: Find the Mean Example 2: Effect of Extreme Values Key Concept: Mean, Median, and Mode Example 3: Choose an Appropriate Measure Lesson Menu

measures of central tendency mean median mode Determine and describe how changes in data values impact measures of central tendency. measures of central tendency mean median mode Main Idea/Vocabulary

Without highest weight: Find the Mean DOGS The weights in pounds for several dogs at a dog show are 15, 45, 26, 55, 73, 15, and 30. Compare the mean of the original data set and the mean when the highest weight is removed? With highest weight: Without highest weight: Answer: By dropping the highest weight, the mean weight decreases from 37 to 31. Example 1

A. The mean increases from 15.7 to 16.7. PHONES Gina is looking at the number of minutes she has spent on some recent phone calls. The times in minutes are 15, 18, 20, 1, 10, 13, and 33. Compare the mean of the original data set and the mean when the phone call with the fewest number of minutes is removed. A. The mean increases from 15.7 to 16.7. B. The mean decreases from 15.7 to 15.6. C. The mean increases from 15.7 to 18.2. D. The mean decreases from 15.7 to 14.7. Example 1 CYP

Effect of Extreme Values ATTENDANCE The number of students in class during one week is shown in the table. What are the mean, median, and mode with and without Tuesday’s attendance? Example 2

Effect of Extreme Values With Tuesday’s Attendance Mean Median 12, 20, 21, 22, 23 Mode no mode Example 2

Effect of Extreme Values Without Tuesday’s Attendance Mean Median 20, 21, 22, 23 21.5 Mode no mode So, Tuesday’s attendance affects the mean and median. The mean is affected the most in this example. Example 2

Effect of Extreme Values Answer: The mean increases from 19.6 to 21.5. The median increases from 21 to 21.5. The mode is not affected. Example 2

JEWELRY The number of rings Susan sold from Sunday to Thursday is shown in the table. What are the mean, median, and mode with and without the rings sold Thursday? A. The mean decreases from 2.8 to 1.6 and the median increases from 1 to 2. The mode is unaffected. B. The mean decreases from 2.8 to 2 and the median increases from 1 to 2. The mode is unaffected. C. The mean decreases from 2.8 to 2. The median and mode are unaffected. D. The mean increases from 2.8 to 3.5 and the median increases from 1 to 2. The mode is unaffected. Example 2 CYP

Key Concept 3

Choose an Appropriate Measure RUNNING The following set of data shows the number of miles Candace ran for the past six days: 4, 5, 4, 4, 6, 4. Which measure of central tendency best represents the data? Justify your selection and then find the measure. Answer: Since four of the six numbers are identical, the mode 4 would best represent the data. Example 3

B. The mean, 5.1, because there are gaps in the middle of the data. WATER The following set of data shows the number of glasses of water Milton drank each day last week: 3, 4, 6, 8, 5, 7, 3. Which measure of central tendency best represents the data? Justify your selection and then find the measure. A. The mode, 3, is the best measure because there is a repeating number. B. The mean, 5.1, because there are gaps in the middle of the data. C. The median, 5, is the best because there is an extreme value. D. The mean, 5.1, or the median, 5, both represent the data well since there are no gaps and no extreme values. Example 3 CYP