Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name ________________________________________ Date __________________ Class __________________ LESSON 9-2 Data Distributions and Outliers Practice and Problem Solving: A/B For each data set, determine if 100 is an outlier. Explain why or why not. 1. 60, 68, 100, 70, 78, 80, 82, 88 2. 70, 75, 77, 78, 100, 80, 82, 88 ________________________________________ ________________________________________ ________________________________________ ________________________________________ The table below shows a major league baseball player’s season home run totals for the first 14 years of his career. Use the data for Problems 3–8. Season 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Home Runs 18 22 21 28 30 29 32 40 33 34 28 29 22 20 3. Find the mean and median. 4. Find the range and interquartile range. ________________________________________ ________________________________________ 5. Make a dot plot for the data. 6. Examine the dot plot. Do you think any of the season home run totals are outliers? Then test for any possible outliers. _________________________________________________________________________________________ _________________________________________________________________________________________ 7. The player wants to predict how many home runs he will hit in his 15th season. Could he use the table or the dot plot to help him predict? Explain your reasoning. _________________________________________________________________________________________ _________________________________________________________________________________________ _________________________________________________________________________________________ 8. Suppose the player hits 10 home runs in his 15th season. Which of the statistics from Problems 3 and 4 would change? _________________________________________________________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 154 showing the data over time, it makes clear that the player’s home run totals have fallen back during the past two seasons to the 18−22 zone. and his interquartile range is more than four times as great. 13. Jin is the more consistent test taker. Her grades show a much smaller range. 8. The mean would decrease to 26.4 and the median would decrease to 28. The range would increase to 30 and the interquartile range would increase to 11. 14. Jin has the standard deviation of 3 and Brad has the standard deviation of 9.6. You can tell because Brad’s test scores are so much more spread out. Practice and Problem Solving: C Reading Strategies 1. 100 is not an outlier because Q3 = 89 and IQR = 17.5. Then 100 < Q3 + 1.5(IQR). 1. when there is an even number of data values 2. mean: 8, median: 8.5, range: 12 2. 100 is not an outlier because Q1 = 110 and IQR = 14. Then 100 > Q1 − 1.5(IQR). Success for English Learners 1. Possible answer: Problem 1 has an odd amount of numbers in the set, so there is a middle. Problem 2 has an even amount of numbers in the set. 3. mean = 54.15; median = 54 4. range = 27; interquartile range = 7 5. 2. by adding the numbers and then dividing by how many numbers are present 3. Mean and median would be 5. 4. Patricia forgot to put the numbers in order from least to greatest first. 6. Possible answer: The line plot makes clear that there is a cluster of data in the 51−56 age range. Eleven of the 20 Presidents were in this range upon taking office. This pattern cannot be seen as clearly by just looking at the original data set. LESSON 9-2 Practice and Problem Solving: A/B 1. 100 is not an outlier because Q3 = 85 and IQR = 16. Then 100 < Q3 + 1.5(IQR). 7. Q1 = 51, Q3 = 58, and IQR = 7. So, if a President’s age upon taking office was less than 51 − 1.5(7) = 40.5 or greater than 58 + 1.5(7) = 68.5, there is an outlier. From the line plot, the only outlier is the President who took office at age 69. 2. 100 is an outlier because Q3 = 85 and IQR = 9. Then 100 > Q3 + 1.5(IQR) 3. mean = 27.57; median = 28.5 4. range = 22; interquartile range = 10 8. Possible answer: Because of the cluster of data in the low 50s and since the mean and median are close to 54, my guess is that Cleveland was 54 years old. 5. 6. Possible answer: The dot plot makes it appear as if 40 is an outlier. However, since Q3 = 32 and IQR = 10, 40 is not an outlier since 40 < 32 + 1.5(10) Practice and Problem Solving: Modified 1. skewed to the left 2. symmetric 7. Possible answer: The dot plot does not help predict. It makes it appear that there are two “zones” where this player tends to hit home runs: from 18 to 22 and from 28 to 34. The table may help predict. By 3. symmetric 4. skewed to the right Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 536