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Chapter 13 Lesson 4

Chapter 13 Lesson 4. Range and Outliers Pages 368-370 1-5 all. Cornell Notes – Chap. 13 Lesson 4. Main Ideas/Cues: Lower extreme Upper extreme Lower quartile Upper quartile Range of a data set. Details: The least value in a data set The greatest value in a data set

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Chapter 13 Lesson 4

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  1. Chapter 13 Lesson 4 Range and Outliers Pages 368-370 1-5 all

  2. Cornell Notes – Chap. 13 Lesson 4 Main Ideas/Cues: Lower extreme Upper extreme Lower quartile Upper quartile Range of a data set Details: The least value in a data set The greatest value in a data set The median of the lower half of a data set The median of the upper half of a data set The difference of the greatest and least values in the data set. Example: The range of the data set 60, 35, 22, 46, 81, 39 is 81 – 22 = 59.

  3. Cornell Notes – Chap. 13 Lesson 4 Main Ideas/Cues: Interquartile range Details: The difference between the upper and lower quartiles in a box-and whisker plot Example: 8 19 26 37 45 The interquartile range is 37 – 19, or 18.

  4. Cornell Notes – Chap. 13 Lesson 4 Main Ideas/Cues: Outlier Box-and-whisker plot Details: A value in the data set that is much greater or much less than the other values. Example: In the data set 6, 17, 19, 23, 24, 24, 32 6 is the outlier. A data display that divides a data set into four parts using the lower extreme, lower quartile, median, upper quartile, and upper extreme.

  5. Problem #1 First Step: Write the Problem Find the median, extremes, quartiles, range, and interquartile range. 1. 48, 52, 59, 61, 64, 64, 86

  6. Problem #1 Second Step: Order the data and identify the median and the extremes. 1. 48, 52, 59, 61, 64, 64, 86 Lower extreme Median Upper extreme

  7. Problem #1 Third Step: Identify the quartiles using the lower and upper halves of the data. 1. 48, 52, 59, 61, 64, 64, 86 Upper Quartile Lower Quartile

  8. Problem #1 Fourth Step: Subtract the extremes to find the range. 1. 48, 52, 59, 61, 64, 64, 86 86 – 48 = 38 Range = 38 What are the extremes? Range answer

  9. Problem #1 Fifth Step: Subtract the quartiles to find the interquartile range. 1. 48, 52, 59, 61, 64, 64, 86 64 – 52 = 12 Interquartile range = 12 What are the quartiles? Interquartile range answer

  10. Problem #1 Answer 1. 48, 52, 59, 61, 64, 64, 86 Median = 61 Extremes = 48 and 86 Quartiles = 52 and 64 Range = 38 Interquartile range = 12 Write the answer labeling each part (Median, extremes, quartiles, range, and interquartile range)

  11. Problem #2 First Step: Write the Problem Find the median, extremes, quartiles, range, and interquartile range. 2. 18, 16, 48, 6, 22, 17, 9, 5, 14, 15

  12. Problem #2 Second Step: Order the data and identify the median and the extremes. 2. 5, 6, 9, 14, 15,16, 17, 18, 22, 48 Lower extreme Median Even number of values, so you need to get the Mean of the two values. Upper extreme 15.5

  13. Problem #2 Third Step: Identify the quartiles using the lower and upper halves of the data. 2. 5, 6, 9, 14, 15,16, 17, 18, 22, 48 Upper Quartile Lower Quartile

  14. Problem #2 Fourth Step: Subtract the extremes to find the range. 2. 5, 6, 9, 14, 15,16, 17, 18, 22, 48 48 – 5 = 43 Range = 43 What are the extremes? Range answer

  15. Problem #2 Fifth Step: Subtract the quartiles to find the interquartile range. 2. 5, 6, 9, 14, 15,16, 17, 18, 22, 48 18 – 9 = 9 Interquartile range = 9 What are the quartiles? Interquartile range answer

  16. Problem #2 Answer 2. 5, 6, 9, 14, 15,16, 17, 18, 22, 48 Median = 15.5 Extremes = 5 and 48 Quartiles = 9 and 18 Range = 43 Interquartile range = 9 Write the answer labeling each part (Median, extremes, quartiles, range, and interquartile range)

  17. Problem #3 First Step: Write the problem. How does the exclusion of the outlier affect the mean, median, mode, and range of the data from the given exercise. 3. Exercise 1: the outlier is 86

  18. Problem #3 Second Step: Find the mean, median, mode, and range for the original data set. 3. 48, 52, 59, 61, 64, 64, 86 48+52+59+61+64+64+86 = 434 434 ÷ 7 = 62; mean = 62 61 is in the middle so the median = 61 64 occurs most often so the mode = 64 86 – 48 = 38; range = 38 Find the mean by adding the values and dividing by 7 Find the median determining which number is in the middle. Find the mode determining which number occurs most often. Find the range by subtracting the lowest value from the highest value.

  19. Problem #3 Third Step: Find the mean, median, mode, and range for the new data set. 3. 48, 52, 59, 61, 64, 64 48+52+59+61+64+64 = 348 348 ÷ 6 = 58; mean = 58 59 and 61 are in the middle so the mean of the two values is the median; median = 60 64 occurs most often so the mode = 64 64 – 48 = 16; range = 16 Find the mean by adding the values and dividing by 6 (Hint: you can use the sum from the original set and subtract the outlier.) Find the median determining which number is in the middle. The new set is even; so you will need to get the mean of the two numbers. Find the mode determining which number occurs most often. Find the range by subtracting the lowest value from the highest value.

  20. Problem #3 Final Step: Compare the mean, median, and mode for the original and new data set. 3. The mean decreased from 62 to 58, the median is decreased from 61 to 60, the mode does not change, and the range decreases from 38 to 16. Answer

  21. Problem #4 First Step: Write the problem. How does the exclusion of the outlier affect the mean, median, mode, and range of the data from the given exercise. 4. Exercise 2: the outlier is 48

  22. Problem #4 Second Step: Find the mean, median, mode, and range for the original data set. 4. 5, 6, 9, 14, 15,16, 17, 18, 22, 48 5+6+9+14+15+16+17+18+22+48 = 170 170 ÷ 10 = 17; mean = 17 15 and 16 are in the middle so the mean of the two values is the median; median = 15.5 No value occurs most often so the mode = none 48 – 5 = 43; range = 43 Find the mean by adding the values and dividing by 10 Find the median determining which number is in the middle. The set is even; so you will need to get the mean of the two numbers. Find the mode determining which number occurs most often. Find the range by subtracting the lowest value from the highest value.

  23. Problem #4 Third Step: Find the mean, median, mode, and range for the new data set. (Round mean to nearest tenth.) 4. 5, 6, 9, 14, 15,16, 17, 18, 22 5+6+9+14+15+16+17+18+22 = 122 122 ÷ 9 = 13.6; mean = 13.6 15 is in the middle so the median = 15 No value occurs most often so the mode = none 22 – 5 = 17; range = 17 Find the mean by adding the values and dividing by 6 (Hint: you can use the sum from the original set and subtract the outlier.) Find the median determining which number is in the middle. Find the mode determining which number occurs most often. Find the range by subtracting the lowest value from the highest value.

  24. Problem #4 Final Step: Compare the mean, median, mode, and range for the original and new data set. 4.The mean decreased from 17 to 13.6, the median is decreased from 15.5 to 15, the mode does not change, and the range decreases from 43 to 17. Answer

  25. Problem #5 First Step: Write the problem 5. The box-and-whisker plot shows the spread of the St. Louis Rams’ game scores for a season. If the outlier 48 is excluded, the median is 31. Compare the medians. Then tell whether the range excluding the outlier is greater or less than the range including the outlier. Explain. 15 25.5 32.5 36.5 48

  26. Problem #5 Second Step: Compare the medians 5. Median in the original set = 32.5 Median in the new set = 31 The median decreased. What is the median in the original set? What is the median in the new set? Did the median increase or decrease?

  27. Problem #5 Third Step: Determine the range in the original set and the new set. 5. 48 – 15 = 33 36.5 – 15 = 21.5 The range decreased. What is the range in the original set? What is the range in the new set? Did the range increase or decrease?

  28. Problem #5 Final Step: Explain your results 5. When the outlier is excluded the median is less and the range is less. The range is less in the new set because the smaller the number you subtract 15 from the smaller the range will be. Answer

  29. Cornell Notes Summary Include the following question and answer in your Cornell Notes Summary. How do you describe the spread of a data set? You find the _____________________.

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