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Outliers

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Do Now Bill Gates makes $100 thousand a year. He s in a room with 9 teachers, 4 of whom make $40k, 3 make $45k, and 2 make $55k a year. What is the mean salary of everyone in the room? What would be the mean salary if Gates wasn t included? Mean With Gates: $50,500 Mean Without Gates: $45,000

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312740914181517 Find the mean and median of the following set of numbers: Mean is 15 Median is 14

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In a set of numbers, a number that is much LARGER or much SMALLER than the rest of the numbers is called an Outlier.

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To find any outliers in a set of data, we need to find the 5 Number Summary of the data.

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Find the 5 Number Summary of the following numbers: 312740914181517 Step 1: Sort the numbers from lowest to highest 379121415171840 Step 2: Identify the Median 379121415171840 Step 3: Identify the Smallest and Largest numbers 379121415171840 Step 4: Identify the Median between the smallest number and the Median for the entire set of data, and between that Median and the largest number in the set. 379121415171840

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These are the five numbers in the 5 Number Summary 3 - Smallest number in the set 9 - Median between the smallest number and the median 14 - Median of the entire set 17 - Median between the largest number and the median 40 - Largest number in the set 379121415171840

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Find the 5 Number Summary for the following set of data: 42 16 38 50 24 29 41 36 18 4 33 37 24 27 45 4 16 18 24 27 29 33 36 37 38 41 42 45 50 Median Smallest Largest Median 4 33 24 50 39.5

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Find the 5 Number Summary for the following set of data: 4 8 2 19 11 6 21 13 5 7 10 20 14 15 18 3 Median = 10.5 Smallest = 2 Largest = 21 Median = 5.5 Median = 16.5 2 3 4 5 6 7 8 10 11 13 14 15 18 19 20 21

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A 5 Number Summary divides your data into four quarters. 379121415171840 1 st Quarter 2 nd Quarter 3 rd Quarter 4 th Quarter

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379121415171840 The Lower Quartile (Q1) is the second number in the 5 Number Summary The Upper Quartile (Q3) is the fourth number in the 5 Number Summary 25% of all the numbers in the set are smaller than Q1 25% of all the numbers in the set are larger than Q3

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379121415171840 What percent of all the numbers are between Q1 and Q3? 50% of all the numbers are between Q1 and Q3 This is called the Inter-Quartile Range (IQR) The size of the IQR is the distance between Q1 and Q3 17 - 9 = 8

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379121415171840 IQR = 8 To determine if a number is an outlier, multiply the IQR by 1.5 8 1.5 = 12 An outlier is any number that is 12 less than Q1 or 12 more than Q3

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379121415171840 IQR = 8 + 12- 12 - 3 39 OUTLIER

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312740914181517 Find the mean and median of the following set of numbers (no outliers): Mean is 15 Median is 14 Mean is 11.875 Median is 13

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Copyright © 2011, Elsevier Inc. All rights reserved. Chapter 6 Author: Julia Richards and R. Scott Hawley.

Copyright © 2011, Elsevier Inc. All rights reserved. Chapter 6 Author: Julia Richards and R. Scott Hawley.

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