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Outliers

Outliers. Do Now. Bill Gates makes $500 million 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: $50,040,500.

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Outliers

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  1. Outliers

  2. Do Now Bill Gates makes $500 million 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: $50,040,500 Mean Without Gates: $45,000

  3. 3 12 7 40 9 14 18 15 17 Find the mean and median of the following set of numbers: Mean is 15 Median is 14

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

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

  6. Find the 5 Number Summary of the following numbers: 3 12 7 40 9 14 18 15 17 Step 1: Sort the numbers from lowest to highest 3 7 9 12 14 15 17 18 40 Step 2: Identify the Median 3 7 9 12 14 15 17 18 40 Step 3: Identify the Smallest and Largest numbers 3 7 9 12 14 15 17 18 40 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. 3 7 9 12 14 15 17 18 40

  7. 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 These are the five numbers in the 5 Number Summary 3 7 9 12 14 15 17 18 40

  8. Find the 5 Number Summary for the following set of data: 4 Smallest 24 Median 33 Median 39.5 Median 50 Largest

  9. Find the 5 Number Summary for the following set of data: Smallest = 2 Median = 5.5 Median = 10.5 Median = 16.5 Largest = 21

  10. A 5 Number Summary divides your data into four quarters. 3 7 9 12 14 15 17 18 40 3rd Quarter 2nd Quarter 1st Quarter 4th Quarter

  11. The Lower Quartile (Q1) is the second number in the 5 Number Summary 25% of all the numbers in the set are smaller than Q1 3 7 9 12 14 15 17 18 40 The Upper Quartile (Q3) is the fourth number in the 5 Number Summary 25% of all the numbers in the set are larger than Q3

  12. What percent of all the numbers are between Q1 and Q3? 50% of all the numbers are between Q1 and Q3 3 7 9 12 14 15 17 18 40 This is called the Inter-Quartile Range (IQR) The size of the IQR is the distance between Q1 and Q3 17 - 9 = 8

  13. To determine if a number is an outlier, multiply the IQR by 1.5 8 • 1.5 = 12 3 7 9 12 14 15 17 18 40 IQR = 8 An outlier is any number that is 12 less than Q1 or 12 more than Q3

  14. - 12 + 12 3 7 9 12 14 15 17 18 40 IQR = 8 - 3 39 OUTLIER

  15. 3 12 7 40 9 14 18 15 17 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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