Outliers. 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.

Outliers

Do NowBill 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

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

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

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

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 numberand 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

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

3 7 9 12 14 15 17 18 40

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

24

27

29

33

36

37

38

41

42

45

50

Median

Smallest

Largest

Median

Median

4

33

24

50

39.5

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

A 5 Number Summary divides your data into four quarters.

3 7 9 12 14 15 17 18 40

1st Quarter

2nd Quarter

3rd Quarter

4th Quarter

3 7 9 12 14 15 17 18 40

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

3 7 9 12 14 15 17 18 40

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

3 7 9 12 14 15 17 18 40

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

3 7 9 12 14 15 17 18 40

IQR = 8

+ 12- 12

- 3 39OUTLIER

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