outliers. do now bill gates makes $100 thousand a year. he s in a room with 9 teachers, 4 of whom...
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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