Outliers
SECONDARY 1 MATH
Describe features of a
Normal Distribution
Box & Whisker Plots
Mean: 10.25
Median and Mean are close together - 10 and 10.25
Distance from Min 🡪 Med = 10
Distance from Med 🡪 Max = 10
Very evenly spread out
Describe features of a
Skew Left Distribution
Box & Whisker Plots
Mean: 14.3
Median is 18, the Mean of 14.3 has been pulled lower by some data points
Distance from Min 🡪 Med = 18
Distance from Med 🡪 Max = 2
Very spread out on the left side!
Describe features of a
Skew Right Distribution
Box & Whisker Plots
Mean: 10.3
Mean of 10.3 is higher than the Median of 6
Distance from Min 🡪 Med = 6
Distance from Med 🡪 Max = 14
More spread out on the right side
You gather data from people in your neighborhood about how much they paid for their most recent vehicle. The prices of the vehicles (in thousands of dollars) were 16, 6, 11, 9, 20, 3, 17, 5
Create a five number summary from the data set by hand
3 5 6 9 11 16 17 20
Min: Q1: Med: Q3: Max:
3
10
20
5.5
16.5
You gather data from people in your neighborhood about how much they paid for their most recent vehicle. The prices of the vehicles (in thousands of dollars) were 16, 6, 11, 9, 20, 3, 17, 5
You had a new neighbor move in and they paid 50 thousand dollars for their car. What is the new
five number summary?
3 5 6 9 11 16 17 20 50
Min: 3 Q1: 5.5 Med: 10 Q3: 16.5 Max: 20
3
11
50
5.5
18.5
Min: Q1: Med: Q3: Max:
Did anything change significantly?
Median & Q3 went up slightly
Max jumped by 30
You gather data from people in your neighborhood about how much they paid for their most recent vehicle. The prices of the vehicles (in thousands of dollars) were 16, 6, 11, 9, 20, 3, 17, 5
A few more people moved into your neighborhood and you asked them how much they paid for
their vehicles. They told you 51, 60, 55, and 54 thousand dollars. Find the 5 number summary
3 5 6 9 11 16 17 20 50 51 54 55 60
Min: 3 Q1: 5.5 Med: 10 Q3: 16.5 Max: 20
3
17
60
7.5
52.5
Min: Q1: Med: Q3: Max:
Did anything change significantly?
Q1, Med, & Max went up
Q3 jumped by 34!
Min: 3 Q1: 5.5 Med: 11 Q3: 18.5 Max: 50
Plot all three Five Number Summaries as Box & Whisker Plots above the same number line.
What do you notice? Why is this happening?
Min: 3 Q1: 5.5 Med: 10 Q3: 16.5 Max: 20
Min
Q1
Med
Q3
Max
Min: 3 Q1: 5.5 Med: 11 Q3: 18.5 Max: 50
Min: 3 Q1: 7.5 Med: 17 Q3: 52.5 Max: 60
Min
Q1
Med
Q3
Max
Min
Q1
Med
Q3
Max
Neighborhood Car Values (Thousands of $)
Outliers
data points that differ significantly from the other collected data
Q1 – 1.5⋅IQR and Q3 + 1.5⋅IQR become the limits to determine outliers
The lowest point that is NOT an outlier becomes the new end for the whisker (Min),
the highest point that is NOT an outlier becomes the new end for the whisker (Max)
Outliers are shown as an asterisk or dot on the Box & Whisker Plot
Calculate if there are any outliers in the 5-number summaries below, and redraw the Box &
Whisker Plots using a dot to indicate that it is an outlier.
Min: 3 Q1: 5.5 Med: 10 Q3: 16.5 Max: 20
Min
Q1
Med
Q3
Max
Min: 3 Q1: 5.5 Med: 11 Q3: 18.5 Max: 50
Min: 3 Q1: 7.5 Med: 17 Q3: 52.5 Max: 60
Min
Q1
Med
Q3
Max
Min
Q1
Med
Q3
Max
Neighborhood Car Values (Thousands of $)
IQR:
Lower Limit:
Upper Limit:
11
−11
33
IQR:
13
LL:
UL:
−14
38
IQR:
45
LL:
UL:
−60
120
Use Graphing Calculators: Ms. Johnson gives a math test to her students.
The student’s test scores are listed below:
85, 74, 86, 78, 100, 77, 81, 87, 84, 74, 85, 74, 80, 78, 87, 85, 77, 75, 85, 84
In a graphing calculator, enter the scores into L1 and create a five-number summary
for the data set. Plot the Box & Whisker including outliers on your calculator.
<<Window: Xmin= 0 Xmax= 105 Xscl=10 >>
IQR:
8
Lower Limit:
Upper Limit:
65
97
The student that scored 100 is an outlier
A student was absent the day of the test, but took it and scored a 33. Enter all the
scores, including the new one into L2. (Do not change L1)
85, 74, 86, 78, 100, 77, 81, 87, 84, 74, 85, 74, 80, 78, 87, 85, 77, 75, 85, 84
What are the new numbers for the five-number summary? Plot the new Box & Whisker
including outliers on your calculator. What has changed from the previous plot?
IQR:
9
Lower Limit:
Upper Limit:
62.5
98.5
Both 33 and 100 are outliers
More students that were absent took the test and scored 40, 85, and 71. Enter all
previous scores and these three new ones into L3. (Do not change L1 or L2)
85, 74, 86, 78, 100, 77, 81, 87, 84, 74, 85, 74, 80, 78, 87, 85, 77, 75, 85, 84, 33
How does the five-number summary change if these three data points are now added to
the data set? Plot the new Box & Whisker including outliers on your calculator. What
do you notice has happened?
IQR:
10.5
Lower Limit:
Upper Limit:
58.75
100.75
100 is no longer an outlier,
but 33 and 40 are