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Warm-Up Interpreting Clusters and Outliers

Lesson Question

?

Lesson Goals

Interpret clusters and outliersin scatterplots.

Identify clusters and

in scatterplots.

Identify outliers in a

set.

Words to Know

Write the letter of the definition next to the matching word as you work through the lesson. You may use the glossary to help you.

cluster A. a value in a data set that varies significantly from the rest of the data

scatterplot B. to examine; to study carefully and in detail

analyze C. a graph where two sets of data are plotted as points so that relationships between the data can be visualized

outlier D. a group of data points that are together

WK2


Warm-Up Interpreting Clusters and Outliers

Recognizing Relationships with Scatterplots

• The scatterplot compares the score on homework with the score on a test.

• Are the variables related?

As homework scores ,

test scores also increased.20

40

60

80

100

20 60 8040 100

Test

Sco

res

Homework Scores

x

y


Instruction

2Slide

Interpreting Clusters and Outliers

Defining Clusters

A cluster is a of data points that are together.

Graphs with clusters:

x

y

x

y

They’re all grouped together in both of these graphs.

Data points that are in clusters tend to indicate that the variables are related.

Graphs without clusters:

x

y

x

y

The data points are just scattered about.

Graphs without clusters tend to indicate that there is no relationship between the variables.


Instruction Interpreting Clusters and Outliers

4Slide

Clusters Formed from Data Grouped Together

• Is there a pattern of data points grouped together in the scatterplot?

, all the data is clustered fairly

close together.

• Is there a relationship between the amount of time in an experiment and the number of bacteria that have grown?

Yes, there is a

between the variables.

It appears that as time goes on, the amount of bacteria increases.N

umbe

r of

Bac

teri

a

Time

x

y

Analysis of a Scatterplot

• Does the scatterplot have a cluster?

, the data points are spread all

over with no grouping together at all.

• Is there a relationship between the population of a city and the amount of rainfall?

There is relationship between

the amount of rainfall that a city receives and the population of that city.

Am

ount

of R

ainf

all

Population of a City

x

y



7Slide

Outliers in a Scatterplot

An outlier is a value in a data set that significantly from the rest of the data.

Outliers represent values.

Are there outliers in this graph?

Number of Cashiers

Sal

es (d

olla

rs)

x

y

1 72 3 4 5 6 8 9

20

40

60

80

100

; when the number of cashiers is high, 8, but the sales are low, $20.



9Slide

12

Outliers in a Table

Are there any outliers?

, where four home runs were

hit total, but the winning team scored a total of 13 runs.

This is an unusual or event

when compared with the rest of the data.

This point then is an .

Total Home Runs in Baseball

Game, x

Final Score of Winning

Team, y

1 32 32 43 54 136 76 87 6

Impact of Outliers

• Outliers do not represent the data set as well as points located in a

.

• Outliers are often extreme values

that occur .

• How would you interpret this cluster?

Test scores tend to increase as the number of hours slept

.

Circle the outliers in the scatterplot.

Sco

re o

n Te

st (p

erce

nt)

Amount of Sleep on Nightbefore Test (hours)

x

y

2 4 8

20

40

80

60

100

6 10



14Slide

Outliers and Interpreting Clusters

When we look at this data set, we might say that the hours slept tends to

as people get older.

Sle

ep, A

vera

ge P

erN

ight

(hou

rs)

Age (years)

x

y

2

4

6

10 20 40 60 80

8

10

• How might the two outliers cause this scatterplot to be misinterpreted?

We might be more reluctant to make the statement about age and amount of sleep that people get.

• Very high values may cause a description of the data set to be

overstated. Very low values may cause the to be understated.

Outliers should be .


Summary Interpreting Clusters and Outliers

?

Answer

Review: Key Concepts

• Clusters

Dis

tanc

e W

alke

d (f

eet)

Time Walked (minutes)

x

y

The cluster shows that there is a relationship between this data. The

distance walked as

the time walked increases.

• Outliers

Am

ount

of R

ainf

all

x

y

Population of a City

In this graph, we see a cluster of data and three other points that are extreme and far away from the rest of the data points. These are called

.

Lesson Question How do you interpret clusters and outliers in a scatterplot?

2


Summary Interpreting Clusters and Outliers

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