Outliers

Outliers

Interquartile Range Lesson 2

Learning Goal

• Describe an overall pattern and any striking deviations from the overall pattern.

Standards

• 6.DS.4 Summarize numerical data sets in relation to their context in multiple ways

Multiple Choice

Review: What is an outlier?

• Someone who lays outside

• A piece of data that lies

• A piece of data that is very different from the other data.

Outlier

A data value that is much lower or much greater than all of the other values in a data set.

Outliers and the Fences

• How low or how high does a data point have to be to be an outlier?

• The upper fence and the lower fence separate outliers from the rest of the data

• Upper fence: $Q_1-1.5\ \cdot IQR$  

• Lower Fence: $Q_3-1.5\ \cdot IQR$  

• Any value less than the lower fence or greater than the upper fence is an outlier. 

IQR or Interquartile Range

Is found by subtracting $Q_1$  from $Q_3$   $\left(Q_3-Q_{1\ }=IQR\right)$  

Lets look at an example

{4,14,30,32,36,40,43,45,46,50,68}

• What's the median?

• What are  $Q_1\ and\ Q_3\ ?$  

• Median is 40, Q1 is 30 Q3 is 46

• What is the IQR? 

• Q3 - Q1 =16

{4,14,30,32,36,40,43,45,46,50,68}

• Q1=30, Q3 = 46, IQR = 16   Find the fences to determine if there are outliers. 

• Lower Fence = Q1 - 1.5(IQR) or 30 - 1.5(16)

• Upper Fence = Q3 +1.5(IQR) or 46 + 1.5(16)

• Lower Fence = 6  Upper Fence =70

• Are there any outliers (>6 or <70)?

Outliers?

• Are the minimum or maximum on this plot outliers?

• What is Q1? What is Q2? What is the IQR?

• What are the upper and lower fences?

• Are there outliers?

Outliers and the Fences

• How low or how high does a data point have to be to be an outlier?

• The upper fence and the lower fence separate outliers from the rest of the data

• Upper fence: $Q_1-1.5\ \cdot IQR$  

• Lower Fence: $Q_3-1.5\ \cdot IQR$  

• Any value less than the lower fence or greater than the upper fence is an outlier. 

Multiple Choice

Use the 1.5 IQR rule to determine if there are any outliers for the following numbers:
84, 88, 72, 74, 98, 16, 94 

• Yes, 16 is an outlier.
• Yes, 33 is an outlier.
• Yes, 98 is an outlier.
• There are no numbers less than 39 or greater than 124, therefore there are no outliers.

Multiple Choice

Find the IQR of the following numbers:
84, 88, 72, 74, 98, 16, 94 

• 78
• 22
• 16
• There is no IQR.

Poll

Can you find the outliers?

• Yes! I've got this.

• With a little practice, I'll have this mastered.

• I's still a little foggy, but I got one right.

• I don't understand this at all!

Still need practice?

Go to lesson 6.07 and do the Practice Questions.

Don't forget to take the Quiz!

• Lesson 6.07 Interquartile Range2

• iReady for 10 minutes (50 minutes a week!)