Lecture 13. Outliers
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1 Lecture 13 Outliers
2 Outliers In this lesson: 1. Finding quartiles in a stem and leaf diagram: 2. One definition of an outlier 3. How to classify an observation as an outlier. What you should be able to do: 1. Find the quartiles and the interquartile range of a stem and leaf diagram. 2. Use the method in this lecture to classify observations in a stem and leaf diagram as outliers or not outliers.
3 Finding Quartiles in a stem and leaf diagram For the following stem and leaf diagram, find Q1, Q3, and the IQR. Then create your own steps for how the problem should be done. Do this problem in your groups. Step 1: Step 2: Step 3: Step 4: Step 5: HINT: How did you find the quartiles in a frequency table of ungrouped data? How do you find the quartiles of a list?
4 Finding Quartiles in a stem and leaf diagram For the following stem and leaf diagram, find Q1, Q3, and the IQR. Then create your own steps for how the problem should be done. Do this problem in your groups. Q1= 3.2 Step 1: Step 2: Step 3: Step 4: Step 5: Q3 = 4.0 IQR = 0.8 HINT: How did you find the quartiles in a frequency table of ungrouped data? How do you find the quartiles of a list?
5 Finding Quartiles in a stem and leaf diagram For the following stem and leaf diagram, find Q1, Q3, and the IQR. Then create your own steps for how the problem should be done. Do this problem in your groups. Q1= 3.2 Step 1: Step 2: Step 3: Step 4: Step 5: 30 4 = Q 1 = x 8 = eigth term = 3. 2 n = Q3 = 4.0 IQR = 0.8 = Q 3 = x 23 = twenty third term = 4. 0 HINT: How did you find the quartiles in a frequency table of ungrouped data? How do you find the quartiles of a list? IQR = Q 3 Q 1 = = 0. 8
6 One Definition of an Outlier Earlier we defined an outlier as an observation that is very far away from other observations. There is, however, a small problem with this definition:
7 One Definition of an Outlier Earlier we defined an outlier as an observation that is very far away from other observations. There is, however, a small problem with this definition: WHAT DOES THIS MEAN?
8 One Definition of an Outlier Earlier we defined an outlier as an observation that is very far away from other observations. There is, however, a small problem with this definition: WHAT DOES THIS MEAN? How do we decide what is very far and what is not? Is it just a personal decision? How do different statisticians agree on what is and is not an outlier if they have different ideas on what is very far? To solve this problem there is one definition we can use:
9 One Definition of an Outlier Earlier we defined an outlier as an observation that is very far away from other observations. There is, however, a small problem with this definition: WHAT DOES THIS MEAN? How do we decide what is very far and what is not? Is it just a personal decision? How do different statisticians agree on what is and is not an outlier if they have different ideas on what is very far? To solve this problem there is one definition we can use: Definition Outlier An outlier is any observation that is 1.5(IQR) away from the first or third quartile Formula: Upper outlier > Q3 +1.5(IQR) Lower outlier < Q1 1.5(IQR)
10 One Definition of an Outlier Earlier we defined an outlier as an observation that is very far away from other observations. There is, however, a small problem with this definition: WHAT DOES THIS MEAN? How do we decide what is very far and what is not? Is it just a personal decision? How do different statisticians agree on what is and is not an outlier if they have different ideas on what is very far? To solve this problem there is one definition we can use: Definition Outlier An outlier is any observation that is 1.5(IQR) away from the first or third quartile Formula: Upper outlier > Q3 +1.5(IQR) Lower outlier < Q1 1.5(IQR) REMEMBER: This is a definition of an outlier, not the definition of an outlier.
11 How to classify an observation as an outlier For the following stem and leaf diagram, find all of the outliers Q1= 3.2 Q3 = 4.0 IQR = 0.8 Step 1: Find Q1 and Q3 Step 2: Find the IQR Step 3: Calculate Q1 1.5(IQR), if any observations are smaller than that number, they are outliers Step 4: Calculate Q (IQR), if any observations are larger than that number, they are outliers
12 How to classify an observation as an outlier For the following stem and leaf diagram, find all of the outliers Q1= 3.2 Q3 = 4.0 IQR = 0.8 Step 1: Find Q1 and Q3 Step 2: Find the IQR Step 3: Calculate Q1 1.5(IQR), if any observations are smaller than that number, they are outliers Step 4: Calculate Q (IQR), if any observations are larger than that number, they are outliers Q IQR = = 2 Q IQR = = 5.2 There are no observations < 2 but 5.5 >5.2, 5.5 is an outlier
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