Mathematics
Grade 9
15 min
Identify an outlier
Identify an outlier
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1
Introduction & Learning Objectives
Learning Objectives
Define an outlier in the context of a data set.
Calculate the first quartile (Q1), third quartile (Q3), and the interquartile range (IQR) for a given set of data.
Apply the 1.5 x IQR rule to determine the upper and lower boundaries for a data set.
Mathematically identify any data points that are outliers.
Explain the potential effect of an outlier on the mean and median of a data set.
Visually estimate potential outliers from a box plot or a list of numbers.
Ever see a basketball player score 50 points in one game when their average is only 15? 🏀 That unusually high score is a potential outlier!
In this tutorial, you will learn the precise mathematical method to identify outliers, which are data points that are significantly different from the rest. Thi...
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Key Concepts & Vocabulary
TermDefinitionExample
OutlierA data point that is numerically distant from the other data points in a set. It 'lies outside' the expected range of values.In the data set {10, 12, 14, 15, 95}, the value 95 is a likely outlier because it is much larger than the other numbers.
Median (Q2)The middle value in a data set that has been sorted in order from least to greatest.In the sorted set {2, 5, 8, 11, 15}, the median is 8.
First Quartile (Q1)The median of the lower half of a sorted data set. It represents the 25th percentile.In the set {2, 5, 8, 11, 15}, the lower half is {2, 5}, so Q1 is the median of {2, 5}, which is (2+5)/2 = 3.5.
Third Quartile (Q3)The median of the upper half of a sorted data set. It represents the 75th percentile.In the set {2, 5, 8, 11, 15}, the upper half i...
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Core Formulas
Interquartile Range (IQR) Formula
IQR = Q_3 - Q_1
Use this formula after you have found the first quartile (Q1) and the third quartile (Q3). The IQR measures the statistical spread of the middle half of your data.
Lower Boundary (Fence) Formula
Lower Fence = Q_1 - (1.5 \times IQR)
Calculate this value to find the minimum threshold for your data. Any data point below this 'fence' is considered an outlier.
Upper Boundary (Fence) Formula
Upper Fence = Q_3 + (1.5 \times IQR)
Calculate this value to find the maximum threshold for your data. Any data point above this 'fence' is considered an outlier.
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Challenging
The upper boundary for outliers in a data set is 95, and the Interquartile Range (IQR) is 10. What is the value of the third quartile (Q3)?
A.70
B.80
C.85
D.Cannot be determined
Challenging
A data set is {10, 12, 14, 15, 17, 19}. A new data point, 'x', is added. What is the smallest integer value of 'x' that would be considered an upper outlier in the new data set?
A.29
B.28
C.30
D.29.5
Challenging
Consider the data set {5, 60, 62, 65, 68, 120}. Both 5 and 120 are outliers. If only the upper outlier (120) is removed, how does the new Interquartile Range (IQR) compare to the original?
A.The IQR stays the same.
B.The IQR increases.
C.The IQR decreases.
D.The IQR becomes zero.
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