Mathematics
Grade 6
15 min
Identify an outlier
Identify an outlier
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define what an outlier is in a data set.
Explain why identifying outliers is important.
Visually identify potential outliers on a number line.
Compare data points to the rest of the set to determine if a value is an outlier.
Identify an outlier in a given set of numerical data.
Understand how outliers can affect measures of central tendency (like the mean).
Articulate strategies for checking if a value is truly an outlier.
Have you ever seen a group of friends, and one person is wearing a winter coat while everyone else is in shorts? 🧥👖 That person really stands out, right? In math, we have something similar called an 'outlier'!
In this lesson, you'll learn what an outlier is and why it's like the 'odd one out' in a grou...
2
Key Concepts & Vocabulary
TermDefinitionExample
Data SetA collection of numbers or information gathered about something.The ages of students in a class: {11, 12, 11, 13, 12}
OutlierA data point in a set that is significantly different from the other data points. It's much larger or much smaller than most of the other values.In the data set {5, 7, 8, 6, 50}, the number 50 is an outlier because it is much larger than the other numbers.
RangeThe difference between the highest and lowest values in a data set. It tells you how spread out the data is.For the data set {2, 5, 8, 10}, the range is 10 - 2 = 8.
Mean (Average)The sum of all values in a data set divided by the number of values. It's a way to find the 'typical' value.For the data set {2, 3, 7}, the mean is (2 + 3 + 7) / 3 = 12 / 3 = 4.
Media...
3
Core Formulas
The 'Sticks Out' Rule
An outlier is a data point that is noticeably much larger or much smaller than the majority of the other data points in a set.
This rule helps you get an initial sense of what an outlier looks like. It's about visual inspection and common sense. If a number seems 'out of place' compared to the others, it's a candidate for an outlier.
The Number Line Visualization Rule
Plotting all data points on a number line can visually reveal an outlier as a point that is isolated or far away from the main cluster of other points.
This is a key strategy for identifying outliers. By seeing the numbers spread out, it becomes much easier to spot a value that is significantly separated from the rest of the data.
The 'Distance Check&...
5 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
The mean of four numbers {18, 22, 25, 21} is 21.5. If a fifth number, X, is added to the set and it is a low outlier, which of these could be the value of X?
A.16
B.20
C.2
D.30
Challenging
The number of pets owned by students are: {1, 2, 1, 0, 2, 1, 15, 3}. A student claims 15 is not an outlier because it's possible for someone to own 15 pets. Why is this reasoning incorrect from a statistical perspective?
A.The reasoning is correct; if a value is possible, it cannot be an outlier.
B.An outlier is defined by its relationship to the other data in the set, not by whether the value is possible in real life.
C.15 is an odd number, which makes it an outlier.
D.The student did not calculate the mean correctly.
Challenging
Consider the data set {10, 20, 22, 25, 50, 55}. Which value is the most likely outlier and why?
A.10, because the gap between 10 and 20 is larger than the gap between 50 and 55.
B.55, because it is the highest value in the set.
C.25, because it is in the middle of the data.
D.Both 10 and 55 are outliers because they are the lowest and highest.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free