Outlier detection is the process of identifying data points that are unusually far from the rest of the dataset, using techniques like the IQR rule, z-scores, or visual inspection of box plots and scatter plots. These anomalous values may indicate measurement errors, data entry mistakes, or genuinely extreme observations.
Outliers are data points that don't fit the pattern. A 7-foot student in a class of average heights, or a \$10 million house in a neighborhood of \$300k homes. They may be errors or genuinely unusual.
Showing a random 20 of 50 problems.
Example 1
hard
A data set has mean xΛ=100 and standard deviation s=15. Using the z-score method, determine whether the values 60, 145, and 155 are outliers (using the threshold β£zβ£>2).
Example 2
medium
Why might using ONLY the z-score method miss outliers in a skewed data set?
Example 3
hard
Why does the IQR rule generally identify FEWER outliers than the β£zβ£>3 rule for skewed data?
Example 4
hard
For data {0.5,1,1.2,1.5,1.8,2,2.2,5} with Q1β=1.1,Q3β=2.1, is 5 an outlier?Is 5 an outlier? (Qβ
Example 5
easy
A data set has Q1β=10 and Q3β=20. Find the IQR.Find the IQR from this box plot.
Example 6
medium
For ages of attendees at a children's birthday party, the value 42 appears next to a long list of values from 4 to 10. Is 42 likely an outlier?
Example 7
challenge
Data: 2,4,6,8,10,12,14,16 with Q1β=5, Q3β=13. Find both fences and state whether any value is an outlier.
Example 8
easy
Data: 4,5,6,7,8,9,100. Which value is most likely an outlier?
Example 9
medium
Test scores: 72, 75, 78, 80, 82, 85, 88, 90, 92, 95. A new student's score of 25 is added. How does this outlier affect the mean and median?
Example 10
easy
True or false: outliers should always be removed before analysis.
Example 11
easy
With Q1β=10, Q3β=20, IQR=10, find the lower fence Q1ββ1.5β IQR.Find the lower fence Qβ β 1.5Β·IQR.
Example 12
easy
In the β£zβ£>3 rule, z stands for what?
Example 13
medium
A z-score is calculated as z=β3.4 for some value x. What does that mean?
Example 14
hard
With Q1β=25,Q3β=75, find both IQR-rule fences.
Example 15
easy
With Q1β=30,Q3β=50,IQR=20, what is the upper fence?Find the upper fence. (Qβ
Example 16
challenge
Explain why the IQR rule is more robust to extreme values than the z-score rule (one concise reason).
Example 17
medium
A value has z-score β2.5 in a roughly normal distribution. By the β£zβ£>3 rule, is it an outlier?
Example 18
medium
For Q1β=12,Q3β=20, is 30 an outlier by the IQR rule?
Example 19
hard
A teacher records 30 students' typing speeds. A z-score β£zβ£>3 rule flags two values. What should the teacher do?
Example 20
medium
A value is 8, the mean is 20, and the SD is 4. Is it an outlier by the β£zβ£>3 rule?