Boxplots and Outliers Worksheet
Boxplots & Outliers Practice Worksheet
Skills Practice
Name: ___________________________ Date: _________________
Class Period: _______
Reference Guide: Anatomy of a Boxplot
Five-Number Summary (In Order):
1. Minimum: Smallest value
2. Q1 (Lower Quartile): Middle of bottom half
3. Median (Q2): True middle value
4. Q3 (Upper Quartile): Middle of top half
5. Maximum: Largest value
Boxplot Anatomy Tips:
• Left Whisker: Starts at Minimum
• The Box: Starts at Q1 and ends at Q3
• Line inside Box: Marks the Median
• Right Whisker: Ends at Maximum
Formula: \(\text{IQR} = \text{Q3} - \text{Q1}\)
Problem 1: Guided Boxplot Construction
Data is already sorted least to greatest
Data Set: 2, 4, 6, 8, 10, 12, 14
Minimum (Smallest)
Q1 (Mid Lower)
Median (Middle)
Q3 (Mid Upper)
Maximum (Largest)
Draw the boxplot above this number line:
0
2
4
6
8
10
12
14
16
Problem 2: Independent Boxplot Practice
Data is already sorted least to greatest
Data Set: 3, 5, 7, 9, 11, 13, 17
Minimum (Smallest)
Q1 (Mid Lower)
Median (Middle)
Q3 (Mid Upper)
Maximum (Largest)
Draw the boxplot above this number line:
0
4
8
12
16
20
24
Part 1: Boxplot Construction Page 1 of 4 Turn page for Reading & Interpreting Boxplots →
Part 2: Reading & Analyzing Boxplots
Analysis Skills
Use this Boxplot for Questions 3 – 7: Study each marked value carefully
4 Min
8 Q1
12 Median
16 Q3
20 Max
3. What is the Median of the boxplot above?
A. 4 B. 8 C. 12 D. 16
4. What is the IQR (Interquartile Range)?
\(\text{IQR} = \text{Q3} - \text{Q1}\)
A. 4 B. 8 C. 12 D. 16
5. What percentage of all data values fall inside the central box (between Q1 and Q3)?
A. 25% B. 50% C. 75% D. 100%
6. Written Explanation: How do you tell the difference between the Median and the Q3 on a boxplot?
Write 1–2 complete sentences explaining where to look on the diagram:
7. If a data value of 28 is added to this data set, where would it lie?
A. Inside the main box B. Past the maximum whisker to the right C. Directly at the median line D. Below the minimum endpoint
Part 2: Boxplot Analysis Page 2 of 4 Turn page for Outlier Fence Calculations →
Part 3: Calculating IQR & Outlier Fences
Step-by-Step Fences
How to Find Outlier Fences: 4-Step Checklist
Step 1: Find IQR
\(\text{IQR} = \text{Q3} - \text{Q1}\)
Subtract Q1 from Q3
Step 2: Multiply
\(1.5 \times \text{IQR}\)
Find fence distance
Step 3: Lower Fence
\(\text{Q1} - (1.5 \times \text{IQR})\)
Subtract from Q1
Step 4: Upper Fence
\(\text{Q3} + (1.5 \times \text{IQR})\)
Add to Q3
Problem 8: Guided Fence Calculation
Follow the 4 steps with given values
Given Data Values: \(\text{Q1} = 6\) | \(\text{Q3} = 12\)
Step 1: Calculate the IQR
\(\text{IQR} = \text{Q3} - \text{Q1}\)
\(12 - 6 =\) ________
Write final IQR: \(\text{IQR} =\) _____
Step 2: Multiply by 1.5
Distance \(= 1.5 \times \text{IQR}\)
\(1.5 \times\) _______ \(=\) ________
Distance value: _____
Step 3: Lower Fence
\(\text{Q1} - (1.5 \times \text{IQR})\)
\(6 -\) _______ \(=\) ________
Lower Fence: _____
Step 4: Upper Fence
\(\text{Q3} + (1.5 \times \text{IQR})\)
\(12 +\) _______ \(=\) ________
Upper Fence: _____
Problem 9: Independent Fence Calculation
Show all calculation steps
Given Data Values: \(\text{Q1} = 10\) | \(\text{Median} = 15\) | \(\text{Q3} = 22\)
Fill in each value:
1. \(\text{IQR} = 22 - 10 =\) ________
2. \(1.5 \times \text{IQR} = 1.5 \times\) ______ \(=\) ________
3. \(\text{Lower Fence} = 10 -\) ______ \(=\) ________
4. \(\text{Upper Fence} = 22 +\) ______ \(=\) ________
Show Your Scratch Work:
Use this space for multiplication and addition:
Tip: An outlier is any number outside these two fences!
Part 3: Fence Calculations Page 3 of 4 Turn page for Outlier Testing & Reasoning →
Part 4: Testing for Outliers & Reasoning
Decision & Reasoning
Problem 10: Temperature Data Analysis (High Outlier)
Read the scenario and decide
A science class measures daily high temperatures (°F): 68, 70, 72, 74, 75, 78, 96
Calculated Fences: Lower Fence = 58°F | Upper Fence = 90°F
Check the Highest Value: 96°F
Is 96 greater than the Upper Fence of 90?
YES NO
Is 96 an outlier? Circle: YES / NO
Complete the Explanation Sentence:
"The temperature of 96°F is / is not an outlier because it is ___________________ than the upper fence of ___________________."
Word bank: greater, less, 90°F, 58°F
Problem 11: Quiz Scores Outlier Test (Low Outlier)
Show full calculations in the box below
A student tracks their quiz scores: 2, 12, 14, 16, 18, 20, 22
Given summary: Q1 = 14, Median = 16, Q3 = 20. Suspicious low score to test: 2.
Step-by-Step Test:
1. \(\text{IQR} = 20 - 14 =\) ________
2. \(1.5 \times \text{IQR} = 1.5 \times\) ______ \(=\) ________
3. \(\text{Lower Fence} = 14 -\) ______ \(=\) ________
4. Is 2 below the Lower Fence? YES / NO
Sentence Explanation:
"The score of 2 is / is not an outlier because it is ___________________ than the lower fence of ___________________."
Identified Outlier: _________________
Problem 12: Math Thinking & Reasoning
Is the greatest number in a data set always an outlier? Explain why or why not.
My Success Checklist:
Found Q1 & Q3 correctly Calculated IQR × 1.5 Compared values to the fences
Part 4: Outlier Testing & Reasoning Page 4 of 4 Worksheet Complete ✓
