Start with the recap, study the fully worked examples, then use the practice problems to
check your understanding of Box Plot.
This page combines explanation, solved examples, and follow-up practice so you can move
from recognition to confident problem-solving in Statistics.
Concept Recap
A visual display of the five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
A box plot is like an X-ray of your data's skeleton. The box shows where the middle 50% of data lives. The line inside is the median. The whiskers stretch to the extremes. You instantly see the center, spread, and any unusual values.
Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:Box Plot organizes data so the right pattern is visible without distorting the counts or scale.
Common stuck point:Students often know a procedure related to box plot but skip the recognition step: Am I choosing or interpreting a display that matches the type of data and the question being asked? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint:Ask: Am I choosing or interpreting a display that matches the type of data and the question being asked?
Worked Examples
Example 1
medium
Dataset 5,7,8,9,10,12,15,18,22 (n=9). Walk through finding the five-number summary.
Answer
min=5,Q1=7.5,median=10,Q3=16.5,max=22
First step
1
Median is the 5th value: 10.
See the full worked solution + why-it-works coaching
Setup·Key insight·Why it works·Common pitfall·Connection
Dataset 12,14,15,16,18,20,22,25 (n=8). Find the IQR and check whether any value is an outlier by Tukey's rule.
Example 3
medium
Data: 2, 4, 5, 7, 8, 9, 11, 13, 15. Find the five-number summary and describe how to draw a box plot.
Example 4
medium
A box plot shows: Min = 10, Q1 = 20, Median = 35, Q3 = 50, Max = 90. Calculate the IQR and determine if a value of 100 would be an outlier using the 1.5×IQR rule.
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
A box plot has min 10, Q1 20, median 30, Q3 40, max 50. What is the median?
Example 2
easy
A box plot has Q1 = 15 and Q3 = 35. What is the interquartile range (IQR)?IQR = Q3 − Q1
Example 3
easy
A box plot has min 5 and max 45. What is the range?Range = max − min
Example 4
easy
A box plot's box spans Q1 = 20 to Q3 = 60. What percent of the data lies inside the box?What percent of data lies inside the box?
Example 5
easy
A box plot has five numbers: min 2, Q1 4, median 6, Q3 9, max 12. What is the third quartile?
Example 6
easy
Two box plots share the same axis. Box A's median is 30, box B's median is 50. Which dataset has the higher center?Which dataset has the higher center?
Example 7
easy
A box plot has a very long right whisker and a short left whisker. What does this suggest about the data's shape?
Example 8
easy
A box plot has min 8, Q1 8, median 12, Q3 16, max 16. The data values 0..20. Which value equals both the min and Q1?
Example 9
medium
A dataset is 3, 5, 7, 9, 11, 13, 15 (already sorted, n=7). Find the median and Q1 for its box plot.
Example 10
medium
A box plot has Q1 = 25, Q3 = 45. Using the 1.5*IQR rule, what is the upper fence (above which a point is an outlier)?Upper fence = Q3 + 1.5 × IQR
Example 11
medium
A box plot has Q1 = 30, Q3 = 50. What is the lower fence by the 1.5*IQR rule?Lower fence = Q1 − 1.5 × IQR
Example 12
medium
A dataset 2, 4, 4, 6, 8, 8, 10, 12 (n=8) is shown as a box plot. Find Q1 and Q3.
Example 13
medium
Two box plots compare two classes. Class A: IQR 10. Class B: IQR 25. Which class has more consistent (less spread) middle scores?Which class has more consistent middle scores?
Example 14
medium
A box plot has min 10, Q1 20, median 35, Q3 40, max 80. Is the maximum likely an outlier by the 1.5*IQR rule?Is 80 an outlier? Upper fence = 40 + 1.5×20 = 70
Example 15
medium
A box plot's median sits much closer to Q1 than to Q3. What does this say about the data within the box?
Example 16
medium
A box plot is built from min 4, Q1 8, median 10, Q3 14, max 20. What percent of data lies between the median and the maximum?
Example 17
medium
A box plot has Q1 = 12, median = 18, Q3 = 30. Between which two adjacent quartiles is the data most spread out?
Example 18
challenge
A dataset 5, 7, 8, 10, 12, 14, 15, 18, 40 (n=9) is shown as a box plot. Find the IQR and determine whether 40 is an outlier.
Example 19
challenge
Two box plots: Class A has median 70, IQR 8; Class B has median 70, IQR 20. The medians are equal. Which statement is best supported: scores are equally typical but Class B is more variable?Same median, different variability
Example 20
challenge
A box plot has min 20, Q1 = a, median 40, Q3 = 55, max 70. The IQR equals the distance from median to max. Find Q1.
Example 21
easy
A box plot has min 4, Q1 9, median 14, Q3 20, max 25. What is the IQR?
Example 22
easy
A box plot has min 0, max 40. What is the range of the data?
Example 23
easy
A box plot has Q1 30 and Q3 60. What percent of the data lies between Q1 and Q3?
Example 24
easy
A box plot has median 50. About what percent of data is at or below 50?
Example 25
easy
Two box plots have medians 40 and 55. Which has the higher center?
Example 26
easy
A box plot has min 10, Q1 12, median 18, Q3 24, max 30. About what percent of data is between 12 and 24?
A box plot has Min = 4, Q1 = 9, Median = 12, Q3 = 18, Max = 21. Find the interquartile range and state the interval containing the middle 50% of the data.