A box plot (box-and-whisker plot) summarises a data set using five key values: the minimum, lower quartile (25th percentile), median, upper quartile (75th percentile), and maximum. This makes it easy to compare the spread and centre of two or more data sets at a glance — a wider box or longer whiskers show more variability, while a shifted box shows a different typical value.
Example
Comparing test scores between two classes: if Class A's box plot sits higher overall with a narrower box, it suggests Class A generally scored higher and more consistently than Class B, whose wider box suggests more variation in results.
Key terms
Median:
The middle value of an ordered data set.
Quartile:
One of the three values dividing a data set into four equal parts.
Box plot:
A chart summarising a data set using its minimum, quartiles and maximum.
Questions
1. A box plot shows a data set's:
Minimum, quartiles, median and maximum
Only the mean
Only the mode
Colour distribution
2. The median is:
The middle value of an ordered data set
Always the highest value
Always the lowest value
The average of all values
3. What are the median and range of: 3, 5, 7, 9, 11?
Median 7, range 8
Median 5, range 8
Median 7, range 11
Median 9, range 8
4. A quartile divides a data set into how many equal parts?
Two
Three
Four
Five
5. A wider box in a box plot generally suggests:
More variability in the data
Less variability in the data
No data at all
An error in the plot
6. The "whiskers" of a box plot show:
The range between the minimum and maximum (excluding the box)
The median only
The mode only
Nothing meaningful
7. A box plot positioned higher overall (on a numeric scale) suggests:
Generally higher values in that data set
Generally lower values
No data was collected
An error in measurement
8. If Class A's box plot is narrower than Class B's for the same test, Class A's results are likely:
More consistent (less spread out)
Less consistent
Identical to Class B's
Impossible to compare
9. The lower quartile represents approximately what percentage of data below it?
25%
50%
75%
100%
10. The upper quartile represents approximately what percentage of data below it?
25%
50%
75%
100%
11. Comparing two box plots with the same median but very different box widths tells you they have:
Similar centres but different spreads
Identical spreads
No possible comparison
The same exact data
12. An outlier in a data set is:
A value far from the rest of the data
The median
The most common value
Always an error
13. Which measure is least affected by outliers?
Median
Mean
Range
Maximum
14. A box plot's "box" specifically represents the range between:
The lower and upper quartiles
The minimum and maximum
The mean and median
Two random points
15. Two data sets have the same median but Data Set A has a much larger range than Data Set B. This suggests:
Data Set A has more variability overall
Both data sets are identical
Data Set B has more variability
Range has no relationship to variability
16. When comparing box plots of two classes' test scores, which is the most complete comparison?
Comparing both the medians AND the spreads (box widths/whiskers)
Only comparing the medians
Only comparing the maximum values
Ignoring the box plots altogether
17. A box plot with a very long whisker on one side compared to the other suggests:
Data is skewed, with more spread on that side
The data is perfectly symmetrical
An error in the box plot
Nothing about the data's distribution
18. Why might comparing means alone be misleading when one data set has an extreme outlier?
The outlier can pull the mean away from what is typical, while the median stays more stable
Means are never affected by outliers
Medians are always more affected by outliers than means
Outliers have no impact on any statistic
19. Two box plots have overlapping boxes but different medians. What can you say about their data sets?
They have some similar values but a somewhat different typical (median) value
They are completely identical
They have absolutely no values in common
The comparison is meaningless
20. Which scenario would produce a box plot with a small box but very long whiskers?
Most values are close together, with a few extreme outliers
All values are identical
Values are evenly spread with no outliers
There is no data at all
21. When reporting on data spread to a non-technical audience, a box plot is useful mainly because it:
Visually summarises the centre and spread of data in one simple chart
Removes the need for any data collection
Only works for very small data sets
Is less informative than a single number
Answer key (parent copy)
1. Minimum, quartiles, median and maximum
2. The middle value of an ordered data set
3. Median 7, range 8
4. Four
5. More variability in the data
6. The range between the minimum and maximum (excluding the box)
7. Generally higher values in that data set
8. More consistent (less spread out)
9. 25%
10. 75%
11. Similar centres but different spreads
12. A value far from the rest of the data
13. Median
14. The lower and upper quartiles
15. Data Set A has more variability overall
16. Comparing both the medians AND the spreads (box widths/whiskers)
17. Data is skewed, with more spread on that side
18. The outlier can pull the mean away from what is typical, while the median stays more stable
19. They have some similar values but a somewhat different typical (median) value
20. Most values are close together, with a few extreme outliers
21. Visually summarises the centre and spread of data in one simple chart