Reading boxplots
Read numerical positions accurately and qualify percentage interpretations
- Landmarks The line inside the box is the median; box edges are quartiles
- Range Use the full data extremes, including separately plotted observations if shown
- Approximate proportions Quartile positions suggest approximate quarter shares. Ties and sample size affect exact counts
- Limits A boxplot does not generally determine the mean, mode, sample size or original data
Worked example
An ordinary boxplot has minimum 2, Q1 5, median 9, Q3 14 and maximum 18 minutes
- \(\displaystyle \mathrm{IQR}=14-5=9\)The middle-half spread is 9 minutes
- \(\displaystyle \mathrm{range}=18-2=16\)The full span is 16 minutes
- \(\displaystyle 100\%-75\%=25\%\)About a quarter lies above Q3 under the usual approximate interpretation. This is not an exact count claim
Common mistakes
Difficulty levels
Questions about this topic
Why say approximately 25%?+
Ties, finite samples and different quartile conventions can change exact counts below a boundary
Can I count observations from box width?+
No. Numerical width measures spread, not frequency
Does the median split the box into equal lengths?+
No. Each side can have a different numerical width
Can two different data sets have the same boxplot?+
Yes. Five summary values discard much of the original detail
Can recorded continuous measurements have ties?+
Yes. Rounding can produce repeated recorded values. Exact counts above or below a quartile need the raw observations and a clear inequality
Does the range include separately plotted outliers?+
Yes. They are still observations. Use the smallest and largest plotted values, not just the two whisker endpoints
Does the modified whisker end at the fence?+
Not necessarily. It ends at the most extreme observed value within or on the fence. The fence may lie between observations
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 11, VCE Units 1 & 2, General Mathematics, chapter 2: Data distributions