1. Further Mathematics
Box plots, 5 number summary and outliers
K McMullen 2012

2. Box plots and friends
A box plot is constructed from the values in a
five-number summary
Features: The whiskers each represent 25% of
the data at the lower and upper ends of the data
The box represents the middle 50% (IQR) of the
data
The vertical line located within the box represents
the median
K McMullen 2012

3. Box plots and friends
To calculate the 5 number summary:
Use CAS
By hand:
1. Place values in order
2. Find the median (middle value)
3. Split the bottom half in two (this will be your lower
quartile)
4. Split the top half in two (this will be your upper
quartile)
5. Minimum and maximum values are just that- the
lowest value and the highest value
K McMullen 2012

4. Box plots and friends
Outliers: extreme values that don’t “fit in” with the
rest of the data set
On CAS- need to plot “mod box plot” (box plot on
CAS won’t show outliers so make sure you
choose “mod box plot”
By hand:
Lower outliers: Q1 --- 1.5xIQR (known as lower
boundary)
Upper outliers: Q3 + 1.5xIQR (known as upper
boundary)
Remember that if there are outliers then these
are your minimum or maximum values too
K McMullen 2012

5. Box plots and friends
Classwork and Homework:
2A: 4, 5, 6, 7
2B: 1, 2, 3, 4, 5, 6
Write own notes for “relating a box plot to
distribution shape” p.45
Write own notes for “ Interpreting box plots:
describing and comparing distributions” p.48
K McMullen 2012