SME
Grade 9 Math · Problem type
Compare two box plots
Use this for “Compare the reading minutes of two classes by their medians and IQRs.”
Chart
Class A: median 25, IQR 14
Class B: median 28, IQR 18
The medians differ by 3: Class B's is higher.
Class B has the wider middle half: more spread.
This is an example. Type your own values to start a new problem.
minA
Class A least
example
Q₁A
Class A first quartile
example
MA
Class A median
example
Q₃A
Class A third quartile
example
maxA
Class A greatest
example
minB
Class B least
example
Q₁B
Class B first quartile
example
MB
Class B median
example
Q₃B
Class B third quartile
example
maxB
Class B greatest
example
IQRA
Class A interquartile range
worked out (not typed)
IQRB
Class B interquartile range
worked out (not typed)
D
Difference of the medians (B − A)
worked out (not typed)
Formulas
IQRA = Q₃A − Q₁A
14 = 32 − 18
IQRB = Q₃B − Q₁B
18 = 40 − 22
D
=
MB
−
MA
3 = 28 − 25
Assumptions
•
Put both box plots on one number line so their boxes line up.
•
Compare the centers with the medians and the spreads with the IQRs.
•
The medians and IQRs are hardly moved by an outlier, so they suit skewed data.
Step-by-step
WE KNOW
minA = 10, Q₁A = 18, MA = 25, Q₃A = 32, maxA = 50, minB = 15, Q₁B = 22, MB = 28, Q₃B = 40, maxB = 55
FIND
class A interquartile range (IQRA), class B interquartile range (IQRB), difference of the medians (B − A) (D)
Step 1 · Find class A interquartile range (IQRA)
Use IQRA = Q₃A − Q₁A
Class A’s box width: the spread of its middle half.
IQRA = 32 − 18
IQRA = 14
Step 2 · Find class B interquartile range (IQRB)
Use IQRB = Q₃B − Q₁B
Class B’s box width.
IQRB = 40 − 22
IQRB = 18
Step 3 · Find difference of the medians (B − A): D
Use D = MB − MA
How far B’s median is above A’s: the difference in centers.
D
=
28
−
25
D
=
3
Check
Put the numbers back in. Both sides should match.
14 = 32 − 18 ✓
18 = 40 − 22 ✓
3 = 28 − 25 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
One-variable statistics: histograms, box plots, standard deviation and outliers
Main lesson
Outliers and the 1.5 × IQR fences
Use this for “The five-number summary is 12, 20, 24, 28, 45. Is 45 an outlier?”
Box plot from a data list
Use this for “Points in nine games: 12, 18, 9, 22, 15, 30, 14, 17, 20. Make a box plot.”
Standard deviation
Use this for “Find the mean and the standard deviation of 1, 3, 3, 5, 5, 7, 7, 9.” From 3 to 8 values.
Histogram from a data list
Use this for “Minutes of homework: 35, 42, 18, 50, 27, 44, 38, 60, 30, 47, 25, 40. Make a relative frequency histogram.”
Dot plot from a data list
Use this for “Books read by 10 students: 3, 5, 2, 4, 5, 9, 5, 1, 4, 2. Make a dot plot and find the mode, median and mean.”