Box and Whisker Diagrams
Objectives:
B Grade
Construct and interpret a Box & Whisker
diagram (also known as a Box Plot)
Compare two set of data using box plots
Prior knowledge
Draw a cumulative frequency diagram
Find the upper and lower quartiles from a
cumulative frequency diagram
Box and Whisker Diagrams
Averages use one number to describe a set of data, this can be
misleading, depending upon which average you use.
Box and whisker diagrams use the
• median,
• upper and lower quartiles and
• range
to draw a picture that can be used to interpret data
Box plots can be drawn in two ways, from
• cumulative frequency diagrams, or
• the raw data
Box and Whisker Diagrams
Cumulative frequency
Box plots from cumulative frequency diagrams
xand UQ from
80
We have already
seen how to find the median, LQ
x
x
a cumulative frequency
diagram
70
x
Extend the
60
the working out
50
x
lines below the
40
x axis
x
30
Median UQ
x
20
LQ
Minimum value
10
0
Maximum value
x
x
x
0
10
20
30
40
50
60
Weight (g)
70
80
90
100
Draw the box
plot like this
Box and Whisker Diagrams
Looking at the box plot on its own:
Median
Minimum value
UQ
LQ
whisker
Maximum value
whisker
Box and Whisker Diagrams
Box plots from raw data
First
them
in order
of size
Fred put
keeps
a record
of his
journey times to school each morning
These are his time to the nearest minute for 25 days:
29, 16,
21, 16, 18,
25, 18,
21, 18
19, 18, 19,
30, 19,
21, 19,
21, 20,
12, 20,
26, 21,
19,
12,
12
18,
21
21, 21,
20, 21,
19, 21,
30, 21,
29, 25,
16, 26,
21, 27,
18, 29,
18, 29,
27, 30,
18, 30
20
25
Minimum value
Maximum value
Median
of pieces of data, n
Lowernumber
Quartile
Median
positionposition
n + 1 = n25+ +1
13+1 = 6.25
Lower
Quartile
1 ==25
Upper
Quartile
2
42
4
Upper Quartile position
3(n + 1) = 3(25 +1) = 18.75
4
4
Box and Whisker Diagrams
Minimum value
Maximum value
Median
Lower Quartile
Upper Quartile
12
30
21
18
25
Draw a sensible scale:
12 14
16 18 20 22
Time (minutes)
24
26
28 30
Box and Whisker Diagrams
Now do this:
Draw a box plot for this data:
18, 8, 19, 15, 27, 13, 10, 4, 8, 31, 26, 11, 29, 28, 23
Solution:
Arrange the data in order of size:
4, 8, 8, 10, 11, 13, 15, 18, 19, 23, 26, 27, 28, 29, 31
Median position n + 1 = 15 +1 = 8
Median = 18
2
2
LQ position
n + 1 = 15 +1 = 4
4
4
LQ = 10
UQ position
3(n + 1) = 3(15 +1) = 12
2
2
UQ = 27
0
4
8
10
14
16
20 24
28
32
Box and Whisker Diagrams
Interpreting Box and Whisker Diagrams
What can you say about the ages of the shoppers and what kind of
shop they are?
Dressnice has a much lower median age, so the shoppers are younger
75% of the Dressnice shoppers are younger than 75% of the
Clotheswell shoppers
Clotheswell has broader appeal because the IQR is bigger
Dressnice is a shop for younger people, perhaps more fashionable