Arrange the data in ascending order:
58
,
59
,
60
,
64
,
64
,
72
,
73
,
74
,
75
,
76
,
78
,
79
,
80
,
81
,
82
,
83
,
84
58,59,60,64,64,72,73,74,75,76,78,79,80,81,82,83,84
Find the median (Q2):
Since there are 17 data points, the median is the value at position
17
+
1
2
=
9
t
h
2
17+1
​
=9
th
position.
So, the median is
75
75.
Find the lower quartile (Q1):
This is the median of the lower half of the data, which consists of the first 8 data points.
The median of the lower half is the value at position
8
+
1
2
=
4.
5
t
h
2
8+1
​
=4.5
th
position.
So,
Q
1
Q1 is the average of the 4th and 5th values, which is
64
+
64
2
=
64
2
64+64
​
=64.
Find the upper quartile (Q3):
This is the median of the upper half of the data, which consists of the last 8 data points.
The median of the upper half is the value at position
8
+
1
2
=
4.
5
t
h
2
8+1
​
=4.5
th
position.
So,
Q
3
Q3 is the average of the 13th and 14th values, which is
79
+
80
2
=
79.5
2
79+80
​
=79.5.
Calculate the interquartile range (IQR):
I
Q
R
=
Q
3
−
Q
1
=
79.5
−
64
=
15.5
IQR=Q3−Q1=79.5−64=15.5.
Identify any outliers:
Outliers are values that fall below
Q
1
−
1.5
×
I
Q
R
Q1−1.5×IQR or above
Q
3
+
1.5
×
I
Q
R
Q3+1.5×IQR.
Draw the box-and-whisker plot:
Draw a box from
Q
1
Q1 to
Q
3
Q3, with a line at the median. Then, draw whiskers extending from the box to the minimum and maximum values within 1.5 times the IQR. If there are outliers, mark them separately.
Once you've followed these steps, you should have a box-and-whisker plot representing the data