Download Box and Whisker Plots

Box and Whisker Plots
Simply done by Mrs. Pullo
Order numbers
3, 5, 4, 2, 1, 6, 8, 11, 14, 13, 6, 9, 10, 7

First, order your numbers from least to
greatest:
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
Median
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

Then find the median (from the ordered list):

Cross off one number from each side until you
reach the middle number (or numbers).
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
Median (continued):
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14
If there are two numbers in the middle,
Add those 2 middle numbers together:
6 + 7 = 13
 Then divide by 2:
13 ÷ 2 = 6.5
 The median is 6.5.

Quartiles (page 1)
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

Then split the numbers on left and right
sides of the median:
1, 2, 3, 4, 5, 6, 6, │7, 8, 9, 10, 11, 13, 14
Quartiles (page 2)
1, 2, 3, 4, 5, 6, 6, │7, 8, 9, 10, 11, 13, 14

Find the median for each half:
1, 2, 3, 4, 5, 6, 6 │ 7, 8, 9, 10, 11, 13, 14
1, 2, 3, 4, 5, 6, 6 │ 7, 8, 9, 10, 11, 13, 14
Left
Median = 4
Right
Median = 10
Quartiles (page 3)
1, 2, 3, 4, 5, 6, 6
Left
Median = 4
│ 7, 8, 9, 10, 11, 13, 14
Right
Median = 10
The left median is called the LOWER
QUARTILE.
 The right median is called the UPPER
QUARTILE.

Number line
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

Draw a number line from the smallest to
the largest number without skipping any
numbers.
1
2
3
4
5
6
7
8
9
10 11
12
13 14
Quartiles on number line
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

Put circles at the LOWER and UPPER
Quartiles.
1
2
3
4
5
6
7
8
9
10 11
12
13 14
Box on Quartiles on number line
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

Draw a box connecting the circles at the
LOWER and UPPER Quartiles.
1
2
3
4
5
6
7
8
9
10 11
12
13 14
Median on number line
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

Put a circle at the median (6.5).
1
2
3
4
5
6
7
8
9
10 11
12
13 14
Median on number line
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

Draw a line connecting the median to the
box.
1
2
3
4
5
6
7
8
9
10 11
12
13 14
Low and high numbers
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

Put circles at the high and low points.
1
2
3
4
5
6
7
8
9
10 11
12
13 14
Low and high numbers
1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

Draw lines that connect the high and low
points to the box.
1
2
3
4
5
6
7
8
9
10 11
12
13 14
Box and Whisker Plot
3, 5, 4, 2, 1, 6, 8, 11, 14, 13, 6, 9, 10, 7
1
2
3
4
5
6
7
8
9
10 11
12
13 14
Here is the completed Box and Whisker
Plot!
Five-Number Summary
Lowest Value or Minimum
 Quartile 1 (Q1)
 Quartile 2 (Q2) or Median
 Quartile 3 (Q3)
 Highest value or Maximum

Five-Number Summary
Example - For the data set
{10,20,30,40,50,60,70}:
 The five number summary is

Lowest number, 10
 Q1, 20
 Median, 40
 Q3, 60
 Highest number, 70

Quartiles

Box Plot is divided into fourth. So we
consider data in the
Quartile 1 (Q1) 25th percentile,
 Quartile 2 (Q2) Median or 50th percentile,
Quartile 3 (Q3) 75th percentile,

Interquartile Range

The interquartile range is the difference
between Q3 and Q1 or Q3 –Q1
IQR Interquartile range
Q3-Q1
 Tells the spread of the middle half (50%)

If 50% of the female population has a
height between 5’3” and 5’6”
 That means that the IQR is 5’6”- 5’3”=3”
 The average height of a female has a
spread of 3”

Modified Box Plot tells you what
outliers exist
Find the IQR and multiply by 1.5
 In the previous example the IQR =3
 So 3(1.5)=4.5
 4.5 is added to Q3 and subtracted to Q1
 That sets the limits
 Any number that falls below or above the
limits is an outlier

Better example of Modified Box Plot
Height of women in ABC Ladies Club
 4.3, 4.6, 4.7, 5.0, 5.0, 5.1, 5.1, 5.1, 5.2,
5.3, 5.3, 5.3, 5.3, 5.4, 5.4, 5.4, 5.4, 5.4,
5.5, 5.5, 5.5, 5.6, 5.6, 5.8, 5.9, 6.2


5 Point Summary

Min 4.3
(Q1) 5.1
Median (Q2) 5.35
Q3 = 5.5
Max = 6.2




Modified Box Plot

5 Point Summary
Min 4.3
(Q1) 5.1
Median (Q2) 5.35
Q3 = 5.5
Max = 6.2
4.3_________5.1_________5.35________5.5______________6.2