Five Number Summary and Box Plots Please view this tutorial and answer the follow-up questions on loose leaf to be handed into your teacher. Five.

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Five Number Summary and Box
Plots
Please view this tutorial and answer the
follow-up questions on loose leaf to be
handed into your teacher.
Five Number Summary and Box Plot
Basics
• The Five Number Summary consists of the
minimum, lower quartile (Q1), median, upper
quartile (Q3), and maximum.
• It is used to determine the variability (or the
differences in data) of a data set and to
construct box plots.
• Box plots are used as a visual representation
of the data.
Five Number Summary
Definitions
• Minimum: the smallest value in a data set
• Lower quartile (Q1): the 25th percentile; 25%
of the information is less than this value
• Median: the 50th percentile or middle value
• Upper quartile (Q3): the 75th percentile; 75%
of the information is less than this value
• Maximum: the largest value in a data set
Example
Next, you’ll break up this
information into quarters.
There will be the same
amount of numbers in each
section.
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6
7
8
9
9
10
11
15
18
19
20
24
Example
First, find the middle number.
Since this list has 13 values,
the middle number would be
the 7th number.
Note: If there was an even
amount of values, you would
find the average of the two
middle numbers.
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6
7
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Example
Now that you have your
halfway point, find the middle
of the top and bottom
sections.
There are six values in the top
section so the middle value
would fall between the 3rd and
4th values.
Find the middle value for the
bottom section.
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6
7
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Example
The middle value would fall
between the 10th and 11th
values.
Now that we have our
intervals set up, we can find
the values for our five number
summary.
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7
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Example
The minimum is 5.
To find the lower quartile (Q1),
find the average of 7 and 8.
Q1 is 7.5.
The median, or middle value is
10.
To find the upper quartile
(Q3), find the average of 18
and 19.
Q is 18.5.
The maximum is 24.
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Example
You would write the five
number summary for this data
set as follows:
minimum= 5
Q1 = 7.5
median= 10
Q3 = 18.5
maximum= 24
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11
15
18
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20
24
Five Number Summary on the
Calculator
To find the five number
summary on the calculator,
first you need to enter your
information into a list then
quit.
Five Number Summary on the
Calculator
Next, hit STAT
then go over to
CALC then to
1:1VarStats( then hit
Enter.
Five Number Summary on the
Calculator
Tell the calculator where your information is
(ex. L1) then hit ENTER
Scroll down to see
the five number
summary.
Making a Box Plot
Using the five number
summary, you can easily
construct a box plot.
minimum= 5
Q1 = 7.5
median= 10
Q3 = 18.5
maximum= 24
First, we need to make a
number line.
Choose your minimum,
maximum and scale based on
Our minimum is 5 and
your five number summary.
maximum is 24. What should
we choose as our minimum,
maximum and scale for our
number line?
Making a Box Plot
0 would be a good choice for
our minimum, 25 for our
maximum with a scale of 5.
Next, we need to mark off the
values for each number in the
five number summary.
0
5
10
15
20
25
minimum= 5
Q1 = 7.5
median= 10
Q3 = 18.5
maximum= 24
Making a Box Plot
Make a small tick mark for the
minimum and maximum.
minimum= 5
Q1 = 7.5
median= 10
Q3 = 18.5
maximum= 24
Make larger tick marks for Q1,
median, and Q3.
0
5
10
15
20
25
Making a Box Plot
Connect the longer tick marks
with two lines to form a box.
minimum= 5
Q1 = 7.5
median= 10
Q3 = 18.5
maximum= 24
Connect the smaller tick marks
with lines to the center of the
box.
0
5
10
15
20
25
Describing a Box Plot
In a box plot, each segment
represents 25% of the
information.
25%
0
5
25%
10
25%
15
minimum= 5
Q1 = 7.5
median= 10
Q3 = 18.5
maximum= 24
25%
20
25
What can you tell
about the way the
information is
grouped based on
this histogram?
Describing a Box Plot
Intervals that are smaller (like
from the minimum to Q1)
have information that is tightly
packed together.
25%
0
5
25%
10
25%
15
minimum= 5
Q1 = 7.5
median= 10
Q3 = 18.5
maximum= 24
25%
20
25
Intervals that are
larger (like from the
median to Q3) have
information that is
more spread out.
Describing a Box Plot
The length of the box (from Q1
to Q3) represents the IQR, or
interquartile range. This is the
middle 50% of the data.
minimum= 5
Q1 = 7.5
median= 10
Q3 = 18.5
maximum= 24
50%
0
5
10
15
20
This value will help you
determine the
variability of a data set
or to compare
variability of more than
25 one set of data.
Describing a Box Plot
The larger the IQR, the larger
the variability of the data set.
The smaller the IQR, the
smaller the variability. The IQR
for this box plot is 11 (Q3-Q1).
minimum= 5
Q1 = 7.5
median= 10
Q3 = 18.5
maximum= 24
50%
You can also look at the
length of the box to
help determine the
variability of the data.
0
5
10
15
20
25
Describing a Box Plot
So along with the five number
summary, you can also talk
about whether the box plot is
skewed or symmetric based on
the size of each interval.
minimum= 5
Q1 = 7.5
median= 10
Q3 = 18.5
maximum= 24
Do you think this box
plot is skewed right,
skewed left, or
symmetric?
0
5
10
15
20
25
Describing a Box Plot
This box plot is skewed to the
right because the intervals
between the median and Q3
and the interval between Q3
and the maximum are very
spread out.
0
5
10
15
20
Sometimes it helps to
compare the box plot
to a histogram to
determine the
skewness of the plot.
25
Describing a Box Plot
0
5
10
15
20
25
0
5
10
15
20
25
Notice that the
histogram is skewed
to the right (the tail is
on the right).
Describing a Box Plot
Here is the correct
description of this
box plot.
0
5
10
15
minimum= 5
Q1 = 7.5
median= 10
Q3 = 18.5
maximum= 24
IQR = 11
range = 19
skewed to the right
20
25
Follow Up Questions
Answer the following questions on loose leaf
and hand them in to your teacher.
The following are scores from 25 students on a unit test in
mathematics.
75
92
62
78
85
77
93
65
80
90
65
50
70
57
98
45
54
73
84
65
50
60
74
85
70
1. Find the five number summary for this data set.
2. Find the interquartile range (IQR).
3. Make a box plot for this information.
4. Describe the distribution.
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70
80
90
100
5. About what percentage of students scored
between 70 and 90 on the test depicted in
the box plot above?
a)
b)
c)
d)
e)
40
50
75
90
Cannot be determined from the information
given

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