Download Statistics and Probability 8.SP.4

!
!
Pomona Unified Math News
th
Domain: 8 Grade Statistics and Probability (SP)
8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying
frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing
data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows
or columns to describe possible association between the two variables. For example, collect data from students
in your class on whether or not they have a curfew on school nights and whether or not they have assigned
chores at home. Is there evidence that those who have a curfew also tend to have chores?
1
Suggested Standards for Mathematical
Practice (MP):
MP 2 Reason abstractly and quantitatively.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
Explained in 8.SP.1
Vocabulary:
(Note: vocabulary will be taught in the context
of the lesson, not before or separate from the
lesson.)
Correlation/association: See 8.SP.1
Bivariate data: See 8.SP.1
Scatter plot: See 8.SP.1
Outlier: See 8.SP.1
Linearity: See 8.SP.1
Line of best fit: A See 8.SP.2
Two-Way Table: These tables of counts
organize data about two categorical variables.
Values of the row variable label the rows that
run across the table, and values of the column
variable label the columns that run down the
table.
Connections: r 8.N
S.1
See Standard 8.SP.1
Explanations and Examples:
Students recognize that categorical data can
also be described numerically through the use
of a two-way table.
1
Adapted from Georgia Math Grade 8 flip book and
www.mathisfun.com
Example 1:
A survey was conducted to determine if boys
eat breakfast more often than girls.
The following table shows the results of this
survey:
Male Female Total
Eat breakfast on a
190
110
300
regular basis
Do not Eat
breakfast on a
130
165
295
regular basis
Total
320
275
595
Sample Solution:
Students use the information from the table to
compare the probabilities of males eating
breakfast (190 of the 320 males = 59%) and
females eating breakfast (110 of the 275
females = 40%). From this data, it can be
determined that the males surveyed eat
breakfast more regularly than the females
surveyed.
Example 2:
The table illustrates the results when 100
students were asked the survey questions: Do
you have a curfew? Do you have assigned
chores? Is there evidence that those who have a
curfew also tend to have chores?
Chores
Yes
No
Total
Yes
40
10
50
Curfew
No
10
40
50
Total
50
50
100
Sample Solution:
Of the students who answered that they had a
curfew, 40 had chores and 10 did not. Of the
!
!
Pomona Unified Math News
th
Domain: 8 Grade Statistics and Probability (SP)
8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying
frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing
data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows
or columns to describe possible association between the two variables. For example, collect data from students
in your class on whether or not they have a curfew on school nights and whether or not they have assigned
chores at home. Is there evidence that those who have a curfew also tend to have chores?
students who answered they did not have a
curfew, 10 had chores and 40 did not. From
this sample, there appears to be a positive
correlation between having a curfew and
having chores.
Part A
Use the results of the survey to complete this
table.
Example 3:
At least one Pet
Yes
No
Total
Jacob surveyed 25 adults to ask whether they
had at least one child under the age of 18 and
whether they had at least one pet. This table
shows the results of the survey.
At least one child under
the age of 18
Yes
No
Total
Part B
Jacob made the conjecture that there is a
possible association between whether an adult
has at least one child under the age of 18 and
whether the adult has at least one pet. State
whether the results of the survey provide
evidence that adults who have at least one child
under the age of 18 also tend to have at least
one pet. Explain your answer.
Sample Response:
Part A:
At least one Pet
Yes
No
Total
At least one child under
the age of 18
Yes
No
Total
9
6
15
2
8
10
11
14
25
Part B:
Yes, there is evidence that the adults who have
at least one child under the age of 18 also tend
to have at least one pet. 82% of the adults who
had at least one child also had at least one pet.
My work is shown below.
!
!
Pomona Unified Math News
th
Domain: 8 Grade Statistics and Probability (SP)
8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying
frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing
data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows
or columns to describe possible association between the two variables. For example, collect data from students
in your class on whether or not they have a curfew on school nights and whether or not they have assigned
chores at home. Is there evidence that those who have a curfew also tend to have chores?
At least one child under the age of 18
At least
one Pet
Yes
No
Yes
No
Total
9/11 =
82%
2/11 =
18%
6/14 =
43%
8/14 =
57%
15/25 =
60%
10/25 =
40%
Common Misconceptions:
See Standard 8.SP.1
• Students often confuse conditional
probability with the probability of an
intersection of two events. For instance, in
the last example, if asked what is the
probability that an adult has at least one
child under the age of 18 and has a pet,
students may answer with the probability
that given an adult has at least one child
under the age of 18, they have a pet. This
indicates a lack of understanding of
conditional probability. In the first case, the
answer is 9/25 and in the second it is 9/11.
Web Help Links (Use a QR scanner to take you
directly to the website)
https://learnzillion.com/resources/51361
https://learnzillion.com/resources/51362
https://learnzillion.com/resources/51358