Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association

We included HMH Into Math Grade 8 Answer Key PDF Module 8 Lesson 1 Construct Scatter Plots and Examine Association to make students experts in learning maths.

HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association

I Can construct a scatter plot, determining whether an association is positive or negative, strong or weak, and nonlinear or linear. I can recognize outliers and clusters.

Spark Your Learning

Mrs. Tenney gave her students a test. The students had 3 weeks to study for the test, and Mrs. Tenney tracked the number of hours that each student studied and the scores they got on the test. Graph the data in the table. Describe the graph.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 1
Answer:
Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association-1
As the study time increases even the test score increased,

Explanation:
Given Mrs. Tenney gave her students a test. The students had 3 weeks to study for the test, and
Mrs. Tenney tracked the number of hours that each student studied and the scores they got on the test. Graphed the data in the table as shown above, As the study time increased the test score also increased.

Turn and Talk Why do you think there is not a constant rate of change for the number of hours studied and the test scores?
Answer:
The number of hours for study time increased, But they did not studied well so did not score well,

Explanation:
As the number of hours for study time increased, But they did not studied well so did not score well,
that’s why there is not a constant rate of chang for the number of hours studied and the test scores.

Build Understanding

An association is the description of the relationship between two data sets. Two data sets have a positive association when their data values increase together or decrease together.

Connect to Vocabulary
A scatter plot is a graph with points plotted to show a possible relationship between two sets of data.

Question 1.
The graph of the data from Mrs. Tenney’s class is shown in a scatter plot.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 2
A. Describe the change that you see in the graph.
As the ____________ increases, the ____________ increases.
Answer:
As the study time increases, the test score increases,

Explanation:
The change that I see in the graph is as the study time increases, the test score increases.

B. When data points lie roughly along a line, the data set displays a linear association. When the data seem to follow a pattern resembling anything other than a line, the data set either displays a nonlinear association or no association at all. Do you think the relation between test scores and study time appears linear? Explain.
Answer:
Yes, I think the relation between test scores and study time appears linear,

Explanation:
As the study time increases, the test score increases, In the graph the data points lie roughly along a line therefore the data set displays a linear association.

Two data sets have a negative association if one set of data values increases while the other decreases.

Mrs. Tenney also tracked the number of hours students spent on social media sites and the scores they got on the test. The data are shown in the scatter plot.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 3

C. Describe the change that you see in the graph.
As the ____________ increases, the ____________ decreases.
Answer:
As the social media time increases, the test score decreases,

Explanation:
Given Mrs. Tenney also tracked the number of hours students spent on social media sites and the scores they got on the test. The data are shown in the scatter plot.
As the social media time increased the test score decreased.

D. Do you think the relation between test scores and social media time appears linear? Explain.
Answer:
Yes, Negatively nonlinear,

Explanation:
Yes, I think the relation between test scores and social media time appears nonlinear as the slope is negative, then there is a negative nonlinear relationship, i.e., as time increases the other variable test score decreases.

Two data sets have no association when there is no relationship between their data values.

Mrs. Tenney wanted to see if there was any relationship between the number of siblings that a student has and their score on the test The data are shown in the scatter plot.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 4

E. Describe the change in test scores that you see in the graph.
Answer:
No, relationship between the number of siblings that a student has and their score on the test,

Explanation:
Given Mrs. Tenney wanted to see if there was any relationship between the number of siblings that a student has and their score on the test using data shown in the scatter plot.
The change in the test scores that I see in the graph is 0 siblings the test scores are between 80 and 90, If 1 siblings the test scores are between 80 and 100, If 2 siblings the test scores are between 78 and 88, If 3 siblings the test scores are between 73 and 100, If 4 siblings the test score is about 88,
If 5 siblings the test scores are between 90 and 99, If 6 siblings the test score is about 72,
If 7 siblings the test score is about 80, If 8 siblings the test score is about 100,
As we see even the number of siblings are increasing from 0 to 8 the test score is almost in between 72 and 100 only not much change in scores, therefore no, relationship between the number of siblings that a student has and their score on the test.

F. Do you think the relation between test scores and number of siblings appears linear? Explain.
Answer:
No, the relation between test scores and number of siblings does not appears linear,

Explanation:
If we see the scatter plot there is no constant increase or constant decrease or data points lie roughly
along a line, So there is no linear relation between test scores and number of siblings.

Connect to Vocabulary

An outlier for a data set of ordered pairs is a point that does riot follow the overall pattern on a graph of the data set.

Step It Out

Question 2.
If a scatter plot has an association, that association can also be strong or weak. For linear data, the association is stronger the closer the points are to making a line.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 5
A. Which scatter plot(s) have a positive association? Is the association of each strong positive or weak positive?
Answer:
Plots A and C have a positive association, Association is strong positive,

Explanation:
If we see the scatter plots plot A and C have a positive association as in the plots the points are closer,
So the association is strong positive.

B. Which graph or graphs appear to have outliers?
Answer:
Graph B appear to have outliers,

Explanation:
As an outlier is an observation of data that does not fit the rest of the data. It is sometimes called an
extreme value. When we graph an outlier, it will appear not to fit the pattern of the graph.
So graph B appear to have outliers.

C. A cluster is a set of closely grouped data. Which graph or graphs appear to have a cluster?
Answer:
Graph C appear to have a cluster,

Explanation:
If we see the graphs, graph C appears to have a cluster
as it has a set of closely grouped data.

Turn and Talk Which scatter plot(s) have a negative association? Is the association of each scatter plot strong negative or weak negative? How do you know?
Answer:
If one variable tends to increase as the other decreases the association is negative.
If the points are close and negative it is strong negative, If the points are far and negative it is weak negative,

Explanation:
A scatter plot matrix shows all pairwise scatter plots for many variables.
If one variable tends to increase as the other decreases the association is negative. When we the scatter plaots if the points are very close or near and negative then it is strong negative and if the points are far and negative then it is weak negative.

Question 3.
Jack earned $60 doing odd JObS tor nis neignbor. Each week he spends some of the money and records the amount of money left.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 6
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 7
A. Graph the data.
Answer:
Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association-2

Explanation:
Graphed the given data as shown above.

B. Does the scatter plot have a negative or positive association?
Answer:
Negative,

Explanation:
The scatter plot have a negative association.

C. Describe and interpret the shape of the graph.
Answer:
The shape of the graph is curve,

Explanation:
The shape of the graph is curve as the weeks are increasing money remaining has decreased but not constantly that’s why the shape is not in negative line but negative slope with curve in shape.

D. Are there any clusters or outliers? If so, what might explain the cluster or outliers?
Answer:
No clusters but one outliers at $19.00,

Explanation:
Sometimes the data points in a scatter plot form distinct groups. These groups are called clusters.
A cluster is formed when several data points lie in a small interval.
In the graph there are no clusters and an outlier is defined as a data point that can be
differentiated from the rest of the data. It is an observation that lies an abnormal distance from
other values in a random sample from a population. Here we have one outlier at 7 week which is at $19.00.

E. Is the association strong or weak?
Answer:
Association is strong,

Explanation:
The association is strong as most of the points are close to each other.

Check Understanding

Question 1.
The table shows the amount of money Anna spends at the thrift store each week.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 8
A. Graph the relationship in the scatter plot.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 9
Answer:
Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association-3

Explanation:
Graphed the relationship in the scatter plot as shown above.

B. Describe the relationship in the scatter plot, including any outliers or clusters.
Answer:
Linear, Strong association, No outliers and no clusters,

Explanation:
As the data increases it is linear
As the item purchase increases mostly money spent also increasesed in the graph the data points lie roughly along a line therefore the data set displays a linear association and they are close to one another they have strong association, No data point lies outside so no outliers and there are no several data points lie in a small interval so no clusters.

Question 2.
Use Structure The Pep Club is selling bracelets to raise money for a pet shelter. The club members staff the booth for a total of 12 hours selling bracelets. The table records the amount of money they earned each hour.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 10
A. Graph the data in the table.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 11
Answer:
Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association-4

Explanation:
Graphed the given data of the table as shown above.

B. Describe in detail the association of the graph. Include whether it is linear or nonlineai whether it is positive or negative, whether it is strong or weak, and whether it has any clusters or outliers.
Answer:
Non linear, Strong association, No outliers and no clusters,

Explanation:
As the data increases and reduces so it is non linear, As the hours increases money earned is not constantly increasing some time more and again less in the graph the data points donot lie along a line therefore the data set displays a non linear association and they are close to one another they have strong association, No data point lies outside so no outliers and there are no several data points lie in a small interval so no clusters.

Question 3.
Bob works at a movie theater collecting tickets. He tracked how many people came to each showing one day. Which showtime is an outlier?
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 12
Answer:
At 6:30 p.m,

Explanation:
Given Bob works at a movie theater collecting tickets.
He tracked how many people came to each showing one day.
The showtime which is an outlier is at 6:30 p.m if we see the attendance it is 115 very high compare to other timings attendance.

Question 4.
Critique Reasoning Chantelle says that the scatter plot has a strong positive association because the numbers at the bottom of the graph are increasing and the shape of the graph is linear. Is she correct? Explain.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 13
Answer:
Association is Strong positive but she is incorrect as the shape of the graph is not linear,

Explanation:
Given Chantelle says that the scatter plot has a strong positive association because the numbers
at the bottom of the graph are increasing and the shape of the graph is linear. She is not correct
as it has strong positive association as points are close but the shape of the graph is not a straight line so it is not linear it is in curve shape.

Question 5.
Open-Ended Ellianna made a scatter plot that showed a positive association and had one outlier. Write a possible scenario for Ellianna’s scatter plot.
Answer:
Scenario:
“In a zoo park from Monday to Sunday daily visitors were increasing on monday it was 500 visitors visited, On tuesday it was 600 visitors on wednesday there were 700 visitiors on thursday there were 800 visitors on friday it was 900 visitors on saturday it was 1000 visitors and on sunday there were 2,500 visitors visited”,

Explanation:
Given Ellianna made a scatter plot that showed a positive association and had one outlier.
Wrote a possible scenario for Ellianna’s scatter plot as “In a zoo park from Monday to Sunday daily
visitors were increasing on monday it was 500 visitors visited, On tuesday it was 600 visitors on wednesday there were 700 visitiors on thursday there were 800 visitors on friday it was 900 visitors on saturday it was 1000 visitors and on sunday there were 2,500 visitors visited”, as the day moved
the number of visitors increased and it shows poitive association, On sunday it was very more in number compared to other days visitors so it is an outlier.

Use the graph to answer Problems 6-8.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 14

Question 6.
Is there any association to the data? If so, which type?
Answer:
Yes data is associated, Non linear , Strong association,

Explanation:
As we see the graph the data is associated it is increasing positively but not in a line so it is nonlinear and points are close so strong association.

Question 7.
Is the scatter plot linear or nonlinear?
Answer:
Nonlinear,

Explanation:
The scatter plot is not in a straight line so it is nonlinear.

Question 8.
Are there any outliers or clusters in the graph?
Answer:
No outliers but clusters,

Explanation:
No points are outside so no outliers but points are very close and near from 12 to 14 from x -axis and
36 to 38 on y axis so we have clusters.

Question 9.
Open-Ended Give an example of a scenario for a scatter plot that would show no association.
Answer:
Scenario:
“Coffee Consumption vs. Intelligence”,

Explanation:
Example of a scenario for a scatter plot that would show no association is ” Coffee Consumption vs. Intelligence “, as there is no relation between the persons intelligence and the persons consuming coffee, The amount of coffee that individuals consume and their IQ level has a correlation of zero. In other words, knowing how much coffee an individual drinks doesn’t give us an idea of what their IQ level might be.

I’m in a Learning Mindset!

What types of decisions did I make when I analyzed scatter plots?
Answer:
Is data assocaiated or not, linear or nonlinear, Strong or weakly related,
Are there any outliers or clusters,

Explanation:
The decisions did I make when I analyzed scatter plots as a scatter plot is a special type of graph designed to show the relationship between two variables.
With regression analysis, we can use a scatter plot to visually inspect the data to see whether X and Y are assocaiated or not, linear or nonlinear, strong or weakly related, are there any outliers or clusters in the data.

Lesson 8.1 More Practice/Homework

Question 1.
The table shows the number of fundraiser items each person in the band sold and how much money each raised.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 15
A. Construct a scatter plot for the data.
Answer:
Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association-5
Explanation:
Constructed a scatter plot for the given data as shown above.

B. Describe the association and any features of the scatter plot.
Answer:
Nonlinear, Strong association,

Explanation:
The graph is nonlinear as it is not a straight line but as items are sold the money raised also increased and as they are close so therefore they are strongly associated.

Use the graph to answer Problems 2-4.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 16

Question 2.
Describe the association, if there is one.
Answer:
Negative nonlinear association,

Explanation:
Yes, I think the relation between data appears nonlinear as the slope is negative, then there is a negative nonlinear relationship as in x axis data increases the other variable decreases which is also not a straight line therefore negative nonlinear association.

Question 3.
Use Structure Does the scatter plot appear linear or nonlinear?
Answer:
Nonlinear,

Explanation:
As the graph is not a straight line so it is nonlinear.

Question 4.
Use Structure Are there any outliers or clusters in the scatter plot?
Answer:
One outlier and no clusters,

Explanation:
Yes there is one outlier at (5,5) and no data points lie in a small interval so no clusters.

Question 5.
Math on the Spot The table shows the number of runs scored by a softball team in their first 7 games of the year. Use the given data to make a scatter plot. Describe the association.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 17
Answer:
Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association-6
Explanation:
Nonlinear association,

Explanation:
Given the table shows the number of runs scored by a softball team in their first 7 games of the year.
Used the given data to make a scatter plot. As it is nonlinear associated because a nonlinear relationship between variables is a relationship whose scatter plot does not resemble a straight line. It resembles a curve or not really resemble anything. An increase in one variable does not result in a proportional increase or decrease in the other variable as the game increased the
score has increased and also decreased therefore nonlinear association.

Test Prep

Question 6.
Choose all the sentences that describe this scatter plot.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 18
(A) It shows a positive association.
(B) It shows a negative association.
(C) It has at least one outlier.
(D) It shows no association.
(E) It shows a cluster.
Answer:
(A) It shows a positive association,
(E) It shows a cluster,

Explanation:
All the sentences that describe this scatter plot are (A) It shows a positive association
as data of x axis increases even data in y axis increases,
(E) It shows a cluster at (4,2), (4,3) and (4,4) few data points lie in a small interval.

Question 7.
Describe each scatters plot as having positive linear, negative linear, positive nonlinear, negative nonlinear, or no association.
HMH Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association 19
Answer:
Into Math Grade 8 Module 8 Lesson 1 Answer Key Construct Scatter Plots and Examine Association-7
Explanation:
First Graph : It is positive nonlinear as x increases the values in y also increases but
not staright so they are associated,
Second Graph : It is negative nonlinear as values of x increases y decreases but not in straight line
so associated,
Third Graph: It has no association as no association means that there is no line and
all the dots are scattered.

Spiral Review

Question 8.
Breck has 22 dimes and nickels. The total value of the coins is $1.45. How many dimes and how many nickels does Breck have?
Answer:
Breck have 15 nickels and 7 dimes,

Explanation:
Given Breck has 22 dimes and nickels. The total value of the coins is $1.45.
So number of dimes and number of nickels does Breck have are we need to set up 2 equations
to solve this problem. The first thing we need to do is to assign variables to the unknown amounts.
Since it’s asking for how many nickels and dimes, let nickels = n and dimes = d. Now, our first equation is always about the number of coins we have.
Since nickels + dimes = 22 our equation would be n + d = 22. The second equation always deals with the value of the coins. Since nickels are worth .05 and dimes are worth .10,
our equation would look like .05n+.10d = 1.45. Now that we have 2 equations with 2 unknowns we can use substitution or elimination to solve the equations. I think substitution would be the simplest in this situation. So we solve the first equation for a variable. n + d = 22 or d = 22 – n
Now we can substitute that in place of d in the second equation.
.05n + .10d = 1.45, So .05n + .10(22-n) = 1.45 now distribute to get .05n + 2.2 – .10n = 1.45,
combine like terms to get -.05n + 2.2 = 1.45 move the 2.2 to the right by subtracting from both sides
to get -.05n = -.75, now divide both sides by -.05 to get n = 15, Since n + d = 22 and we now know n = 15 we can find d. 15 + d = 22 or d = 7, therefore Breck have 15 nickels and 7 dimes.

Question 9.
Solve this system of linear equations.
4x + 4y = 12
6x – 4y = -32
Answer:
x = -2, y = 5,

Explanation:
Given eqautions as 4x + 4y = 12 — equation (1) and
6x – 4y = -32 — equation (2) adding equation (1) and (2)
4x + 4y = 12
6x – 4y = -32
10x = -20 ,
So x = -20/20 = -2, substituting x = -2 in equation (1) we get
4 (-2) + 4y = 12,
-8 + 4y = 12,
4y = 12 + 8,
4y = 20, so y = 20/4 = 5.

Question 10.
Find an equation of the line with a slope of -7 that passes through the point (-3, 12).
Answer:
The equation of the line is y = -7x – 9,

Explanation:
Given to find an equation of the line with a slope of -7
that passes through the point (-3, 12). As we have formula
y – y1 = m (x – x1) where m is the slope so
y – 12 = -7(x – (-3)),
y – 12 = -7x – 21,
y = -7x – 21 + 12 = -7x – 9, therefore the equation is
y = -7x – 9.

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