· web view70 1 1 5 5 6 6 8 82 2 2 3 4 90 0 4 6 6 8 8 8 8 100 0 key 8 2 = 82% standard: s.id.1...

8th Grade Algebra I - Descriptive Statistics 1

CC 2011 (This work protected by a Creative Commons AttributionNonCommercial License) Fayette County Public Schools

Standard: S.ID.1

Difficulty: Easy

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Depth of Knowledge: 2

Common Core State Standard Description:

Represent data with plots on the real number line (dot plots, histograms, and box plots).

Clusters with Instructional Notes:

Summarize, represent, and interpret data on a single count or measurement variable. In grades 6-7, students describe center and spread in a data distribution, such as the shape of the distribution or the existence of extreme data points.

Question:

The scores from a math test are recorded in a stem-and-leaf plot. Create a histogram using the data from the stem-and-leaf plot.

Stem Leaf3 55 6 6 87 0 1 1 5 5 6 6 88 2 2 2 3 49 0 0 4 6 6 8 8 8 810 0 0

Key8 2 = 82%



Standard: S.ID.1

Difficulty: Medium

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Represent data with plots on the real number line (dot plots, histograms, and box plots)



Question:

A gym class made up of 26 students takes their pulse rate after running a mile. The data given is the pulse rate, in beats per minute, of the 26 students in the gym class.

66 60 78 66 66 80 72 76 92 68 80 72 68

68 84 72 66 88 78 80 66 80 84 64 72 66

a) Create a dot plot using the given data. b) Create a box plot using the given data.



Standard: S.ID.2

Difficulty: Medium

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Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) or two or more different data sets.



Question:

State whether each statement is true or false and explain your reasoning using specific data from the box plots.

A) More students in Mrs. Plum's class scored between 66.5% and 84% than between 84% AND91% because the box is longer between 66.5% and 84% than between 84% AND 91%.

B) A greater percentage of students scored a 70% or higher in Mr. Scarlet’s class.

C) Since about 50% of the scores in Mr. Scarlet's class are above 78, and about 50% of the scores in Mrs. Plum class are above 84, the mean score for Mrs. Plum's class must be higher than the mean score for Mr. Scarlet's class.



Standard: S.ID.2

Difficulty: Medium

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Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) or two or more different data sets.



Question:

Data Set A {10, 30, 50, 70, 90} Data Set B {40, 45, 50, 55, 60}

Compare the measure of center of the two data sets.Compare the measure of spread and variation of the two data sets.



Standard: S.ID.3

Difficulty: Easy

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Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).



Question:

The two box plots represent the distribution of scores on a math test for two different Algebra classes. (The top box plot is Class A and the bottom box plot is Class B)

a. Which class had the highest performing student? Lowest performing student?

b. Which class performed better? Explain.

c. How does the outlier in Class B effect the shape, center and/or spread of the class data?

Student Pre-Test Post-TestAriana 80 90Amanda 76 83Robert 82 86Frank 66 81Meg 75 78Cilka 85 93Amy 88 94Avery 70 72Ismael 70 75 Sc

ore

on P

ost-

Test



Standard: 8.SP.1

Difficulty: Medium

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Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.


Investigate patterns of association in bivariate data. While this content is likely subsumed by S.ID.6-9, it could be used for scaffolding instruction to the more sophisticated content found there.

Question:

Students took a pre and post-test on a math unit. Use the data in the chart to complete the scatter plot.

Test Scores

Score on Pre-Test

Use the scatter plot to describe the relationship between a student’s pretest and post-test score.

Based on the scatter plot, if a student scored 72 on the pre-test, what score could they expect on the poet-test?



Standard: 8.SP.1

Difficulty: Medium

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Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.



Question:

The table below shows the results of the U.S. Census.

YearU.S. Population

(in millions) YearU.S. Population

(in millions)1900 76.2 1960 179.3

1910 92.2 1970 203.3

1920 106 1980 226.5

1930 123.2 1990 248.7

1940 132.2 2000 281.4

1950 151.3

1. Make a scatter plot. Describe the relationship between population and year

2. Based on the scatter plot, predict the U.S. population in the year 2010.

3. Predict the census results for the U.S. population in 1890

4. Suppose the population in 1890 was actually 150 million. How would you describe that point on the scatter plot?



Standard: 8.SP.2

Difficulty: Medium

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Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.



Question:

Plot the data set shown in the table. Is there a linear trend in the data? Explain. If so, give the equation of the line. If not, explain why not.

X Y

3 11

4 9

5 8

6 5

7 4

8 3



Standard: 8.SP.2

Difficulty: Medium

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Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.



Question:

The table shows Kate’s scores on her first seven math quizzes

Test Quiz Score

1 81

2 83.5

3 85

4 85

5 87

6 88

7 90

1. Make a scatter plot of the data and draw a line of best fit. Then give the equation of the line.

2. Use the line of best fit to predict Kate’s score on her eighth quiz.



Standard: 8.SP.3

Difficulty: Medium

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Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.



Question:

The number of seeding trees that can be planted in one day depends on the number of students in the work group. Data from several different work groups is shown in the next graph.

a. Draw a line that estimates the pattern in (workers, trees) data.

b. Write an equation for your graph model relating trees planted to number of workers.

c. Use your linear model to estimate how many trees will be planted by a work crew of 14. Show how you find your answer.

d. Use your linear model to estimate how many workers will be required to plant 270 trees. Show how you find your answer.

e. What is the slope of your linear model? What does that slope tell about the relationship between the variables?



Standard: 8.SP.3

Difficulty: Medium

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Question:

At Metropolis Middle School the student government earns money by recycling cans and bottles after school events.

Some sample (attendance, containers) data are shown in the graph below, along with a line modeling the pattern in the data.

a. Use the linear model to estimate answers for the next questions. Explain how each estimate can be found from the graph.

i. About how many containers will be recycled if 125 people attend a chorus concert?

ii. What attendance at a basketball game will produce about 125 containers to be recycled?

b. Use the points (200, 100) and (50, 25) to find an equation in the form

y = mx + b for the modeling line. Show your work.

c. Explain what the values of m and b in your equation tell about the relationship between number of containers to be recycled and attendance at the school event.



Standard: 8.SP.3

Difficulty: Easy

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Question:

Giselle pays $210 in advance on her account at the athletic club. Each time she uses the club, $15 is deducted from the account. Model the situation with a linear function and a graph.

a.b = 210 – 15x

c.b = 195 + 15x



b. b = 210 + 15x

d. b = 195 – 15x



Standard: 8.SP.3

Difficulty: Medium

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Question:

A balloon is released from the top of a building. The graph shows the height of the balloon over time.

a. What does the slope and y-intercept reveal about the situation?b. For a similar situation, the slope is 35 and the y-intercept is 550. What can you conclude?



Standard: 8.SP.3

Difficulty: Medium

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Question:

The range of a car is the distance R in miles that a car can travel on a full tank of gas. The range varies directly with the capacity of the gas tank C in gallons.

a. Find the constant of variation for a car whose range is 341 mi with a gas tank that holds22 gal.

b. Write an equation to model the relationship between the range and the capacity of the gas tank.



Standard: 8.SP.4

Difficulty: Medium

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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?



Question:

Antonio surveyed 60 of his classmates about their participation in school activities as well as whether they have a part-time job. The results are shown in the two-way frequency table below. Use the table to complete the exercises.

Activity

Job

ClubsOnly

SportsOnly Both Neither Total

Yes 12 13 16 14

No 3 5 5 2

Total

1. Complete the table by finding the row totals, column totals, and grand total.



2. Create a two-way relative frequency table using decimals.Activity

Job

ClubsOnly

SportsOnly Both Neither Total

Yes

No

Total

3. Give each relative frequency as a percent.a. The joint relative frequency of students surveyed who participate in school clubs only and have part-time jobs: b. The marginal relative frequency of students surveyed who do not have a part-time job:

c. The conditional relative frequency that a student surveyed participates in both school clubs and sports, given that the student has a part-time job:

4. Discuss possible influences of having a part-time job on participation in school activities. Support your response with an analysis of the data.



Standard: 8.SP.4

Difficulty: Medium

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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?



Question:

For her survey, Jenna also recorded the gender of each student. The results are shown in the two-way frequency table below. Each entry is the frequency of students who prefer a certain pet and are a certain gender. For instance, 8 girls prefer dogs as pets. Complete the table.

PreferredPet

GenderDog Cat Other Total

Girl 8 7 1

Boy 10 5 9

Total

1. Find the total for each gender by adding the frequencies in each row. Write the row totals in theTotal column.

2. Find the total for each preferred pet by adding the frequencies in each column. Write the column totals in the Total row.

3. Find the grand total, which is the sum of the row totals as well as the sum of the column totals.Write the grand total in the lower-right corner of the table (the intersection of the Total columnand the Total row)

4. Where have you seen the numbers in the Total row before?5. In terms of Jenna's survey, what does the grand total represent?



Standard: S.ID.5

Difficulty: Easy

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Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.


Summarize, represent, and interpret data on two categorical and quantitative variables. Students take a more sophisticated look at using a linear function to model the relationship between two numerical variables. In addition to fitting a line to data, students assess how well the model fits by analyzing residuals.

Question:

Dance Sports Academic TeamBoys 0 38 5

GirlsDanceSportsAcademic Team

Summarize the above data in a two-way frequency table including both marginal and joint frequencies.



Standard: S.ID.5

Difficulty: Easy

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Question:

Car Riders Bus Riders Walkers6th 52 129 187th 82 115 288th 76 100 52

Compute the marginal frequencies for the chart above.



Standard: S.ID.5

Difficulty: Hard

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Question:


What is the relative frequency of Car Riders given a student chosen from the 7th Grade?



Standard: S.ID.5

Difficulty: Medium

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Question:


What are two trends or associations with the data above?



Standard: S.ID.5

Difficulty: Medium

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Question:


a. What is the relative frequency of Car Riders at the school?b. What is the relative frequency of 7th grade students at the school?



Standard: S.ID.6.a

Difficulty: Medium

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Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.


Summarize, represent, and interpret data on two categorical and quantitative variables. Students take a more sophisticated look at using a linear function to model the relationship between two numerical variables. In addition to fitting a line to data, students assess how well the model fits by analyzing residuals. S.ID.6b should be focused on linear models, but may be used to preface quadratic functions in the Unit 6 of this course.

Question:

Determine a reasonable equation for the line of best fit for the scatter plot below.



Standard: S.ID.6.a

Difficulty: Easy

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Question:

The scatterplot below shows the relation between two variables.

Which of the following statements are true?

I. The relation is strong.II. The slope is positive. III. The slope is negative.



Standard: S.ID.6.a

Difficulty: Easy

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Question:

Graph the set of data. Decide whether a linear model is reasonable. If so, draw a trend line and write its equation.

{(1, 7), (–2, 1), (3, 13), (–4, –3), (0, 5)}

a. yes; c.yes;

b. yes;

d. yes;

a. Make a scatter plot.b. Draw a trend line forc. Write a linear equatio



Standard: S.ID.6.a

Difficulty: Easy

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Question:

Use the following data: .

your scatter plot.n for your trend line. Show your work.



Standard: S.ID.6.b

Difficulty: Medium

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Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.b. Informally assess the fit of a function by plotting and analyzing residuals.



Question:

Plot the following points and determine if the given function fits the data.

Explain your decision.

X Y3.1 1.384.5 1.95.18 3.686.14 3.642.06 .77.46 4.967.16 5.886 .44



Standard: S.ID.6.b

Difficulty: Medium

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Question:

Plot the following points and determine if the function 𝑦 = 1.2𝑥 − 3 fits the data.


X Y3.1 1.384.5 1.95.18 3.686.14 3.642.06 .77.46 4.967.16 5.886 .44



Standard: S.ID.6.b

Difficulty: Medium

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Question:

Plot the following points and determine if the function 𝑦 = .08𝑥 + 4.5 fits the data.


X Y1.9 2.75.9 6.75.3 4.02.2 2.510.7 4.510.7 2.29.9 9.714.5 7.1



Standard: S.ID.6.b

Difficulty: Medium

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Question:

Plot the following points and determine if the given function fits the data.


X Y1.9 2.75.9 6.75.3 4.02.2 2.510.7 4.510.7 2.29.9 9.714.5 7.1



Standard: S.ID.6.c

Difficulty: Hard

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Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.c. Fit a linear function for a scatter plot that suggests a linear association.



Question:

Fit a linear function to the given data. Write the function in slope-intercept form.


X Y.7 4.33.7 3.74.3 5.55.4 5.27.8 7.58.6 6.76.7 6.410.6 8.32.6 4.4



Standard: S.ID.6.c

Difficulty: Medium

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Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.c. Fit a linear function for a scatter plot that suggests a linear association.



Question:

Fit a linear function to the given data. Write the function in slope-intercept form.




Standard: S.ID.7

Difficulty: Medium

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Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.


Interpret linear models. Build on students’ work with linear relationship and introduce the correlation coefficient. The focus here is on the computation and interpretation of the correlation coefficient as a measure of how well the data fit the relationship. The important distinction between a statistical relationship and a cause-and-effect relationship arises in S.ID.9.

Question:

Describe the slope and y-intercept in the context of the situation presented in the data below.



Standard: S.ID.7

Difficulty: Medium

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Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.



Question:

a. What is the slope of the graph? What does the slope describe in terms of the situation?b. What is the y-intercept of the graph? What does the y-intercept describe in terms of the

situation?



Standard: S.ID.8

Difficulty: Hard

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Compute (using technology) and interpret the correlation coefficient of a linear fit.



Question:

Compute the correlation coefficient of a linear fit for the following data. Interpret the fit of the correlation coefficient to the data.



Standard: S.ID.8

Difficulty: Hard

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Question:




Standard: S.ID.8

Difficulty: Hard

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Question:


Arm Length Shoe Size27 cm29 cm26 cm29 cm30 cm

28.5 cm



Standard: S.ID.8

Difficulty: Hard

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Question:


Salary Birth Year$59,020 1982$85,255 1975$32,045 1965

$120,802 1998$93,531 1980$45,983 1992



Standard: S.ID.9

Difficulty: Hard

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Distinguish between correlation and causation.



Question:

Does the chart below show correlation or causation? Why?



Standard: S.ID.9

Difficulty: Hard

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Question:

Does the chart below show correlation or causation? Why?

Arm Length Shoe Size27 cm29 cm26 cm29 cm30 cm

28.5 cm



Standard: S.ID.9

Difficulty: Hard

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Question:

Compare and contrast correlation and causation in regards to statistical data and the relationship between two variables.

· web view70 1 1 5 5 6 6 8 82 2 2 3 4 90 0 4 6 6 8 8 8 8 100 0 key 8 2 = 82% standard: s.id.1...

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