Name class date Algebra 1 Unit 6 Practice · Name class date © 2014 College Board. All rights...

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1© 2014 College Board. All rights reserved. SpringBoard Algebra 1, Unit 6 Practice

LeSSon 36-1 1. Chloe and her friend Amanda decide to record the amount of time they exercise each day.

The result is in the table below.

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Chloe 30 min 15 min 15 min 15 min 15 min 15 min 30 minAmanda 45 min 18 min 20 min 10 min 0 min 12 min 25 min

Algebra 1 Unit 6 Practice

a. What can you tell about Chloe’s exercise routine by looking at her data? Find the mean and range of Chloe’s data.

b. What can you tell about Amanda’s exercise routine by looking at her data? Find the mean and range of Amanda’s data.

c. Reason abstractly. What can you say about each girl’s exercise routine by comparing the mean and range of the data sets?

2. Find the mean absolute deviation (MAD) of Chloe’s data set.

a. Complete the table below. Use the mean for Chloe’s data that you calculated in Item 1.

Chloe Deviation Absolute Deviation

Time Time 2 Mean Time 2 Mean

30 30 2 19151515151530

b. What is the MAD for Chloe’s data set?

3. Find the mean absolute deviation (MAD) of Amanda’s data set.

a. Complete the table below. Use the mean for Amanda’s data that you calculated in Item 1.

Amanda Deviation Absolute Deviation

Time Time 2 Mean Time 2 Mean

45 45 2 19 5 26182010 01225

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b. Find Amanda’s MAD.

c. Is Chloe’s MAD the same as Amanda’s MAD? Explain.

4. Classify each as a sample or a census.

a. Surveying every student in school about distance traveled to school each day.

b. Asking Seniors about after school activities.

c. Selecting every tenth student who arrives in the morning to gather information about tardiness.

d. Asking Juniors in school about Junior sports.

5. Which of the following questions is NOT a statistical question?

A. How many students are in your class?

B. Do you like classical music?

C. How many cousins do you have?

D. How many books did you read last year?

LeSSon 36-2 6. Determine each sum.

a. ∑5

ii 5

10

b. ∑ 25

i 15i 12

19

c. ∑52

i3i 2

4

d. ∑i31

6

e. ∑ 2

5

2ii

1

0

3

7. Use appropriate tools. Calculate the mean and standard deviation of the data in the following table.

a. Complete the table.

xi x | xi 2 x | ( )x xi2

2

x1 5 12x2 5 9.5x3 5 11x4 5 10.25x5 5 13

∑ 55

xii 1

5

∑ 2 55

x xii 1

5

∑( )2 55

x xii

2

1

5

b. Find the MAD.

c. Find the standard deviation.

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8. Prospect Creek Camp, Alaska is one of the coldest places in the United States. The average monthly temperature in degrees Celsius is shown in the table below.

Prospect Creek Camp, Alaska

Month Jan Feb Mar Apr May Jun Jul Aug Sep oct nov Dec

Average low 8C 230.5 230.8 223.7 214.2 20.7 5.6 7.8 4.5 21.9 213.7 223.3 229.6

a. Organize the information in the table below. Then complete the table. Round your answers to the nearest hundredths.

xi xi | xi 2 xi | ( )x xi i2

2

∑ 55

xii 1

12

∑ 2 55

x xi ii 1

12

∑( )2 55

x xi ii

2

1

12

b. Find the MAD.

c. Find the standard deviation.

9. Arhmando did a project for homework and gathered the following statistical data: 30.8, 7.2, 31.5, 33.5. Which is the standard deviation for Arhmando’s set of data?

A. 9.275

B. 12.41947

C. 25.75

D. 37.25841

10. Reason abstractly. Find the MAD and the standard deviation of 28, 9, 15, and 210. Compare the two measures. What can you say about the data?

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LeSSon 37-1 Ms. Noone’s class at Riverside High School did a survey of all the students in the school to determine how

many hours students spend doing homework each week. They separated the questionnaires that were returned by grade level. Then picked a random sample of 10 students from each grade level and placed the results in the table below.

Time Spent on Homework each Week (Hours)

Sophomores 6 12 15 7 11 12 10 12 3 10Juniors 5 10 13 10 12 13 15 16 13 12Seniors 14 11 9 15 11 14 10 15 17 15

11. a. Construct a dot plot for each set of data above.

Sophomores

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2043210

Juniors

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2043210

Seniors

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2043210

b. Describe the three data sets with specific attention to center and spread.

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12. For each group, complete the five-number summaries of the data.

Sophomores Juniors Seniors

Minimum

First quartile

Median

Third quartile

Maximum

13. a. Use the summaries in Item 12 to construct box plots of the three data sets:

Sophomores

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2043210

Juniors

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2043210

Seniors

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2043210

b. Which data set seems to have the least overall spread in its middle 50%?

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14. Reason abstractly. Based on the data and graphs, does it appear that there is a change in the amount of time students spend on homework as they advance to a higher grade level? Explain.

15. Which type of graph makes it easier to compare centers and spreads?

A. Bar graph

B. Box plot

C. Dot plot

D. Line graph

LeSSon 37-3 16. What does a z-score tell us about a data value?

17. How do you calculate a z-score?

18. The daily high mean temperature for February in Fairbanks, Alaska is shown in the table. For each data value, calculate the deviation from the mean and the z-score.

Daily High Mean Temperature in February Fairbanks, Alaska

DateTemperature

8F( x 2 x )

x xs2

1 9 2 5 3 6 4 6 5 7 6 7 7 7 8 8 9 810 911 912 1013 1014 1115 1116 1217 1218 1319 1320 1421 1422 1523 1524 1625 1626 1727 1728 18

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19. Assuming the temperature highs are normally distributed, what is the probability that the high temperature will be above 10°F on a randomly selected day in February in Fairbanks, Alaska?

A. 0.35

B. 0.50

C. 0.85

D. 0.95

20. Estimate the probability that the mean high temperature will be below 7°F on a randomly selected day in February in Fairbanks, Alaska.

LeSSon 38-1 21. Which of the following might show a strong

negative relationship between the two variables?

A. age and weight

B. money in a savings account and monthly withdrawals

C. number of siblings and hours of sleep

D. number of pets and annual vet bill

22. Reason quantitatively. Describe the relationship between the number of hours studying for a test and the grade on the test.

23. Model with mathematics. Describe the trend in each scatter plot. Explain what the graphs may mean about the relationship between the two variables.

a.

Test

Gra

de

Student Height

b.

Sal

es

Price

Price vs. Sales

c.

Dis

tanc

e

Time

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24. a. Make a scatter plot of the data in the table.

Hours in Practice and Games Won

Hours 1 2 3 4 5 6 7 8 9 10Games Won 1 0 1 4 2 1 3 5 3 4

b. Describe the trend in the scatter plot.

c. What are some things that might affect whether or not a team wins a game?

25. What trend might you see in a scatter plot with a horizontal scale of outdoor temperature and a vertical scale of energy used for heat?

LeSSon 38-2 26. What does the correlation coefficient measure?

27. A scatter plot has a correlation coefficient of 20.159. What does this suggest about the relationship between the two variables?

28. When will the correlation coefficient be 0?

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29. Match the scatter plot with its correlation coefficient.

A. r 5 20.95 _____

B. r 5 0.981 _____

C. r 5 20.772 _____

D. r 5 0.043 _____

E. r 5 0.828 _____

F. r 5 20.238 _____

G. r 5 0.310 _____

x

y

710 2 3 4 5 6

5

4

3

2

1

Scatter Plot 1

x

y

710

0

0

2 3 4 5 6

5

4

3

2

1

Scatter Plot 2

x

y

81 2 3 4 5 76

6

5

4

3

2

1

Scatter Plot 3

x

y

51 2 3 4

6

5

4

3

2

1

Scatter Plot 4

x

y

71 2 3 654

71 2 3 654

71 2 3 654

87654321

Scatter Plot 5

x

y6

5

4

3

2

1

Scatter Plot 6

x

y5

4

3

2

1

Scatter Plot 7

x

y

710 2 3 4 5 6

5

4

3

2

1

Scatter Plot 1

x

y

710

0

0

2 3 4 5 6

5

4

3

2

1

Scatter Plot 2

x

y

81 2 3 4 5 76

6

5

4

3

2

1

Scatter Plot 3

x

y

51 2 3 4

6

5

4

3

2

1

Scatter Plot 4

x

y

71 2 3 654

71 2 3 654

71 2 3 654

87654321

Scatter Plot 5

x

y6

5

4

3

2

1

Scatter Plot 6

x

y5

4

3

2

1

Scatter Plot 7

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30. Reason quantitatively. What is the range of values for r? What do these values indicate?

LeSSon 39-1 31. Using your best judgment, draw a line that you feel

best represents the linear relationship between the variables in the scatter plot.

32. The relationship between age and weight in adult black bears can be approximately described by the line y 5 23.69 1 0.115x where y is age in years and x is weight in pounds. Answer each of the following to the nearest hundredth.

a. What is the predicted age of a bear that weighs 120 pounds?

b. What is the predicted age of a bear that weighs 205 pounds?

c. What is the predicted weight of a 5-year old bear?

33. Make use of structure. The owner of a café kept records on the daily high temperature and the number of hot apple ciders sold on that day. Some of the data is in the table.

Daily High Temperature (8F )

32 75 80 48 15

number of Hot Apple Ciders Sold

51 22 12 40 70

The equation of the best-fit line for this data is y 5 80.13 2 0.82x where x represents the daily high temperature in degrees Fahrenheit and y represents the number of hot apple ciders sold.

a. Predict the number of hot apple ciders that will be sold on a day when the high temperature is 258F.

b. Predict the number of hot apple ciders that will be sold on a day when the high temperature is 60°F.

c. Predict the temperature on a day when 60 hot apple ciders are sold.

d. Suppose you used the equation for the line of best fit to predict the number of hot apple ciders that would be sold on a day when the high temperature is 15°F. How far off would you be from the actual data? Explain.

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34. Suppose the equation for a line of best fit is y 5 1.05x 1 1.48. For what value of x will y be 50?

A. 28

B. 32

C. 46

D. 85

35. The data points on a scatter plot do not cluster around the line of best fit. What can be said about the relationship between the bivariate data sets?

LeSSon 39-2 36. Roni wanted to determine if there was a

relationship between the fuel efficiency of a car and its mass. Roni researched the fuel efficiency of 12 different models of cars. The table shows the fuel efficiency and mass of these 12 cars.

Car Fuel efficiency

city highway combined mpg mass(kg)

1 11 17 13 1695 2 12 19 15 1560 3 16 26 19 1519 4 19 27 21 1305 5 19 27 21 1330 6 14 20 16 1635 7 22 29 25 1589 8 26 35 29 1115 9 22 28 24 130710 20 26 22 149711 21 31 25 149812 17 24 19 1950

a. Model with mathematics. Construct a scatter plot of the combined mpg and the mass of the 12 cars.

b. Based on the scatter plot, how would you describe the relationship between the combined mpg and the mass of a car?

c. Use technology to find the equation of the best-fit line.

d. Use the best-fit line to predict the combined mpg to the nearest unit of a car with a mass of 1500 kg.

37. The best-fit line for city mpg and the mass of a car is y 5 37.25 2 0.013x. To the nearest whole kilogram which is the predicted mass of a car with a fuel efficiency of 15 mg in the city.

A. 1635 kg

B. 1685 kg

C. 1712 kg

D. 1925 kg

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38. Make use of structure. Car 6 has a mass of 1635 kg and an actual fuel efficiency of 20 mpg on the highway. Find the predicted highway fuel efficiency of car 6 on the line of best fit y 5 48.245 2 0.015x. Why does the predicted highway fuel efficiency of car 6 differ from the actual highway fuel efficiency?

39. What is a residual? When is a residual negative?

40. The line of best fit for the fuel efficiency on the highway of the twelve cars is y 5 48.245 2 0.015x. Complete the table by finding the predicted fuel efficiency and the residual for each car. Round your answers to the nearest whole unit.

Fuel EfficiencyCar Mass

(kg)Highway

mpgPredicted

mpgResidual

1 1695 17 2 1560 19 3 1519 26 4 1305 27 5 1330 27 6 1635 20 7 1589 29 8 1115 35 9 1307 2810 1497 2611 1498 3112 1950 24

LeSSon 39-3 41. A survey of the heights of mothers and daughters

resulted in a best-fit line of y 5 69 2 0.0849x where x represents the height of the mother in inches.

a. Interpret the value of the slope in the context of this problem.

b. Make sense of problems. What other things might influence the height of the daughter besides the height of the mother?

42. Reason abstractly. When would you not use the line of best fit to make a prediction?

43. The equation of the best-fit quadratic curve for marathon data of woman is y 5 473.3 2 15.8x 1 0.203x2 where x is the age of the runner and y is the finish time in minutes. What is the predicted finish time of a 25-year-old woman?

A. 83 minutes

B. 205 minutes

C. 598 minutes

D. 995 minutes

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44. The scatter plot for the age and finish time of marathon women is shown.

325Finish Time vs. Age

Fini

sh T

ime

(min

) 300

275

250

225

200

10 20 30 40Age (years)

50

y

x60 700

What does this scatter plot suggest?

45. Data of the CO2 concentration and temperature (°C) was collected for ten years. The range of the CO2 concentration was 314 to 369 parts per million. Does it make sense to predict the temperature at a CO2 concentration of 350 parts per million? Explain.

LeSSon 39-4 46. The data for the CPI (Consumer Price Index)

and the cost of a subway ride in a city is shown in the table.

CPI Subway Fare ($)

Predicted Fare ($)

Residual

30.2 0.1548.3 0.35

112.20 1.00162.2 1.35191.9 1.50197.8 2.00

a. Construct a scatter plot for this data set. Describe the relationship between the variables in terms of strength, direction, and shape.

b. Find the equation of the best-fit line.

c. Compute the predicted values and the residuals to the nearest cent, and place these values in the table.

d. Construct a residual plot.

e. Does the residual plot support your description of the relationship between the two variables? Explain.

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47. Make use of structure. Samantha constructed a residual plot of the data she collected. The residuals are scattered randomly above and below zero. What does this tell Samantha about the best-fit line of her data?

48. What does a strong pattern in the residual plot tell you about the use of the best-fit line to describe the relationship between the variables?

49. Suppose you graphed the best-fit line on a scatter plot. How would you know whether a point had a positive or negative residual?

50. What characteristic of the residual plot suggests that the line of best fit is a good representation of the data?

A. a strong pattern in the residual plot

B. a linear pattern in the residual plot

C. a curved pattern in the residual plot

D. a random pattern in the residual plot

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LeSSon 40-1 Use the table that is in the U.S. Senate report of the Loss of S.S. “Titanic” to answer Items 51–55.

Investigation into Loss of S. S. “Titanic”

CPI on Board Saved LostPercent savedWomen and

ChildrenMen Total

Women and Children

Men TotalWomen and

ChildrenMen Total

PassengersFirst ClassSecond ClassThird Class

156128224

173157486

145104105

541569

1124

119

119142417

Total passengers

. . .

Crew 23 876 20 194 3 682Total

51. a. How many second-class passengers were there?

b. How many second-class passengers were women and children?

c. How many second-class passengers were lost?

d. Reason quantitatively. Compare the number of second-class women and children lost to the number of third-class women and children lost.

52. Determine the marginal totals. Fill in the appropriate columns and rows in the table.

53. Determine the percent of passengers saved by class and percent of crew saved. Fill in the last column in the table.

54. There were 536 third-class passengers who were lost. The total number of passengers who were lost was 1324. Which is the relative frequency of the third class passengers who were lost?

A. 0.405

B. 0.536

C. 0.595

D. 0.788

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55. Critique the reasoning of others. Bonnie stated that about 77% of the women and children who were lost were third-class passengers. Do you agree with that statement? Why or why not?

LeSSon 40-2 56. The table shows multimedia usage in the U.S. for

three consecutive years.

United States Usage of Multimedia in Minutes Per Day

YearWeb

BrowsingMobile

ApplicationsTelevision Total

2010 70 66 1622011 72 94 1682012 70 127 168Total

a. Complete the table by filling in the totals.

b. Use the frequencies in the table to complete the Raw Percentages table. Round the percentages to the nearest tenth of a percent.

Raw Percentages U.S. Usage of Multimedia in

Minutes per Day

YearWeb

BrowsingMobile

ApplicationsTelevision Total

201020112012

c. Make a segmented bar graph to display the data in the table.

d. Reason quantitatively. Does it appear from the segmented bar graph that the distributions of multimedia usage are very similar for the three years, or are they noticeably different? How are the distributions similar or different?

57. What does a segmented bar graph represent? How is it made?

58. In a vitamin C study of 279 skiers, 31 skiers out of the 140 skiers who received a placebo caught a cold. What percentage of the skiers who took a placebo caught a cold?

A. 11%

B. 22%

C. 35%

D. 50%

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59. The information in the table below was gathered from a survey by the Transportation Committee of an industrial complex to determine the mode of transportation used by employees.

Drive Alone CarpoolPublic

Transportationother Means

Start at 8:00 64 38 10 6Start at 8:30 94 44 11 8Start at 9:00 158 45 14 8

The Transportation Committee wants to present the results of the survey in a report to the manager of the industrial complex. Describe what should be included in the report.

60. Use the information in Item 59 to describe the association between the mode of transportation and the time an employee begins work.

Name class date Algebra 1 Unit 6 Practice · Name class date © 2014 College Board. All rights...

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