Algebra 2 11 Data Analysis and Statistics Practice ...rwright/algebra2/homework...Algebra 2 11 Data...

Algebra 2 11 Data Analysis and Statistics Practice Problems

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11.1 Find Measures of Central Tendency and Dispersion 1. Copy and complete: Measures of __?__ represent the center or middle of a data set. Measures of __?__ tell you

how spread out the values in a data set are.

Find the mean, median, and mode of the data set. 2. The numbers of mice born in nine different litters: 5, 7, 6, 3, 8, 6, 4, 5, 4

3. The heights (in inches) of the members of a men’s college basketball team:

69, 70, 75, 84, 73, 78, 74, 73, 78, 71

4. What is the median of 0.5, 0.6, 0.7, 1.2, 1.5, and 1.5?

(A) 0.7 (B) 0.95 (C) 1 (D) 1.5

Describe and correct the error in finding the measure of central tendency. 5. The median of the data set below is 5 because 5 is the middle number.

12, 8, 9, 5, 10, 10, 3

Find the range and standard deviation of the data set. 6. 7, 4, 6, 8, 5, 9, 5, 7

7. 3.1, 2.7, 6.0, 5.6, 2.3, 2.0, 1.3

8. 135, 142, 148, 136, 152, 140, 158, 154

Identify the outlier in the data set. Then find the mean, median, mode, range, and standard deviation of the data set when the outlier is included and when it is not.

9. 2, 2, 3, 3, 4, 4, 4, 6, 68

10. 10.9, 12.4, 0.7, 11.6, 12.8, 11.6

Word problems 11. The data set below gives the numbers of trials required by 10 puppies to learn a trick.

20, 23, 19, 25, 21, 23, 5, 24, 19, 23

a. Identify the outlier of the data set.

b. Find the mean, median, mode, range, and standard deviation of the data set when the outlier is included

and when it is not.

c. Describe the outlier’s effect on the measures of central tendency and dispersion.

Mixed Review 12. (10.6) Calculate the probability of randomly guessing 0 correct answers on a 30-question multiply choice

exam that has choices A, B, C, and D for each question.

13. (10.5) Find the probability of drawing the a club, then a spade from a standard deck of 52 cards (a) with

replacement and (b) without replacement.

14. (8.6) Solve 5

𝑥− 2 =

2

𝑥+3

15. (7.6) Solve 76𝑥 = 12


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11.2 Apply Transformations to Data 1. Copy and complete: Multiplying each value in a data set by a constant is an example of a(n) __?__ of the data.

Find the mean, median, mode, range, and standard deviation of the given data set and of the data set obtained by adding the given constant to each data value.

2. 14, 15, 17, 17, 19, 21, 23; constant: 6

3. 74, 76, 77, 77, 78, 81, 83; constant: 17

4. 53, 64, 51, 60, 53, 45, 66; constant: -21

5. The standard deviation of a data set is 10. Describe and correct the error in finding the standard deviation

if 3 is added to each data value.

New standard deviation:

10 + 3 = 13

Find the mean, median, mode, range, and standard deviation of the given data set and of the data set obtained by multiplying each data value by the given constant.

6. 58, 58, 59, 62, 64, 65, 67; constant: 4

7. 88, 91, 99, 102, 102, 107; constant: 2.5

8. 222, 231, 222, 212, 250, 235; constant: 0.9

Word problem 9. Let 𝑥1, 𝑥2, … , 𝑥𝑛 be the values in a data set, and let 𝑥 be the mean of the data set. Show that the mean of

𝑎𝑥1, 𝑎𝑥2, … , 𝑎𝑥𝑛 is 𝑎𝑥.

10. The data set gives the winning distances (in meters) in the women’s Olympic long jump event from 1952 to

2004.

6.24, 6.35, 6.37, 6.76, 6.82, 6.78, 6.72, 7.06, 6.96, 7.40, 7.14, 7.12, 6.99, 7.07

a. Find Statistics in Meters Find the mean, median, mode, range, and standard deviation of the distances in

meters.

b. Find Statistics in Feet Find the statistics listed in part (a) for the distances in feet. (Note: 1 meter ≈ 3.28

feet.)

Mixed Review 11. (11.1) The data set below gives the numbers of passing touchdowns for the 12 quarterbacks who threw the

most touchdowns during the 2004 NFL regular season. Find the mean, median, mode, range, and standard

deviation.

49, 39, 31, 30, 29, 28, 27, 27, 27, 22, 21, 21

12. (10.6) Calculate the probability of tossing a coin 20 times and getting 9 heads.

13. (10.2) A relay race has a team of 4 runners who run different parts of the race. There are 20 students on

your track squad. In how many ways can the coach select students to compete on the relay team?

14. (8.1) The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then

find y when x = 3.

15. (5.7) Find all the zeros of the polynomial function 𝑔(𝑥) = 𝑥4 − 9𝑥2 − 4𝑥 + 12


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11.3 Use Normal Distributions 1. Copy and complete: A(n) __?__ is a bell-shaped curve that is symmetric about the mean.

A normal distribution has mean 𝒙 and standard deviation σ. Find the indicated probability for a randomly selected x-value from the distribution.

2. 𝑃(𝑥 ≤ 𝑥 − 𝜎) 3. 𝑃(𝑥 ≤ 𝑥 + 𝜎) 4. 𝑃(𝑥 − 𝜎 ≤ 𝑥 ≤ 𝑥 + 𝜎)

Give the percent of the area under the normal curve represented by the shaded region.

5. A normal distribution has a mean of 33 and a standard deviation of 4. Find the probability that a randomly selected x-value from the distribution is in the given interval.

6. Between 29 and 37 7. Between 21 and 41 8. At least 29

9. A normal distribution has a mean of 84 and a standard deviation of 5. What is the probability that a

randomly selected x-value from the distribution is between 74 and 94?

(A) 0.475 (B) 0.68 (C) 0.95 (D) 0.997

A normal distribution has a mean of 64 and a standard deviation of 7. Use the standard normal table on page 759 to find the indicated probability for a randomly selected x-value from the distribution.

10. 𝑃(𝑥 ≤ 68)

11. 𝑃(𝑥 ≤ 45)

12. 𝑃(𝑥 ≤ 64)

13. 𝑃(𝑥 ≥ 75)

14. 𝑃(45 ≤ 𝑥 ≤ 65)

Word problems 15. In a study, the wheat yields (in bushels) for several plots of land were normally distributed with a mean of

4 bushels and a standard deviation of 0.25 bushel. Describe and correct the error in finding the probability

that a plot yielded at least 3.8 bushels.

𝑧 =𝑥−𝑥

𝜎=

3.8−4

0.25= −0.8

From the standard normal table, 𝑃(𝑧 ≤ −0.8) = 0.2119. So, the probability that a plot yielded at least 3.8

bushels is 0.2119.

16. A study found that the wing lengths of houseflies are normally distributed with a mean of about 4.6

millimeters and a standard deviation of about 0.4 millimeter. What is the probability that a randomly

selected housefly has a wing length of at least 5 millimeters?

17. Boxes of cereal are filled by a machine. Tests of the machine’s accuracy show that the amount of cereal in

each box varies. The weights are normally distributed with a mean of 20 ounces and a standard deviation

of 0.25 ounce.

a. Find the z-scores for weights of 19.4 ounces and 20.4 ounces.

b. What is the probability that a randomly selected cereal box weighs at most 19.4 ounces?

c. What is the probability that a randomly selected cereal box weighs between 19.4 ounces and 20.4

ounces? Explain your reasoning.

Mixed Review 18. (11.2) The data set below gives the annual salaries (in thousands of dollars) of nine DJs working at a local

radio station.

39, 29, 42.5, 28.5, 48, 45, 38, 36.5, 28.5


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a. Find the mean, median, mode, range, and standard deviation of the salaries.

b. Each DJ receives an annual bonus of $1200. Find the mean, median, mode, range, and standard deviation

of the salaries including the bonus.

19. (10.3) A card is randomly drawn from a standard deck of 52 cards. Find the probability of drawing a face

card (K, Q, or J).

20. (7.4) Simplify log5 125𝑥.


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11.4 Select and Draw Conclusions from Samples 1. Copy and complete: A sample for which each member of a population has an equal chance of being selected

is a(n) __?__ sample.

Identify the type of sample described. Then tell if the sample is biased. Explain your reasoning. 2. A taxicab company wants to know if its customers are satisfied with the service. Each driver surveys every

tenth customer during the day.

3. An English teacher needs to pick 5 students to present book reports to the class. The teacher writes the

names of all students in the class on pieces of paper, puts the pieces in a hat, and chooses 5 names without

looking.

Find the margin of error for a survey that has the given sample size. Round your answer to the nearest tenth of a percent.

4. 1000

5. 6400

6. 525

7. 10,000

Find the sample size required to achieve the given margin of error. Round your answer to the nearest whole number.

8. ±3%

9. ±10%

10. ±5.6%

11. ±6.5%

12. The margin of error for a poll is 62%. What is the size of the sample?

(A) 200 (B) 400 (C) 1000 (D) 2500

Word problems 13. A survey claims the percent of a city’s residents that favor building a new football stadium is likely between

52.3% and 61.7%. How many people were surveyed?

14. Based on the newspaper

report shown below, is it

reasonable to assume

that Kosta is certain to

win the election?

Explain.

15. The staff for a student

newsletter wants to conduct a survey of students’ favorite TV shows. There are 1225 students in the school.

The newsletter staff would like to survey 250 students. Describe a method for selecting an unbiased,

random sample of students.

Mixed Review 16. (11.3) A normal distribution has a mean of 33 and a standard deviation of 4. Find the probability that a

randomly selected x-value is between 33 and 45.

17. (11.3) A normal distribution has a mean of 51 and a standard deviation of 3. What is the probability that a

randomly selected x-value is at most 48?

18. (11.3) A normal distribution has a mean of 64 and a standard deviation of 7. Use the standard normal table

to find the probability that 𝑃(𝑥 ≤ 80).

19. (11.1) The data set below gives the scores of the contestants in the first round of a junior archery

competition. Find the mean, median, mode, range, and standard deviation.

111, 114, 97, 102, 120, 113, 116, 114, 106, 110

20. (10.6) Calculate the probability of tossing a coin 20 times and getting exactly 1 head.


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11.5 Choose the Best Model for Two-Variable Data 1. Copy and complete: A function of the form 𝑦 = 𝑎𝑏𝑥 is a(n) __?__ function.

Use a graphing calculator to find a model for the data. Then graph the model and the data in the same coordinate plane.

2. x 1 2 3 4 5 6 7

y 16 17 16 14 11 9 5

3. Which type of function best models the data points?

(A) Linear (B) Quadratic

(C) Cubic (D) Exponential

4. Describe and correct the error made in using the information on a graphing

calculator screen to write a model.

5. The function 𝑦 = 5𝑥2.3 models a table of data in which x-values are measured in inches and y-values are

measured in pounds. If the table is changed to give the x-values in feet, what function models the revised

data?

6. The table shows the ages x (in years) and trunk diameters y (in inches) of several Texas grapefruit trees.

Use a graphing calculator to find a model for the data.

x 1 4 8 12 16 20 24

y 1.1 3.9 6.2 7.6 9.1 11.4 15.2

7. The manager of a restaurant kept a record of the number y of customers each hour, where x = 3 represents

3:00 P.M.

x 3 4 5 6 7 8 9 10

y 9 24 44 56 48 42 38 22

a. Make a scatter plot of the data and determine the type of function that best models the data.

b. Use a regression feature of a graphing calculator to find a function that models the data.

c. Graph the function and data to verify that the function is a good model.

d. Do you think the function you found would accurately predict the number of customers at 1 P.M.?

Explain.

8. The table shows the relationship between a car’s engine speed (in revolutions per minute) and the power

(in horsepower) that the engine produces. Use a graphing calculator to find a model for the data. What

engine speed maximizes this car’s engine power?

Engine speed (rpm) 1000 2000 3000 4000 5000 6000

Engine power (hp) 16 35 55 72 77 68

Mixed Review 9. (11.4) Identify the type of sample described. Then tell if the sample is biased.

A town council wants to know if residents support having an off-leash area for dogs in the town park.

Eighty dog owners are surveyed at the park.


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10. (11.4) In a survey of 439 teenagers in the United States, 14% said that they worked during their summer

vacation.

a. What is the margin of error for the survey?

b. Give an interval that is likely to contain the exact percent of all U.S. teenagers who worked during their

summer vacation.

11. (11.4) Find the sample size required to achieve a ±8% margin of error.

12. (11.3) A normal distribution has a mean of 33 and a standard deviation of 4. Find the probability that a

randomly selected x-value is at most 37.

13. (11.3) A normal distribution has a mean of 64 and a standard deviation of 7. Find the probability that

𝑃(𝑥 ≥ 59).

14. (11.2) Find the mean, median, mode, range, and standard deviation of the given data set and of the data set

obtained by multiplying each data value by 3.

19, 23, 23, 26, 30, 31, 34


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11.Review Answer the questions about the following data set. (Round to 1 decimal place.): 84, 85, 84, 83, 90, 50, 91

1. Identify the outlier in the data set. Then find the mean, median, mode, range, and standard deviation of the

data set when the outlier is included.

2. Find the mean, median, mode, range, and standard deviation of the data set when the outlier is not

included.

Answer the questions about the following data set. (Round to 1 decimal place.): 20, 24, 21, 25, 23, 21

3. Find the mean, median, mode, range, and standard deviation.

4. Find the mean, median, mode, range, and standard deviation after 25 is added to each number.

5. Find the mean, median, mode, range, and standard deviation after 3 has been multiplied to each number.

A normal distribution has a mean of 50 and a standard deviation of 5. Find the probability that a randomly selected x-value from the distribution is in the given interval.

6. Between 40 and 55

7. At most 42

8. At least 60

9. Greater than 57

Word problems 10. A study found that the number of students per classroom is normally distributed with a mean of 18

students and a standard deviation of 3 students. What is the probability that a randomly selected classroom

will have less than 20 students?

11. In a survey of 312 people at the local shopping center, 73% favored eating food. Find the margin of error

for the survey, and give an interval that is likely to contain the exact percent of all people who favor eating

food.

Identify the type of sample described. Then tell if the sample is more likely to be biased or unbiased. 12. A student is surveying people in her town to find out how involved they are in their local charities. The

student asks only his or her own family members.

13. A faculty committee wants to know what the students think about taking extra math classes. They have a

computer to generate a list of 20 students to survey.

Find the margin of error for a survey with the given sample size. Round your answers to the nearest tenth of a percent.

14. 5000 15. 100

Find the sample size required to achieve the given margin of error. Round your answers to the nearest whole number.

16. ±2% 17. ±20%

Graph the data points and classify the best-fitting model for the data. 18.

x 1 2 3 4 5 6 y 2 16 54 128 250 432

19.

x 0 2 4 6 8 10 y 5 1 -3 -7 -11 -15

20.

x 1 2 3 4 5 6 y 5 2.5 1.25 0.63 0.31 0.16


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Answers

11.1 1. Central tendency; dispersion 2. 5.3; 5; 4, 5, 6 3. 74.5; 73.5; 73, 78 4. B 5. The numbers need to be written in

increasing order prior to choosing the median; 9.

6. 5; 1.6 7. 4.7; 1.7

8. 23; 8.1 9. 68; about 10.7, 4, 4, 66, about 20.3;

3.5, 3.5, 4, 4, about 1.2 10. 0.7; 10, 11.6, 11.6, 12.1, about 4.2;

about 11.9, 11.6, 11.6, 1.9, about 0.67

11. (a) 5 (b) 20.2, 22, 23, 20, about 5.4; about 21.9, 23, 23, 6, about 2.1 (c) The mean and the median increase

when the outlier is removed and the range and standard deviation decrease.

12. 0.00018

13. 3

169;

4

221

14. −3±√129

4

15. 0.213

11.2 1. tranformation 2. 18, 17, 17, 9, about 3.0; 24, 23, 23,

9, about 3.0 3. 78, 77, 77, 9, about 2.8; 95, 94, 94,

9, about 2.8 4. 56, 53, 53, 21, about 7.0; 35, 32, 32,

21, about 7.0 5. The standard deviation does not

change when adding a constant; 10. 6. about 61.9, 62, 58, 9, about 3.36;

about 248, 248, 232, 36, about 13.4

7. about 98.2, 100.5, 102, 19, about 6.62; about 245.5, about 251.3, 255, 47.5, about 16.6

8. about 229, 226.5, 222, 38, about 12.0; about 206.1, about 203.9, 199.8, 34.2, about 10.8

9. 𝑎𝑥1+𝑎𝑥2+⋯+𝑎𝑥𝑛

𝑛=

𝑎(𝑥1+𝑥2+⋯+𝑥𝑛)

𝑛=

𝑎𝑥

10. about 6.84, 6.89, no mode, 1.16, about 0.324; about 22.4, about 22.6, no mode, about 3.80, about 1.06

11. about 29.3, 27.5, 27, 28, about 7.6 12. 0.160 13. 116,280

14. 𝑦 =2

𝑥;2

3

15. -2, -2, 1, 3

11.3 1. Normal curve 2. 0.16 3. 0.84 4. 0.68 5. 0.16 6. 0.68 7. 0.9735 8. 0.84

9. C 10. 0.7257 11. 0.0035 12. 0.5 13. 0.0548 14. 0.5363 15. The table was interpreted incorrectly;

𝑃(𝑧 ≥ −0.8) = 1 − 0.2119 = 0.7881

16. 0.16 17. -2.4, 1.6; 0.0082; 0.937 18. about 37.2, 38, 28.5, 19.5, about 6.9;

about 38.4, 39.2, 29.7, 19.5, about 6.9

19. 3

13

20. 3x

11.4 1. Random 2. Systematic; unbiased; the sample is

representative of the customers. 3. Random; unbiased; each student has an

equal chance of being selected. 4. ±3.2% 5. ±1.3% 6. ±4.4% 7. ±1.0% 8. 1111

9. 100 10. 319 11. 237 12. D 13. 453 people 14. No. Sample answer: Since the margin of

error is 65%, Kosta could have 49% of the votes and Murdock could have 51% of the votes.

15. Sample answer: Assign each student a number from 1 to 1225 and use a random number generator to generate 250 unique numbers from the given set of numbers.

16. 0.4985 17. 0.16 18. 0.9893 19. about 110, 112, 114, 23, about 6.5 20. 0.000019

11.5 1. Exponential 2. 𝑓(𝑥) = −0.381𝑥2 + 1.12𝑥 + 15.7 3. D 4. The x and the value of b have been

interchanged; 𝑦 = 9.71(1.55)𝑥.

5. 𝑦 = 5 (𝑥

12)2.3

6. Sample answer: 𝑦 = 0.00211𝑥3 −0.0766𝑥2 + 1.26𝑥 − 0.0664

7. Quadratic; 𝑦 = −2.97𝑥2 + 40.4𝑥 − 85.9; No, at 1:00 PM, the function predicts a negative number of customers.

8. Sample answer: 𝑓(𝑥) =−0.00000357𝑥2 + 0.0365𝑥 − 19.8; about 5112 rpm

9. Convenience; biased. Sample answer: The opinions of the sampled dog

owners may not represent the population.

10. ±4.8%; between 9.2% and 18.8% 11. 156 12. 0.84 13. 0.758 14. about 26.6, 26, 23, 15, about 4.9; about

79.8, 78, 69, 45, about 14.7


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11.Review 1. Outlier: 50; Mean: 81; Median: 84;

Mode: 84; Range: 41; Standard

Deviation: 13.0

2. Mean: 86.2; Median: 84.5; Mode:

84; Range: 8; Standard Deviation:

3.1

3. Mean: 22.3; Median: 22; Mode: 21;

Range: 5; Standard Deviation: 1.8

4. Mean: 47.3; Median: 47; Mode: 46;


5. Mean: 67; Median: 66; Mode: 63;


6. 0.815 (Calc 0.819)

7. 0.0548

8. 0.025 (Calc 0.023)

9. 0.0808

10. 0.7580 (Calc 0.7475)

11. 𝐸𝑟𝑟𝑜𝑟 = ±5.7%, 67.3% to 78.7%

12. Convenience; biased

13. Random; unbiased

14. ±1.4%

15. ±10%

16. 2500

17. 25

18. Power;

19. Linear;

20. Exponential;

0

100

200

300

400

500

0 2 4 6

-20

-15

-10

-5

0

5

10

0 5 10

0

1

2

3

4

5

6

0 2 4 6

Algebra 2 11 Data Analysis and Statistics Practice ...rwright/algebra2/homework...Algebra 2 11 Data...

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