grade12-dataanalysis

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Grade 12

Data Analysis and Probability

Sample Questions and Answers

This booklet contains sample items from the National Assessment of Educational

Progress (NAEP). Additional items can be accessed at

www.nces.ed.gov/nationsreportcard/itmrls.

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Centerfor Education Statistics (NCES), National Assessment of Educational Progress (NAEP)
http://www.nces.ed.gov/nationsreportcard/itmrlshttp://www.nces.ed.gov/nationsreportcard/itmrls


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NAEP Grade 12 Data Analysis and Probability

ContentsNAEP Grade 12 Data Analysis and Probability......................................................................2

Contents............................................................................................................................... 2Introduction ......................................................................................................................... 3

Question 1............................................................................................................................ 4

Question 2............................................................................................................................ 5

Question 3............................................................................................................................ 6

Question 4............................................................................................................................ 8

Question 5............................................................................................................................ 9

Question 5, continued.........................................................................................................10

Question 6.......................................................................................................................... 10

Question 6, continued.........................................................................................................11

Question 7.......................................................................................................................... 12

Question 8.......................................................................................................................... 13

Question 9.......................................................................................................................... 14

Question 10........................................................................................................................ 16

Question 11........................................................................................................................ 17

2NAEP Grade 12 Data Analysis and Probability Practice TestFlorida Department of EducationDivision of Accountability, Research, and MeasurementOffice of Assessment


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Introduction

This practice Data Analysis and Probability test includes a sample of publicly

released items from NAEP. Included with each item are the correct answer(indicated by an asterisk) and the distracters; the percentage of Floridas

responses to each of the possible answers; and the Description, Difficulty, and

Complexity of each item.

Additional publicly released items and item data may be accessed through the

NAEP Questions Tool (NQT) at

http://nces.ed.gov/nationsreportcard/itmrlsx/default.aspx . The NQT is an

interactive tool that provides access to over 2000 released questions from NAEP

assessments in all NAEP subject areas. It is also used to access NAEP assessmentitems, their correct answers and distracters, and their scoring results by subject,

grade, item type, difficulty, content classification, frameworks, year, and key

words.

For more information about NAEP results, go to the NAEP Data Explorer (NDE) at

http://nces.ed.gov/nationsreportcard/naepdata/ . The NDE is an interactive tool

that provides access to a wide variety of data about what students know and can

do, as well as demographic and contextual factors that may affect their

performance. The NDE produces charts, customized tables, and graphics based on

NAEP results by year and jurisdiction; significance between jurisdictions, withinvariables, and across years; and gap analyses between jurisdictions or across

years and between groups, between years, and between groups and years.

Additional information about the knowledge and skills the mathematics

assessment is designed to measure can be found in the 2011 Mathematics

Framework, http://www.nagb.org/publications/frameworks/math-2011-

framework.pdf. The current NAEP Mathematics Framework guided the

development of all Mathematics assessments since 2005. The previous NAEP

Mathematics Framework guided the development of the mathematics assessmentsbetween 1990 and 2003.

http://nces.ed.gov/nationsreportcard/itmrlsx/default.aspxhttp://nces.ed.gov/nationsreportcard/naepdata/http://www.nagb.org/publications/frameworks/math-2011-framework.pdfhttp://www.nagb.org/publications/frameworks/math-2011-framework.pdfhttp://nces.ed.gov/nationsreportcard/itmrlsx/default.aspxhttp://nces.ed.gov/nationsreportcard/naepdata/http://www.nagb.org/publications/frameworks/math-2011-framework.pdfhttp://www.nagb.org/publications/frameworks/math-2011-framework.pdf


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NAEP GRADE 12

DATA ANALYSIS and PROBABILITY

SAMPLE QUESTIONS and ANSWERS

Question 1

The table below shows the high and low temperatures on October 1st for five cities.

Which city had the greatest temperature range?

a. City Ab. City B

c. City C

d. City D

e. City E

Answers

Percent chosen by Floridasparticipating students

*A 58%

B 17%

C 4%

D 5%

E 16%

Description: Solve problem using data in table

Difficulty: Easy

Complexity: Low



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Question 2

The scatterplot below shows data for groups R and S. Which of the followingstatements is true about the correlation between thexandyvalues of group R and

the correlation between thexandyvalue of group S?

a. Thexandyvalues appear to be negatively correlated in both R and S.

b. Thexandyvalues appear to be positively correlated in both R and S.

c. Thexandyvalues appear to be negatively correlated in R, but positively

correlated in S.

d. Thexandyvalues appear to be positively correlated in R, but negativelycorrelated in S.

e. Thexandyvalues appear to be more highly correlated in R than is S.

Answers


*C 59%

A 4%

B 18%

D 11%

E 6%

Description: Analyze correlations of two data sets in a scatterplot

Difficulty: Easy



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Complexity: Low

Question 3

A random sample of graduates from a particular college program reported their

ages and incomes in response to a survey. Each point on the scatterplot below

represents the age and income of a different graduate.

Of the following equations, which best fits the data above?

a.

b.



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c.

d.

e.

Question 3, continued

Answers


*C 44%

A 4%

B 12%

D 20%

E 20%Omitted

1%

Description: Identify linear equation that best fits data in a scatterplot

Difficulty: Medium

Complexity: Moderate



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Question 4

The principal of a high school would like to determine why there has been a large

decline during the year in the number of students who purchase food in the

schools cafeteria. To do this, 25 students from the school will be surveyed. Whichmethod would be the most appropriate for selecting the 25 students to participate

in the survey?

a. Randomly select 25 students from the senior class

b. Randomly select 25 students from those taking physics

c. Randomly select 25 students from a list of all students at the school?

d. Randomly select 25 students from a list of students who eat in the

cafeteria

e. Give the survey to the first 25 students to arrive at school in the morning

Answers


*C 59%

A 5%

B 2%

D 31%

E 2%

Description: Identify appropriate method for selecting random sample

Difficulty: Medium




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Question 5

A random sample of graduates from a particular college program reported their

ages and incomes in response to a survey. Each point on the scatterplot above

represents the age and income of a different graduate.

Based on the data in the above scatterplot, predictions can be made about the

income of a 35-year-old and the income of a 55-year-old. For which group is the

prediction more likely to be accurate?

______ 35-year-olds ______ 55-year-olds

Solution: 35-year-olds

Justification:The prediction for the 35 year old is more likely to be accurate because the age 35is contained within the interval of the data set. The age 55 is outside the interval of

the data set, so any prediction for the income of a 55 year old would be anextrapolation.

Score & Description

CorrectCorrect oval filled in with acceptable justification



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PartialIncorrect oval or neither oval filled in with justification that supports correct oval


Incorrect 1

Correct oval filled in with incorrect or missing justificationIncorrect 2Other incorrect responses

Description: Make a prediction based on data in a scatterplot

Difficulty: MediumComplexity: Moderate

Question 6

Marissa is going on a trip. She will be taking a taxi, a flight, and then a train.

Marissa will choose the following three companies based on their claims.

Tammys Taxi Service claims that it is on time 95% of the time

Friendly Flyer Airlines claims that it is on time 93% of the time Rapid Railways claims that it is on time 98% of the time

Based on the t here companies claims, what is the approximate probability that all

three parts of Marissas trip will be on time, assuming that all three probabilities

are independent?



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Answer: _______________________


Solution:Answer: 87% or 0.87 (Accept answers from 0.86 to 0.87, inclusive.)

Solution (not required in response):

Score & Description

CorrectAnswer of 87%

IncorrectIncorrect response

Description: Calculate probability of independent events

Difficulty: Hard

Complexity: Low



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Question 7

An election involving four candidates for mayor has been held. Of the following,

which is the best way to present the percentage of votes each candidate received?

a. Circle graphb. Line graph

c. Box plot

d. Scatterplot

e. Histogram

The correct answer is A

National Results

Description: Determine the type of graph to best represent a situation

Difficulty: Easy

Complexity: Low



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Question 8

The table below shows the gender and color of 7 puppies. If a puppy is selected at

random from the group is brown, what is the probability it is a male?

a.

b.

c.

d.

e.

The correct answer is A

National Results



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Description: Determine conditional probability from two-way table

Difficulty: Medium

Complexity: Low

Question 9

Vanessas Vans finds that about 40% of the time a person who makes an advance

reservation for transportation does not keep the reservation. Therefore, for each

of their 10-passenger vans, Veronicas Vans schedules 13 persons on the basis of

advance reservations.

On any given day, how many persons who made and kept their advance

reservations would not have a seat in the van on that day? Justify your answer

Solution:Answer should be the number of kept reservations above 10 minus 10, with

justification. (i.e., if there are 12 kept reservations, then there are 12 - 10 = 2people who cannot be seated).

Justification must demonstrate either directly or indirectly that the van can seat upto ten people.

Number of Kept Reservations Number that Cannot be Seated0 - 10 0

11 112 213 3

Notes: Calculations may count as justification, but are not required to be shown.

The driver is not counted as part of the ten passengers/seats.

Do not accept negative numbers.

Score & Description

CorrectCorrect response with justification.

PartialCorrect response, but with incomplete or no justification.

IncorrectIncorrect response.



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National Results

Description: Solve a data-related problem and justify the answer

Difficulty: Medium

Complexity: Low



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Question 10

The pulse rate per minute of a group of 100 adults is displayed in the histogram

below. For example, 5 adults have a pulse rate from 40-49 inclusive. Based on

these data, how many individuals from a comparable group of 40 adults would beexpected to have a pulse rate of 80 or above?

Answer: __________________

Solution:8 or (0.20)(40)=8

Score & Description

CorrectCorrect response

IncorrectIncorrect response

National Results



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Description: Use survey results to make an inference

Difficulty: Hard


Question 11

Suppose that square lunchroom trays are assembled using 4 smaller square

pieces. Each piece is a single color. If the smaller pieces are available in red and

green only, how many different colored patterns of trays can be made? (Patterns

of colors that result from rotating the tray such as

and

are not considered different.)Illustrate below the different patterns corresponding to your answers.

Since rotations are not considered different, the possible combinations of red andgreen squares are as follows:

Tray 4 Red 3 Red 2 Red 1 Red 0 RedColors 0 Green 1 Green 2 Green 3

Green4

GreenPossibl

e

Patterns

1 1 2 1 1

6 different color patterns are available

Score & Description



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ExtendedCorrect Response. Student finds all 6 possible color patterns (response mustinclude the given pattern along with the other five patterns) with no repeats orcontradictory information.

Note: With any number of repeats the maximum score is 4.

SatisfactoryHas 4 or 5 correct color patterns that are different than the given pattern.

PartialHas 2 or 3 correct color patterns that are different than the given pattern.


Minimal

Has 1 correct color pattern that is different than the given pattern.OR

States that there are 6 possible color patterns with no or incomplete work.

IncorrectIncorrect response (Includes only repeating the given pattern).

National Results

Description: Solve a problem involving color patterns

Difficulty: Medium



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19NAEP Grade 12 Data Analysis and Probability Practice TestFlorida Department of EducationDivision of Accountability, Research, and Measurement

grade12-dataanalysis

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