
1. 
Jerry spun one of the spinners below 1,000 times and obtained the results shown in the table above. Which spinner did Jerry probably use?  
A)  
B)  
C)  
D)  
E)  
 
2. 
According to the boxandwhisker plot above, threefourths of the cars made by Company X got fewer than how many miles per gallon?  
A)  20  
B)  24  
C)  27  
D)  33  
E)  40  




GENDER AND COLOR OF PUPPIES
 
9. 
The table above shows the gender and color of 7 puppies. If a puppy selected at random from the group is brown, what is the probability it is a male?  
A)  
B)  
C)  
D)  
E)  
Did you use the calculator on this question? 
10. 
A particular flu vaccine is effective for 90 percent of the patients who receive it. What is the probability that it will be effective for both of the next two randomly selected patients?  
A)  0.54  
B)  0.63  
C)  0.72  
D)  0.81  
E)  0.90  
Did you use the calculator on this question? 
11. 
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 graph  
B)  Line graph  
C)  Box plot  
D)  Scatterplot  
E)  Histogram  
Did you use the calculator on this question? 
12. 
A clock manufacturer has found that the amount of time their clocks gain or lose per week is normally distributed with a mean of 0 minutes and a standard deviation of 0.5 minute, as shown below. In a random sample of 1,500 of their clocks, which of the following is closest to the expected number of clocks that would gain or lose more than 1 minute per week?  
A)  15  
B)  30  
C)  50  
D)  70  
E)  90  
Did you use the calculator on this question? 




 
17. 
According to the graph above, the temperature at 10 a.m. is approximately how many degrees greater than the temperature at 8 a.m.?  
A)  1  
B)  1.5  
C)  2  
D)  2.5  
E)  3  
18. 
Which of the following pieces of information would NOT be useful in deciding what type of car is the most economical to drive?  
A)  Median income of drivers  
B)  Range of insurance costs  
C)  Average miles per gallon  
D)  Typical cost of repairs per year  
E)  Cost of routine maintenance  

 
20. 
The table above shows the scores of 10 students on a final examination. What is the range of these scores?  
A)  33  
B)  40  
C)  55  
D)  88  
21. 
From a shipment of 500 batteries, a sample of 25 was selected at random and tested. If 2 batteries in the sample were found to be dead, how many dead batteries would be expected in the entire shipment?  
A)  10  
B)  20  
C)  30  
D)  40  
E)  50  
 
22. 
The total distances covered by two runners during the first 28 minutes of a race are shown in the graph above. How long after the start of the race did one runner pass the other?  
A)  3 minutes  
B)  8 minutes  
C)  12 minutes  
D)  14 minutes  
E)  28 minutes  

 
24. 
The entire circle shown above represents a total of 2,675 radios sold. Of the following, which is the best approximation of the number of radios represented by the shaded sector of the circle?  
A)  70  
B)  275  
C)  985  
D)  25,880  
E)  98,420  
Did you use the calculator on this question? 
 
25. 
In the graph above, each dot shows the number of situps and the corresponding age for one of 13 people. According to this graph, what is the median number of situps for these 13 people?  
A)  15  
B)  20  
C)  45  
D)  50  
E)  55  
Did you use the calculator on this question? 
26. 
A certain company keeps a list of 50 employees and their annual salaries. When the salary of the very highly paid president is added to this list, which of the following statistics is most likely to be approximately the same or nearly the same for the original list and the new list?  
A)  The highest salary  
B)  The range  
C)  The mean  
D)  The median  
E)  The standard deviation  
27. 
The average weight of 50 prizewinning tomatoes is 2.36 pounds. What is the combined weight, in pounds, of these 50 tomatoes?  
A)  0.0472  
B)  11.8  
C)  52.36  
D)  59  
E)  118  
 
28. 
The nine chips shown above are placed in a sack and then mixed up. Madeline draws one chip from this sack. What is the probability that Madeline draws a chip with an even number?  
A) 
 
B) 
 
C) 
 
D) 
 
E) 
 
OF EIGHTH GRADE STUDENTS
 
29. 
According to the graph above, about how many students chose skiing as their favorite winter sport?  
A)  3½  
B)  4  
C)  12½  
D)  14  
E)  16  
Did you use the calculator on this question? 
30. 
A contractor is building 5 different model homes on 5 adjacent lots on one side of a street. If 1 house is to be built on each lot, how many different arrangements of the 5 houses are possible?  
A)  120  
B)  60  
C)  25  
D)  10  
E)  5  
Did you use the calculator on this question? 




Scoring Guide 
Solution: Expected number of no shows: 13(.40) = 5.2, so 5 no shows.
Note: The number of no shows on Tuesday is 6. Scorers have to count the number of no shows on Wednesday. 
Score & Description  
 
 


Correct  Student Response 
4 
In the table below, data are provided for 13 reservations for Tuesday.  
Scorer Comments: This response received full credit because the student chose the correct day based on the data generated and justified the answer. 

Partial  Student Response 
4 
In the table below, data are provided for 13 reservations for Tuesday.  
Scorer Comments: This response received partial credit because the student chose the correct day based on the data generated, but did not provide a justification. 

Incorrect  Student Response 
4 
In the table below, data are provided for 13 reservations for Tuesday.  
Scorer Comments: This response received no credit because the student chose the wrong day based on the data generated. 

Scoring Guide 
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 = 2 people who cannot be seated). Justification must demonstrate either directly or indirectly that the van can seat up to ten people.
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  
 
 

Correct  Student Response 
5 
Based on the outcomes you generated for Wednesday, how many persons who made and kept their advance reservations could not be seated in the van that day? Justify your answer.  
Scorer Comments: This response received full credit because the student correctly determined the number of people who could not be seated based on the data generated and justified the answer. 

Partial  Student Response 
5 
Based on the outcomes you generated for Wednesday, how many persons who made and kept their advance reservations could not be seated in the van that day? Justify your answer.  
Scorer Comments: This response received partial credit because the student correctly determined the number of people who could not be seated based on the data generated, but did not provide any justification. 

Incorrect  Student Response 
5 
Based on the outcomes you generated for Wednesday, how many persons who made and kept their advance reservations could not be seated in the van that day? Justify your answer.  
Scorer Comments: This response received no credit because the student incorrectly determined the number of people who could not be seated based on the data generated. 

Scoring Guide 
Solution: Answer should be 10 minus the number of kept reservations, with justification. (i.e., if there are 8 kept reservations, then there are 10  8 = 2 vacant seats) OR The number of no shows minus 3. (i.e., if there are 5 no shows, then there are 5  3 = 2 vacant seats) Justification must demonstrate either directly or indirectly that the van can seat up to ten people. 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  
 
 

Correct  Student Response 
6 
Based on the outcomes you generated for Wednesday, how many vacant seats will there be in the van that day? Justify your answer.  
Scorer Comments: This response received full credit because the student correctly determined the number of vacant seats based on the data generated, and justified the answer. 

Partial  Student Response 
6 
Based on the outcomes you generated for Wednesday, how many vacant seats will there be in the van that day? Justify your answer.  
Scorer Comments: This response received partial credit because the student correctly determined the number of vacant seats based on the data generated, but did not provide any justification. 

Incorrect  Student Response 
6 
Based on the outcomes you generated for Wednesday, how many vacant seats will there be in the van that day? Justify your answer.  
Scorer Comments: This response received no credit because the student incorrectly determined the number of vacant seats based on the data generated. 

Scoring Guide 
Solution: 8 or (0.20)(40)=8 
Score & Description  
 

Correct  Student Response 
7 
The pulse rate per minute of a group of 100 adults is displayed in the histogram above. For example, 5 adults have a pulse rate from 4049 inclusive. Based on these data, how many individuals from a comparable group of 40 adults would be expected to have a pulse rate of 80 or above? 
Incorrect  Student Response 
7 
The pulse rate per minute of a group of 100 adults is displayed in the histogram above. For example, 5 adults have a pulse rate from 4049 inclusive. Based on these data, how many individuals from a comparable group of 40 adults would be expected to have a pulse rate of 80 or above? 
Scoring Guide 
Solution: Since rotations are not considered different, the possible combinations of red and green squares are as follows:

Score & Description  
 
 
 
 

Extended  Student Response 
8 
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. (You may want to use the squares labeled R and G in your packet.)  
Scorer Comments: This response received full credit because the student correctly found all six possible color patterns that can be made. 

Satisfactory  Student Response 
8 
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. (You may want to use the squares labeled R and G in your packet.)  
Scorer Comments: This response received a satisfactory score because the student has four color patterns that are different than the given pattern. 

Partial  Student Response 
8 
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. (You may want to use the squares labeled R and G in your packet.)  
Scorer Comments: This response received partial credit because the student has three color patterns that are different than the given pattern. 

Minimal  Student Response 
8 
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. (You may want to use the squares labeled R and G in your packet.)  
Scorer Comments: This response received minimal credit because the student gave an answer without showing any supporting work. 

Incorrect  Student Response 
8 
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. (You may want to use the squares labeled R and G in your packet.)  
Scorer Comments: This response received no credit because the student has only repeated the given pattern and has also specified an incorrect number of color patterns. 





Scoring Guide 
Solution: N, because more students chose it. OR N, because it was first choice in one class and second choice in the other classes. "Majority" is acceptable (taken to mean most.) If student says the most classes, do not accept. Scoring Guide In this question, a student has to read and interpret information from a chart. A student then has to make a decision on which of the shapes should be the choice for the class. To earn full credit the student has to tell which of the three pieces should be the choice for the class and then explain why he or she chose that shape. 
Score & Description  
 
 
 

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit. 
Correct  Student Response 
13 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
13 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Incorrect #3  Student Response 
13 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
13 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Incorrect #2  Student Response 
13 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
13 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Incorrect #1  Student Response 
13 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
13 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Scoring Guide 
Solution: Average hourly wage for Thursday  $5.75 Scoring Guide In this question, a student needed to read and compute with data from a table. This problem could be solved in many different ways. One way is to use the total earnings from the five days ($153.50) to find the total daily earnings on Thursday ($34.50). The average hourly wage for Thursday can be found by dividing $34.50 by 6 (number of hours worked). To answer the second part of the question, a student should have looked at the data in the table to reason at what time the hourly wage rate changes. To earn full credit, a student has to give the correct average hourly wage for Thursday as well as give the time when the hourly wage rate changes. Partial credit could be earned if a student gives one correct answer, either the correct hourly average rate for Thursday or the correct time the wage rate changes. 
Score & Description  
 
 

Correct  Student Response 
14 
According to the information above, what is the average hourly wage for Thursday's earnings if the total earnings for the five days was $153.50 ? 
14 
According to the information above, what is the average hourly wage for Thursday's earnings if the total earnings for the five days was $153.50 ? 
Partial  Student Response 
14 
According to the information above, what is the average hourly wage for Thursday's earnings if the total earnings for the five days was $153.50 ? 
14 
According to the information above, what is the average hourly wage for Thursday's earnings if the total earnings for the five days was $153.50 ? 
Incorrect  Student Response 
14 
According to the information above, what is the average hourly wage for Thursday's earnings if the total earnings for the five days was $153.50 ? 
14 
According to the information above, what is the average hourly wage for Thursday's earnings if the total earnings for the five days was $153.50 ? 
Scoring Guide 
Solution: Possible outcomes are BB, BW, WB, and WW. Only BB will win. The actual chance of a win is 1 in 4, or 25% Scoring Guide In this question, a student has to determine the probability of a simple event. A student could have listed a sample space and used the information to describe and make a prediction about the expected outcome. Full credit was earned for a response that included the correct answer of 1 in 4, or 25%, with a complete justification (i.e., a list of the possible outcomes). Partial credit could have been earned if a student listed the sample space but the explanation was either incomplete or missing. 
Score & Description  
 
 

Correct  Student Response 
15 
The two fair spinners shown above are part of a carnival
game. A player wins a prize only when both arrows land on black
after each spinner has been spun once.
James thinks he has a 5050 chance of winning. Do you agree? 
15 
The two fair spinners shown above are part of a carnival
game. A player wins a prize only when both arrows land on black
after each spinner has been spun once.
James thinks he has a 5050 chance of winning. Do you agree? 
Partial  Student Response 
15 
The two fair spinners shown above are part of a carnival
game. A player wins a prize only when both arrows land on black
after each spinner has been spun once.
James thinks he has a 5050 chance of winning. Do you agree? 
15 
The two fair spinners shown above are part of a carnival
game. A player wins a prize only when both arrows land on black
after each spinner has been spun once.
James thinks he has a 5050 chance of winning. Do you agree? 
Incorrect  Student Response 
15 
The two fair spinners shown above are part of a carnival
game. A player wins a prize only when both arrows land on black
after each spinner has been spun once.
James thinks he has a 5050 chance of winning. Do you agree? 
15 
The two fair spinners shown above are part of a carnival
game. A player wins a prize only when both arrows land on black
after each spinner has been spun once.
James thinks he has a 5050 chance of winning. Do you agree? 
Scoring Guide 
Solution: Selects and provides appropriate explanation for why the mean is a better measure for the typical attendance for Theater B and the median is the better measure for Theater A. An explanation for Theater A should include the idea that the attendance on day 4 is much different than the attendance numbers for any other days for Theater A. An appropriate explanation for Theater B should include the following ideas
a justification that conveys the idea that 82 is a better indicator of where the "center" of the 5 data points is located Scoring Guide In this question, a student has to look at the data and determine which measure, the median or the mean, would best describe the typical daily attendance at each Theater. A student has to have an understanding of the meaning of mean and median in order to provide a correct answer and explanation. For full credit a student has to answer the median for part a and include an explanation that would include that day 4's attendance is significantly different than the rest of the days and the mean for part b with an explanation that shows an understanding that the mean is a better indicator because all of the attendance numbers for Theater B are clustered. Varying levels of partial credit (satisfactory, partial, and minimal) could be earned depending on how well the student reasons and communicates the correct answer. 
Score & Description  
 
 
 
 

Extended  Student Response 
16 
The table below shows the daily attendance at two movie theaters for 5 days and the mean(average) and the median attendance. 
16 
The table below shows the daily attendance at two movie theaters for 5 days and the mean(average) and the median attendance. 
Satisfactory  Student Response 
16 
The table below shows the daily attendance at two movie theaters for 5 days and the mean(average) and the median attendance. 
16 
The table below shows the daily attendance at two movie theaters for 5 days and the mean(average) and the median attendance. 
Partial  Student Response 
16 
The table below shows the daily attendance at two movie theaters for 5 days and the mean(average) and the median attendance. 
16 
The table below shows the daily attendance at two movie theaters for 5 days and the mean(average) and the median attendance. 
Minimal  Student Response 
16 
The table below shows the daily attendance at two movie theaters for 5 days and the mean(average) and the median attendance. 
16 
The table below shows the daily attendance at two movie theaters for 5 days and the mean(average) and the median attendance. 
Incorrect  Student Response 
16 
The table below shows the daily attendance at two movie theaters for 5 days and the mean(average) and the median attendance. 
16 
The table below shows the daily attendance at two movie theaters for 5 days and the mean(average) and the median attendance. 


Scoring Guide 
Solution: All 5 of these horizontal arrangements listed in any order Scoring Guide In this question, a student had to list all the 5 possibilities for how an event could occur given that A sat in the aisle seat. Different levels of incorrect could be earned depending on the number of possibilities that the student had listed. 
Score & Description  
 
 
 

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit. 
Correct  Student Response 
19 
Four people  A, X, Y, and Z  go to a movie and sit in adjacent seats. If A sits in the aisle seat, list all possible arrangements of the other three people. One of the arrangements is shown below. 
19 
Four people  A, X, Y, and Z  go to a movie and sit in adjacent seats. If A sits in the aisle seat, list all possible arrangements of the other three people. One of the arrangements is shown below. 
Incorrect #3  Student Response 
19 
Four people  A, X, Y, and Z  go to a movie and sit in adjacent seats. If A sits in the aisle seat, list all possible arrangements of the other three people. One of the arrangements is shown below. 
19 
Four people  A, X, Y, and Z  go to a movie and sit in adjacent seats. If A sits in the aisle seat, list all possible arrangements of the other three people. One of the arrangements is shown below. 
Incorrect #2  Student Response 
19 
Four people  A, X, Y, and Z  go to a movie and sit in adjacent seats. If A sits in the aisle seat, list all possible arrangements of the other three people. One of the arrangements is shown below. 
19 
Four people  A, X, Y, and Z  go to a movie and sit in adjacent seats. If A sits in the aisle seat, list all possible arrangements of the other three people. One of the arrangements is shown below. 
Incorrect #1  Student Response 
19 
Four people  A, X, Y, and Z  go to a movie and sit in adjacent seats. If A sits in the aisle seat, list all possible arrangements of the other three people. One of the arrangements is shown below. 
19 
Four people  A, X, Y, and Z  go to a movie and sit in adjacent seats. If A sits in the aisle seat, list all possible arrangements of the other three people. One of the arrangements is shown below. 



Scoring Guide 
Score & Description  
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
23 
The pulse rate for a group of 100 people is shown in the
graph above. What is the average pulse rate per minute for these 100
people? (Note: Use the midpoint of each interval to represent the pulse rate for the entire interval. For example, 55 would be used for the pulse rate of the 15 people in the 5060 group.) 
23 
The pulse rate for a group of 100 people is shown in the
graph above. What is the average pulse rate per minute for these 100
people? (Note: Use the midpoint of each interval to represent the pulse rate for the entire interval. For example, 55 would be used for the pulse rate of the 15 people in the 5060 group.) 
Incorrect #2  Student Response 
23 
The pulse rate for a group of 100 people is shown in the
graph above. What is the average pulse rate per minute for these 100
people? (Note: Use the midpoint of each interval to represent the pulse rate for the entire interval. For example, 55 would be used for the pulse rate of the 15 people in the 5060 group.) 
23 
The pulse rate for a group of 100 people is shown in the
graph above. What is the average pulse rate per minute for these 100
people? (Note: Use the midpoint of each interval to represent the pulse rate for the entire interval. For example, 55 would be used for the pulse rate of the 15 people in the 5060 group.) 
Incorrect #1  Student Response 
23 
The pulse rate for a group of 100 people is shown in the
graph above. What is the average pulse rate per minute for these 100
people? (Note: Use the midpoint of each interval to represent the pulse rate for the entire interval. For example, 55 would be used for the pulse rate of the 15 people in the 5060 group.) 
23 
The pulse rate for a group of 100 people is shown in the
graph above. What is the average pulse rate per minute for these 100
people? (Note: Use the midpoint of each interval to represent the pulse rate for the entire interval. For example, 55 would be used for the pulse rate of the 15 people in the 5060 group.) 







Scoring Guide 
Score & Description  
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
31 
A fair coin is to be tossed three times. What is the probability that 2 heads and 1 tail in any order will come up? 
Incorrect #1  Student Response 
31 
A fair coin is to be tossed three times. What is the probability that 2 heads and 1 tail in any order will come up? 
Incorrect #2  Student Response 
31 
A fair coin is to be tossed three times. What is the probability that 2 heads and 1 tail in any order will come up? 