NAEP NQT v3.0 -- Print Output

Additional Materials (1)

Additional Materials (2)

Additional Materials (3)

Additional Materials (4)

Additional Material (1)


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 box-and-whisker plot above, three-fourths 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

3.	In a school fund-raiser, 10 students in class A sold an average (arithmetic mean) of 4 boxes of cookies. In class B, 15 students sold an average of 9 boxes. What was the average number of boxes of cookies sold by the 25 students?

	A)
	B)	1
	C)
	D)	7
	E)

Question 4 refers to Additional Materials (3)

The following question refer to the following information.

Easy Ride Van Company finds that about 40 percent 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, the Easy Ride Van Company schedules 13 persons on the basis of advance reservations.

In the table below, data are provided for 13 reservations for Tuesday.

(a) Use the spinner provided to generate the data for 13 reservations for Wednesday. After each spin, record the outcome in the table.

Tuesday			Wednesday
Spin	Show	No-Show	Spin	Show	No-Show
1	1		1
2	1		2
3		1	3
4		1	4
5	1		5
6	1		6
7		1	7
8		1	8
9	1		9
10		1	10
11	1		11
12		1	12
13	1		13

(b) For which day do the 13 outcomes more closely match the expectations for the number of persons who do not keep their advance reservations? Justify your answer.

The following question refer to the following information. Easy Ride Van Company finds that about 40 percent 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, the Easy Ride Van Company schedules 13 persons on the basis of advance reservations.
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.

The following question refer to the following information. Easy Ride Van Company finds that about 40 percent 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, the Easy Ride Van Company schedules 13 persons on the basis of advance reservations.
6.	Based on the outcomes you generated for Wednesday, how many vacant seats will there be in the van that day? Justify your answer.


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 40-49 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?

	Answer: _________________________

Question 8 refers to Additional Materials (4)

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.)

GENDER AND COLOR OF PUPPIES

Male

Female

Black
1

2

Brown
1

3

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?

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?

Question 13 refers to Additional Material (1)

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.

	Class 1	Class 2	Class 3
Shape N	9	14	11
Shape P	1	9	17
Shape Q	22	7	2

Using the information in the chart, Mr. Bell must select one of the shapes to be the symbol. Which one should he select and why?

The shape Mr. Bell should select:____________________

Explain:

TIME CARD Name: J. Jasmine	Number of hours	Average Hourly Wage	Total Daily Earnings
Mon. 10:00 a.m. - 3:00 p.m.	5	5.50	27.50
Tues. 9:00 a.m. - 4:00 p.m.	7	5.50	38.50
Wed. 3:00 p.m. - 7:00 p.m.	4	5.75	23.00
Thurs. 2:00 p.m. - 8:00 p.m.	6
Fri. 5:00 p.m. - 10:00 p.m.	5	6.00	30.00

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 ?

Answer:____________________

The hourly wage rate changes at some hour during the day. At what time does the hourly wage rate change?

Answer:____________________

Did you use the calculator on this question?


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 50-50 chance of winning. Do you agree?
	Justify your answer.

Did you use the calculator on this question?

This question requires you to show your work and explain your reasoning. You may use drawings, words, and numbers in your explanation. Your answer should be clear enough so that another person could read it and understand your thinking. It is important that you show all of your work.

16.

The table below shows the daily attendance at two movie theaters for 5 days and the mean(average) and the median attendance.

	Theater A	Theater B
Day 1	100	72
Day 2	87	97
Day 3	90	70
Day 4	10	71
Day 5	91	100
Mean (average)	75.6	82
Median	90	72

(a) Which statistic, the mean or the median, would you use to describe the typical daily attendance for the 5 days at Theater A? Justify your answer.

(b) Which statistic, the mean or the median, would you use to describe the typical daily attendance for the 5 days at Theater B? Justify your answer.

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

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.

Student	Score
A	88
B	65
C	91
D	36
E	72
F	57
G	50
H	85
I	62
J	48

20.

The table above shows the scores of 10 students on a final examination. What is the range of these scores?

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


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 50-60 group.)
	Answer:____________________

Did you use the calculator on this question?


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 sit-ups and the corresponding age for one of 13 people. According to this graph, what is the median number of sit-ups 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 prize-winning 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?

FAVORITE WINTER SPORTS
OF EIGHTH GRADE STUDENTS

Figure Skating	$\'1$ $\'1/2$
Ice Hockey	$\'1$ $\'1$ $\'3/4$
Skiing	$\'1$ $\'1$ $\'1$ $\'1/2$
Sledding	$\'1$ $\'1$ $\'1$ $\'1$ $\'1$ $\'1$
Speed Skating	$\'1$

Legend: $\'1$ = 4 students

29.

According to the graph above, about how many students chose skiing as their favorite winter sport?

3½

12½

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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?

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?
	Answer: ____________________

Did you use the calculator on this question?

Question 1

Key


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)

Question 2

Key


2.	According to the box-and-whisker plot above, three-fourths 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

Question 3

Key


3.	In a school fund-raiser, 10 students in class A sold an average (arithmetic mean) of 4 boxes of cookies. In class B, 15 students sold an average of 9 boxes. What was the average number of boxes of cookies sold by the 25 students?

	A)
	B)	1
	C)
	D)	7
	E)

Question 4

Scoring Guide

Solution:

Expected number of no shows: 13(.40) = 5.2, so 5 no shows.

Number of No Shows on Wednesday

Day with Closest Expected Value

0 - 4

Tuesday

5

Wednesday

6

the same

7-13

Tuesday

Note: The number of no shows on Tuesday is 6. Scorers have to count the number of no shows on Wednesday.

Score & Description

Correct

Selects correct day and has a justification based on the expected number of no shows (5.2) or shows that the percentage of no shows for that day is closer to 40%.

Selects correct day and has a justification based on the expected number of kept reservations (7.8) or shows that the percentage of kept reservations is closer to 60%.

If the responses generated by the student for Wednesday contain the same number of no shows as Tuesday (6), then their response must indicate that the outcomes for both days are the same.

Partial

Selects correct day, but with incomplete or no justification.

Correctly calculates the percentage of no shows for both days, but does not specify which day is closer to the expected number of no shows.

	Incorrect
	Incorrect response.

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.

Question 5

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.

Number of Kept Reservations

Number that Cannot be Seated

0 - 10

0

11

1

12

2

13

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

	Correct
	Correct response with justification.

	Partial
	Correct response, but with incomplete or no justification.

	Incorrect
	Incorrect response.

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.

Question 6

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)

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
	Correct response with justification.

	Partial
	Correct response with incomplete or no justification.

	Incorrect
	Incorrect response

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.

Question 7

Scoring Guide

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

Score & Description

	Correct
	Correct response

	Incorrect
	Incorrect response

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 40-49 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 40-49 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?

Question 8

Scoring Guide

Solution:

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

Tray

Colors

4 Red

3 Red

2 Red

1 Red

0 Red

0 Green

1 Green

2 Green

3 Green

4 Green

Possible Patterns

6 different color patterns are possible

Score & Description

Extended

Correct Response. Student finds all 6 possible color patterns (response must include the given pattern along with the other five patterns) with no repeats or contradictory information.

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

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

	Partial
	Has 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.

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

	Incorrect
	Incorrect response (Includes only repeating the given pattern).

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.

Question 9

Key


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)

Question 10

Key


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

Question 11

Key


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

Question 12

Key


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

Question 13

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

	Correct
	Correct response

	Incorrect #3
	Piece Q chosen, with an explanation that refers to a number of votes

	Incorrect #2
	Piece N chosen, but explanation not given or is inadequate with incorrect computation

	Incorrect #1
	Any incorrect response other than those described above

* 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.

Question 14

Scoring Guide

Solution:

Average hourly wage for Thursday - $5.75
Hourly wage rate changes at 5pm
Hourly wage from 9am - 5pm - $5.50/hr
Hourly wage from 5pm - 10pm - $6.00/hr

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
	Correct average hourly rate for Thursday and the correct time of 5 pm when the wage rate changes

	Partial
	Either correct average hourly rate for Thursday OR correct time the wage rate changes

	Incorrect
	Incorrect response

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 ?

Question 15

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
	Correct response

	Partial
	Lists sample space correctly with less than a complete explanation OR draws a correct tree diagram with less than a complete explanation OR just states 1 in 4 chance

	Incorrect
	Incorrect response

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 50-50 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 50-50 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 50-50 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 50-50 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 50-50 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 50-50 chance of winning. Do you agree?

Question 16

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

There are two clusters of data
The median is representative of only one of the clusters while the mean is representative of both

OR
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
	Indicates the better measure for each theater and gives a complete explanation for each measure

	Satisfactory
	Indicates the better measure for each theater and gives a complete explanation for one measure

	Partial
	Indicates mean for Theater B and median for Theater A with either no explanation or an incomplete explanation OR selects the better measure for one theater and gives an appropriate explanation

	Minimal
	Indicates the mean for Theater B with no explanation or an incomplete explanation OR indicates the median for Theater A with no explanation or an incomplete explanation

	Incorrect
	Incorrect response

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.

Question 17

Key


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

Question 18

Key


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

Question 19

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

	Correct
	Correct response

	Incorrect #3
	3 or 4 correct arrangements other than XYZ

	Incorrect #2
	1 or 2 correct arrangements other than XYZ

	Incorrect #1
	Any incorrect response other than as described above

* 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.

Question 20

Key


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

Question 21

Key


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

Question 22

Key


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

Question 23

Scoring Guide

Score & Description

Correct

(15×55)+(30×65)+(35×75)+(30×85)

—————————————— = 71

100

	Incorrect #2
	70(average of midpoints of each interval).

	Incorrect #1
	Any incorrect response other than as described in Incorrect #2.

*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 50-60 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 50-60 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 50-60 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 50-60 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 50-60 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 50-60 group.)

Question 24

Key


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

Question 25

Key


25.	In the graph above, each dot shows the number of sit-ups and the corresponding age for one of 13 people. According to this graph, what is the median number of sit-ups for these 13 people?

	A)	15
	B)	20
	C)	45
	D)	50
	E)	55

Question 26

Key


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

Question 27

Key


27.	The average weight of 50 prize-winning 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

Question 28

Key

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?

Question 29

Key


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

Question 30

Key


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

Question 31

Scoring Guide

Score & Description

	Correct
	3/8 or 3:8 or .375 or any equivalent answer

	Incorrect #1
	Incorrect answer other than 1/8

	Incorrect #2
	1/8

*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?