Public Release Item: Public Release items have appeared on HSA forms and then are released for public viewing and use. Releasing items is one step to ensuring that schools, districts, and other stakeholders understand how the core learning goals are assessed on the HSA.
 Goal 3 Data Analysis And Probability Expectation 3.1 The student will collect, organize, analyze, and present data. Indicator 3.1.2 The student will use the measures of central tendency and/or variability to make informed conclusions. Assessment Limits: Measures of central tendency include mean, median, and mode. Measures of variability include range, interquartile range, and quartiles. Data may be displayed in a variety of representations which may include: frequency tables, box and whisker plots, and other displays.

### Selected Response Item - Released in 2001

Each year Ms. Fong, a physics teacher, has her students build bridges out of toothpicks. Last year Ms. Fong recorded the number of toothpicks that 20 of her students used. Her list is shown below.

Ms. Fong will use the mode of this data set to determine the number of toothpicks needed for each student this year. How many toothpicks will be needed for each student?

1. 147
2. 150
3. 157
4. 200
/share/clg/xml/public_release/mathematics/2001_312_alg17.xml

Correct Answer:
C

### Selected Response Item - Released in 2001

A businesswoman calculates that the median cost of her five business trips last month was \$600. Which of these statements is correct?

1. She spent a total of \$3,000 on business trips last month.
2. She spent \$600 on most of the business trips last month.
3. She spent \$600 or more on at least half of the business trips last month.
4. She spent \$600 more on her most expensive business trip than she did on her least expensive trip.
/share/clg/xml/public_release/mathematics/2001_312_alg27.xml

Correct Answer:
C

### Selected Response Item - Released in 2001

The box-and-whisker plot below summarizes the test scores of an algebra class.

Based on the box-and-whisker plot, which of these must be true?

1. The median score is 70.
2. The lower quartile score is 50.
3. Half of the scores are between 60 and 75.
4. The interquartile range is half of the range.
/share/clg/xml/public_release/mathematics/2001_312_alg31.xml

Correct Answer:
D

### Brief Constructed Response (BCR) Item - Released in 2001

The table below shows the salaries of the teachers at Polk High School.

Complete the following in the Answer Book:

• What are the median and mean of this salary data? Use mathematics to explain how you determined your answers. Use words, symbols, or both in your explanation.
• A journalist who believes that teachers earn too much money is going to write an article based on this data. Which measure of central tendency (mean or median) should the journalist use to convince the public to agree with her opinion? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2001_312_alg40.xml

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### Selected Response Item - Released in 2002

The growing season is defined as the average number of days between the last frost in the spring and the first frost of the fall. The table below shows the average growing season for nine major U.S. cities.

If the circled number 156 is changed to 256, how would the mean, median, and mode of this data change?

1. increase mean, median, and mode
2. decrease mean, median, and mode
3. increase mean, median, eliminate mode
4. increase mean and mode, decrease median
/share/clg/xml/public_release/mathematics/2002_312_alg23.xml

Correct Answer:
C

### Brief Constructed Response (BCR) Item - Released in 2002

The table below shows the number of medals won by 24 countries during the 1998 Winter Olympic Games.

Complete the following in the Answer Book:

• Use the data from the table to create a box-and-whisker plot on the grid provided in the Answer Book.
• What was the least number of medals won by a country in the top 25% of the final medal standings? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

/share/clg/xml/public_release/mathematics/2002_312_alg31.xml

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### Brief Constructed Response (BCR) Item - Released in 2005

A cereal company awards a prize to anyone who collects all 5 different game pieces. Each game piece has an equal chance of being placed in a box of cereal. Each box of cereal contains 1 game piece. A class of 20 students conducted a simulation to see how many boxes of cereal must be purchased to collect all 5 different game pieces. Their results are shown in the table below.

Complete the following in the Answer Book:

• What are the mean, median, and mode of the data?
• A box of cereal costs \$2.80. Based on the simulation results, how much money must a consumer spend to collect all 5 different game pieces? Use measures of central tendency to justify your answer.
• One student in the class suggested that the data point of 26 should be ignored. Will ignoring this data point have a greater influence on the mean or the median? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2005_312_alg06.xml

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### Selected Response Item - Released in 2005

While studying a school's top 10 college entrance exam scores, a guidance counselor found the mean score to be 1,472. In looking at the calculations, the counselor realized he had made a mistake. One of the student's scores was 10 points greater than the counselor used in his calculations. What is the correct mean score?

1. 1,462
2. 1,472
3. 1,473
4. 1,482
/share/clg/xml/public_release/mathematics/2005_312_alg31.xml

Correct Answer:
C

### Selected Response Item - Released in 2005

Four teachers gave a test to their classes. A summary of the test results is shown below.

Which teacher's class has the widest spread in the middle 50% of the test scores?

1. Mrs. Lee
2. Mr. Green
3. Mrs. Smith
4. Mr. Wang
/share/clg/xml/public_release/mathematics/2005_312_alg34.xml

Correct Answer:
A

### Selected Response Item - Released in 2001

The table below shows the average daily temperatures, in degrees Fahrenheit (°F), for four selected cities. The average daily temperatures are given for the months of January and July.

According to the information in the table, which city experiences the greatest range of temperatures between January and July?

1. Baltimore
2. Mexico City
3. Tokyo
4. Toronto
/share/clg/xml/public_release/mathematics/2001_312_alg11.xml

Correct Answer:
D

### Selected Response Item - Released in 2003

The table below shows the percentages of high school students who took a college entrance examination in 1997 in 7 states.

Which of these states' percentages is at the third quartile?

1. Maryland
2. Massachusetts
3. New Jersey
4. Pennsylvania
/share/clg/xml/public_release/mathematics/2003_312_alg05.xml

Correct Answer:
D

### Selected Response Item - Released in 2003

The table below shows the number of points scored by the winner of the men's ski jumping competition during the Olympics from 1980 to 1994.

After the 1998 Olympics, the mean number of points scored by all winners since 1980 was 241.9. Which of these might have been the winning number of points in 1998?

1. 217.5
2. 234.6
3. 243.1
4. 248.4
/share/clg/xml/public_release/mathematics/2003_312_alg22.xml

Correct Answer:
B

### Selected Response Item - Released in 2004

Paul earned scores of 76, 78, and 86 on his first three science tests. What score does he need on his fourth test to earn a mean score of 82?

1. 78
2. 80
3. 84
4. 88
/share/clg/xml/public_release/mathematics/2004_312_alg03.xml

Correct Answer:
D

### Brief Constructed Response (BCR) Item - Released in 2004

Matt caught 6 fish and recorded each of their weights as shown in the table below.

Complete the following in the Answer Book:

• Find the mean and the median of the data.
• Which measure of central tendency, mean or median, should Matt use to best represent the typical weight of the fish he caught? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2004_312_alg05.xml

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### Selected Response Item - Released in 2004

A credit card company investigates any purchase that is larger than the third quartile of a customer's last 12 purchases. Mike's last 12 purchases are shown below.

What is the largest purchase Mike could make next without having his purchase investigated?

1. \$26.25
2. \$28.84
3. \$38.75
4. \$43.25
/share/clg/xml/public_release/mathematics/2004_312_alg25.xml

Correct Answer:
C

### Selected Response Item - Released in 2009

Stephanie scored 88, 70, 84, and 72 on her first four science tests. What score does Stephanie need on her fifth science test to receive a mean score of 80?

1. 79
2. 80
3. 82
4. 86
/share/clg/xml/public_release/mathematics/2009_312_alg01.xml

Correct Answer:
D

### Student Produced Response (SPR) Item - Released in 2009

The test scores for two classes are shown below.

What is the difference between the ranges of the scores for class A and class B?

/share/clg/xml/public_release/mathematics/2009_312_alg14.xml

Correct Answer:
9

### Student Produced Response (SPR) Item - Released in 2009

The table below shows the number of people on the boards of directors of 23 companies.

What is the median number of people on the boards of directors of these 23 companies?

/share/clg/xml/public_release/mathematics/2009_312_alg22.xml

Correct Answer:
4

### Selected Response Item - Released in 2009

The growing season of a major city is defined as the average number of days between the last frost in the spring and the first frost of the fall. Study the table below showing the average growing seasons of thirty major U.S. cities.

If the circled number 279 is changed to 179, how would the mode of this data change?

1. mode would not change
2. mode would decrease from 213 to 210
3. mode would decrease from 196 to 193
4. there would be two modes: 156 and 179
/share/clg/xml/public_release/mathematics/2009_312_alg25.xml

Correct Answer:
D

### Selected Response Item - Released in 2009

The test scores of 8 students are listed below.

Which students’ scores would fall above the third quartile?

1. Rhonda and Abe
2. Melanie and Nate
3. Steve and Daniel
4. Abe and Steve
/share/clg/xml/public_release/mathematics/2009_312_alg50.xml

Correct Answer:
B

### Selected Response Item - Released in 2002

An athletic director asked 4 groups of students, “What is the most that you would pay for an athletic event?” The responses are shown below.

Which group's answers showed the least variability?

1. Group 1
2. Group 2
3. Group 3
4. Group 4
/share/clg/xml/public_release/mathematics/2002_312_alg25.xml

Correct Answer:
D

### Brief Constructed Response (BCR) Item - Released in 2003

Amar compared the ages of the U.S. presidents who served between 1789 and 1845 at their first inaugurations to the ages of the presidents who served between 1945 and 2000 at their first inaugurations, as shown below.

Complete the following in the Answer Book:

• What are the mean and median for each group of U.S. presidents?
• Amar wanted to use this data to show that the ages of the U.S. presidents at their first inaugurations have decreased between 1789 and 2000. How could Amar use this data to support his conclusion?
• Do you think the data provides Amar with support strong enough to make his conclusion valid? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2003_312_alg17.xml

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### Selected Response Item - Released in 2006

Christine has a mean score of 18 points per game in her first four basketball games of the season. How many points must she score in her next game to raise her mean score to 20 points per game?

1. 20
2. 22
3. 25
4. 28
/share/clg/xml/public_release/mathematics/2006_312_alg07.xml

Correct Answer:
D

### Brief Constructed Response (BCR) Item - Released in 2006

The student government wants to determine if students get better grades in morning or afternoon classes. They randomly surveyed 20 students that take math class in the morning and 20 students that take math class in the afternoon. The survey results are shown in the stem-and-leaf plots below.

Complete the following in the Answer Book:

• What are the mean, median, and mode for each class?
• Based on the data, do students get better grades in the morning classes? Use measures of central tendency to justify your answer.

/share/clg/xml/public_release/mathematics/2006_312_alg28.xml

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### Selected Response Item - Released in 2006

Look at the bowling scores in the table below.

Which of these is the range of the bowling scores?

1. 10
2. 26
3. 34
4. 54
/share/clg/xml/public_release/mathematics/2006_312_alg32.xml

Correct Answer:
D

### Selected Response Item - Released in 2007

Edwin records the number of geese that live in a wildlife park from February through October. His results are shown in the table below. The mean of the data is 174. The median of the data is 180.

 Month Number of Geese Feb. Mar. Apr. May June July Aug. Sept. Oct. 60 161 178 188 203 228 196 180 172

Which of these best explains why the mean is less than the median?

1. The data set only includes 9 months.
2. The range of the data set is very large.
3. The minimum value of 60 is well below the other numbers in the data set.
4. The maximum value of 228 is well above the other numbers in the data set.
/share/clg/xml/public_release/mathematics/2007_312_alg05.xml

Correct Answer:
C

### Selected Response Item - Released in 2007

The table below shows the points scored by a basketball team during its first 5 games.

After the first 6 games, the team had a mean score of 64 points per game. How many points did the basketball team score in game 6?

1. 63
2. 64
3. 66
4. 69
/share/clg/xml/public_release/mathematics/2007_312_alg23.xml

Correct Answer:
D

### Selected Response Item - Released in 2008

In a class of 15 students, each student has a different test score. The median test score is 79. How many students scored higher than 79?

1. 6
2. 7
3. 8
4. 9
/share/clg/xml/public_release/mathematics/2008_312_alg05.xml

Correct Answer:
B

### Selected Response Item - Released in 2008

The table below shows the average life span of United States currency.

According to the data, which of these conclusions can be made about the life span of United States currency?

1. The mode is 9 years.
2. The range is 7 years.
3. The mean is 4 years.
4. The median is 3 years.
/share/clg/xml/public_release/mathematics/2008_312_alg37.xml

Correct Answer:
A

### Brief Constructed Response (BCR) Item - Released in 2008

Nineteen families live in a small town. The income for each family is listed in the table below.

Complete the following in the Answer Book:

• What are the median and mean family incomes for this small town?
• Should the mean or median be used to describe the typical family income in this small town? Use mathematics to justify your answer.
• If each family’s income increases by \$1,000, Alison believes the mean family income will increase more than the median family income. Do you agree with Alison? Use mathematics to justify your answer.

/share/clg/xml/public_release/mathematics/2008_312_alg22.xml

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 Resources for 3.1.2: Skill Statements | PUBLIC RELEASE ITEMS | Lesson Plans |