PSAT/NMSQT Math: Problem and Data Analysis Questions and Answers

Question 1

The two-way table below shows the results of a survey of 200 high school students regarding their primary mode of transportation to school, categorized by grade level.

| | Bus | Car | Walk | Total |
|---|---|---|---|---|
| Junior | 45 | 30 | 15 | 90 |
| Senior | 25 | 70 | 15 | 110 |
| Total | 70 | 100 | 30 | 200 |

Of the students who ride the bus to school, what percentage are juniors? (Round to the nearest tenth of a percent)

Accepted Answer

64.3%

Answer

22.5%

Answer

45.0%

Answer

70.0%

Question 2

A biologist is studying the growth of a certain plant species. The scatterplot for the plant's height over time shows a positive linear association. The line of best fit is given by the equation y = 1.8x + 5.2, where y is the height of the plant in centimeters and x is the number of weeks since the study began. What is the best interpretation of the slope of the line of best fit?

Accepted Answer

For each additional week, the plant's predicted height increases by 1.8 cm.

Answer

The plant's predicted initial height at the start of the study was 1.8 cm.

Answer

For each additional week, the plant's predicted height increases by 5.2 cm.

Answer

The plant's predicted initial height at the start of the study was 5.2 cm.

Question 3

The list below shows the number of goals scored by a soccer player in 9 consecutive games:

2, 3, 0, 1, 3, 4, 2, 1, 3

If the player scores 10 goals in the tenth game, which of the following statistical measures of the data will change the most?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 4

A map of a state park is drawn to scale. The legend indicates that 2 inches on the map represents 5 miles in the park. Two trailheads are 7 inches apart on the map. What is the actual distance between the two trailheads in miles?

Accepted Answer

17.5 miles

Answer

15.5 miles

Answer

14.0 miles

Answer

20.0 miles

Question 5

A technology blogger wants to determine the most popular brand of smartphone among young adults in a particular city. The blogger conducts a survey by asking the first 100 people who visit their tech blog on a Monday morning to name their smartphone brand. Why might the conclusion drawn from this survey NOT be reliable for the city's entire young adult population?

Accepted Answer

The sample is likely biased because it is not representative of all young adults in the city.

Answer

The sample size of 100 people is too small to draw any conclusions.

Answer

The survey was conducted on a Monday, when people are typically busy.

Answer

The survey should have been conducted in person instead of online.

Question 6

A company that manufactures light bulbs tests a random sample of 500 bulbs from a production batch of 20,000 bulbs. The test finds that 8 of the bulbs are defective. Based on this sample, what is the best estimate for the total number of defective bulbs in the entire batch?

Accepted Answer

320

Answer

128

Answer

400

Answer

1,600