Free SAT Data Analysis & Statistics Questions and Answers

Question 1

The scores for 7 students on a quiz were 72, 78, 81, 85, 92, 92, and 98. If an 8th student takes the quiz and scores a 60, how will the mean and median of the scores change?

Accepted Answer

Both the mean and the median will decrease.

Answer

The original median is the 4th value, 85. With the new score of 60, the ordered list is 60, 72, 78, 81, 85, 92, 92, 98. The new median is the average of the 4th and 5th values, (81+85)/2 = 83. The original mean was (72+78+81+85+92+92+98)/7 ≈ 85.4. The new score of 60 is lower than the original mean, so it will pull the mean down. Therefore, both the mean and the median will decrease.

Question 2

A scatterplot shows the relationship between the number of hours a student studies per week and their grade point average (GPA). The data is fitted with a line of best fit given by the equation `y = 0.15x + 1.8`, where `y` is the GPA and `x` is the hours studied. What is the best interpretation of the slope of this line?

Accepted Answer

For each additional hour of study, the GPA is predicted to increase by 0.15.

Answer

The slope of a line represents the change in `y` for a one-unit change in `x`. In this context, the slope is 0.15. This means that for each additional hour a student studies per week (`x`), their GPA (`y`) is predicted to increase by 0.15 points.

Question 3

Two different classes, Class A and Class B, took the same science test. The test scores for each class are summarized in two box plots. The box for Class A is much wider than the box for Class B. Which of the following is a correct conclusion from this information?

Accepted Answer

The variability in scores for the middle 50% of students is greater in Class A.

Answer

In a box plot, the width of the box represents the interquartile range (IQR), which is the range of the middle 50% of the data (Q3 - Q1). A wider box indicates a larger IQR. Therefore, the test scores for the middle 50% of students in Class A are more spread out than the scores for the middle 50% of students in Class B.

Question 4

The table shows the distribution of 200 students at a high school by grade level and their primary mode of transportation. Of the students who are juniors, what fraction walk to school?

| Grade   | Car | Bus | Walk | Total |
|---------|-----|-----|------|-------|
| Junior  | 30  | 20  | 10   | 60    |
| Senior  | 70  | 40  | 30   | 140   |
| Total   | 100 | 60  | 40   | 200   |

Accepted Answer

1/6

Answer

The question asks for the fraction of juniors who walk. First, find the total number of juniors, which is given in the table as 60. Then, find the number of juniors who walk, which is 10. The fraction is the part (juniors who walk) over the whole (total juniors), which is 10/60, simplifying to 1/6.

Question 5

Data set A and Data set B each contain 100 numbers. The frequency distribution for Data set A is tall and narrow, while the frequency distribution for Data set B is short and wide. Which of the following statements is most likely true?

Accepted Answer

The standard deviation of B is greater than the standard deviation of A.

Answer

Standard deviation is a measure of how spread out the numbers in a data set are from their mean. A tall and narrow distribution (like in Data set A) indicates that most data points are clustered closely around the mean, resulting in a small standard deviation. A short and wide distribution (like in Data set B) indicates that the data points are more spread out, resulting in a larger standard deviation.

Bluebook SAT Practice Test Practice Test

Bluebook SAT Practice Test Practice Test

Free SAT Data Analysis & Statistics Questions and Answers