Free SAT Data Analysis & Statistics Questions and Answers 1 — 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?
- The mean will decrease, and the median will increase.
- The mean will increase, and the median will decrease.
- Both the mean and the median will decrease. (Correct answer)
- Both the mean and the median will increase.
Correct answer: Both the mean and the median will decrease.
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?
- A student who doesn't study is predicted to have a GPA of 0.15.
- For each additional hour of study, the GPA is predicted to increase by 0.15. (Correct answer)
- The average GPA of all students is 0.15.
- The maximum possible GPA is 0.15 points higher than the minimum.
Correct answer: For each additional hour of study, the GPA is predicted to increase by 0.15.
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?
- The median score of Class A is higher than the median score of Class B.
- The mean score of Class A is higher than the mean score of Class B.
- The variability in scores for the middle 50% of students is greater in Class A. (Correct answer)
- Class A had more students than Class B.
Correct answer: The variability in scores for the middle 50% of students is greater in Class A.
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 |
- 1/20
- 1/6 (Correct answer)
- 1/4
- 3/10
Correct answer: 1/6
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?
- The mean of A is greater than the mean of B.
- The standard deviation of A is greater than the standard deviation of B.
- The standard deviation of B is greater than the standard deviation of A. (Correct answer)
- The range of A is equal to the range of B.
Correct answer: The standard deviation of B is greater than the standard deviation of A.
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.
Question 6: The salaries of 10 employees at a small company are listed. Nine employees earn between $40,000 and $60,000, while the CEO earns $350,000. Which measure of center would be most affected by the CEO's salary?
- The mean (Correct answer)
- The median
- The mode
- The range
Correct answer: The mean
The mean is calculated by summing all values and dividing by the count, so it is highly sensitive to extreme values (outliers). The CEO's salary is a significant outlier and will pull the mean much higher. The median is the middle value when the data is ordered, so it is resistant to outliers. Therefore, the mean is the measure that is most affected.
Question 7: A dot plot displays the number of siblings for each of the 20 students in a class. The minimum value on the dot plot is 0 and the maximum value is 5. What is the range of the data?
- 3
- 4
- 5 (Correct answer)
- 20
Correct answer: 5
The range of a data set is the difference between the maximum value and the minimum value. In this case, the maximum number of siblings is 5 and the minimum is 0. The range is calculated as Maximum - Minimum = 5 - 0 = 5.
Free SAT Data Analysis & Statistics Questions and Answers 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?