SAT Math
One-Variable Data
One-Variable Data is a skill in the Problem-Solving and Data Analysis domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.
9 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.
Sample questions
Open a question to see the answer choices and the correct answer.
What is the median of the following data set? 4, 7, 7, 9, 12, 12, 12, 19
- A. 10.25
- B. 12
- C. 9
- D. 10.5 ✓
Correct answer: D. With 8 values, the median is the average of the 4th and 5th values in order (9 and 12): (9 + 12)/2 = 10.5.
Data set A: 40, 42, 44, 46, 48 Data set B: 30, 35, 50, 60, x Data set A and data set B each contain 5 numbers. If the mean of data set A is equal to the mean of data set B, what is the value of x?
- A. 45 ✓
- B. 44
- C. −45
- D. 105
Correct answer: A. The mean of data set A is (40+42+44+46+48)/5 = 220/5 = 44, so the sum of data set B must also be 220; since 30+35+50+60 = 175, x = 220 − 175 = 45.
A set of nine employees' salaries has a median of $52,000. One employee, whose salary is far higher than the others, leaves the company and is not replaced, and the remaining eight salaries are unchanged. Which of the following best describes the most likely effect on the mean and median of the remaining employees' salaries?
- A. Both the mean and the median will increase, since removing an employee always raises the remaining average.
- B. The mean will decrease by more than the median does, since removing a high outlier affects the mean more than it affects the median. ✓
- C. The median will decrease by more than the mean does, since removing any data point always affects the middle value the most.
- D. Neither the mean nor the median will change, since removing one value out of nine has a negligible effect on both measures.
Correct answer: B. The mean is sensitive to extreme values, so removing a very high salary pulls the mean down noticeably, while the median, based on the middle of the ordered data, is much less affected by extreme values.
Data set A contains the values 4, 7, 9, 12, and x. Data set B contains the values 2, 6, 10, 14, and 18. If the mean of data set A equals the mean of data set B, what is the value of x?
- A. 18 ✓
- B. 10
- C. 22
- D. 13
Correct answer: A. Correct — the mean of data set B is (2+6+10+14+18)/5 = 10, so 4+7+9+12+x must equal 50; since those four known values sum to 32, x = 18.
A data set of 12,15,18,20, and 22 has a mean of 17.4 and a median of 18. A new value of 85 is added to the set. Which statement correctly compares the effect on the mean and median?
- A. The median increases by far more than the mean, since medians are based on the largest value in a data set.
- B. The mean increases by far more than the median, since the median is resistant to extreme values while the mean is not. ✓
- C. Both the mean and median increase by the same amount, since adding any value shifts every summary statistic equally.
- D. Neither the mean nor the median changes, since a single added value cannot affect summary statistics.
Correct answer: B. Correct — recalculating with the added value, the new mean rises to about 28.7 (an increase of over 11), while the new median rises only from 18 to 19, showing the median resists the outlier's influence much more than the mean does.