The rules that solve most questions
- Mean = sum ÷ number of values. So sum = mean × number of values, which solves missing-value questions.
- Median: sort the values first. For an even count, average the two middle values.
- An outlier pulls the mean toward it much more than the median.
- Range = maximum − minimum; it measures spread, not center.
Traps the wrong answers are built on
- Taking the middle value of an unsorted list as the median.
- Forgetting to include the missing value when multiplying the mean by the count.
Worked example
What is the median of the data set 12, 25, 9, 21, 3, 13, 19?
- A. 21
- B. 14
- C. 13
- D. 12
Answer: C. Put the values in order: 3, 9, 12, 13, 19, 21, 25. With 7 values, the median is the middle one, the 4th: 13. Taking the middle value of the unsorted list is the most common mistake.
Practice set
Answer each question to see whether you're right and why. When you finish, draw a new set: the numbers change every time.
0 of 10 answered · 0 correct · set 1
- Question 1Medium
What is the median of the data set 12, 25, 9, 21, 3, 13, 19?
Show answer and explanation
Answer: C
Put the values in order: 3, 9, 12, 13, 19, 21, 25.
With 7 values, the median is the middle one, the 4th: 13.
Taking the middle value of the unsorted list is the most common mistake.
- Question 2Medium
What is the median of the data set 12, 22, 8, 5, 10, 4, 18?
Show answer and explanation
Answer: B
Put the values in order: 4, 5, 8, 10, 12, 18, 22.
With 7 values, the median is the middle one, the 4th: 10.
Taking the middle value of the unsorted list is the most common mistake.
- Question 3Medium
What is the median of the data set 23, 29, 15, 20, 17, 2?
Show answer and explanation
Answer: B
Put the values in order: 2, 15, 17, 20, 23, 29.
With 6 values, the median is the mean of the two middle values: (17 + 20) / 2 = 18.5.
Taking the middle value of the unsorted list is the most common mistake.
- Question 4Medium
What is the median of the data set 29, 30, 29, 23, 26?
Show answer and explanation
Answer: B
Put the values in order: 23, 26, 29, 29, 30.
With 5 values, the median is the middle one, the 3th: 29.
Taking the middle value of the unsorted list is the most common mistake.
- Question 5Medium
What is the median of the data set 9, 8, 11, 7, 15?
Show answer and explanation
Answer: D
Put the values in order: 7, 8, 9, 11, 15.
With 5 values, the median is the middle one, the 3th: 9.
Taking the middle value of the unsorted list is the most common mistake.
- Question 6Medium
The mean of 6 numbers is 18. 5 of the numbers are 26, 26, 6, 26, 4. What is the remaining number?
Show answer and explanation
Answer: B
If the mean of 6 numbers is 18, their total is 6 × 18 = 108.
The 5 known numbers add to 88.
The remaining number is 108 − 88 = 20.
- Question 7Medium
The mean of 6 numbers is 19. 5 of the numbers are 28, 19, 7, 3, 4. What is the remaining number?
Show answer and explanation
Answer: D
If the mean of 6 numbers is 19, their total is 6 × 19 = 114.
The 5 known numbers add to 61.
The remaining number is 114 − 61 = 53.
- Question 8Medium
What is the median of the data set 18, 19, 17, 10, 16?
Show answer and explanation
Answer: C
Put the values in order: 10, 16, 17, 18, 19.
With 5 values, the median is the middle one, the 3th: 17.
Taking the middle value of the unsorted list is the most common mistake.
- Question 9Medium
What is the median of the data set 25, 6, 27, 8, 29, 26, 12?
Show answer and explanation
Answer: A
Put the values in order: 6, 8, 12, 25, 26, 27, 29.
With 7 values, the median is the middle one, the 4th: 25.
Taking the middle value of the unsorted list is the most common mistake.
- Question 10Medium
The mean of 7 numbers is 15. 6 of the numbers are 13, 13, 16, 14, 12, 11. What is the remaining number?
Show answer and explanation
Answer: A
If the mean of 7 numbers is 15, their total is 7 × 15 = 105.
The 6 known numbers add to 79.
The remaining number is 105 − 79 = 26.
More Problem-Solving and Data Analysis practice
Questions people ask
Is this one-variable data: mean and median practice like the real SAT?
The questions follow the format of the digital SAT's Problem-Solving and Data Analysis domain: four answer choices built from common mistakes. They are written for this site; they are not official College Board questions.
How many practice questions are there?
As many as you want. Each math question is generated from a template with new numbers, and its answer is checked by code. Use "New set" for another ten.
Where is the domain on the test?
Problem-Solving and Data Analysis is one of the four content domains of the SAT Math section, alongside Algebra, Advanced Math, Geometry and Trigonometry.