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SAT Math skill page

SAT Mean and Median Practice

Know when the SAT wants the arithmetic average and when it wants the middle value.

Practice mean and median in Dolphin SATPractice questions
10-16 min practice time3 questions on pageProblem Solving and Data Analysis
Practice time10-16 min
Question bank3 questions
Best forProblem Solving and Data Analysis

What this tests

What to know for this SAT skill

Dolphin question bank

Practice your skill

Question 1 of 3Medium
The mean and the median of the five numbers above are equal. Which of the following is NOT a possible value of x?
  1. 6
  2. 11
  3. 16
  4. 21
Show answer and solution
Correct answerA. 6

Solution walkthrough

  1. If is 6, then the five numbers in the given list are 15, 14, 18, 17, 6.
  2. The mean of these five numbers is the sum of all the values divided by the number of values, or \[ = 14.
  3. \] The median of these five numbers can be found by ordering the numbers from least to greatest and determining the middle value.
  4. When ordered from least to greatest, the numbers in the given list are 6, 14, 15, 17, 18, and the middle value is 15.
  5. Since the mean is 14 and the median is 15, the mean and median aren’t equal when is 6.
Why the other choices miss
Choices B, C, and D are incorrect. If any of these values is substituted for , the mean and median of the data set would be equal.
Question 2 of 3Easy
The list gives the number of penguins in each of 6 colonies: 21, 5, 18, 22, 19, 7.
The list gives the number of penguins in each of 6 colonies: 21, 5, 18, 22, 19, 7.

What is the median number of penguins in the 6 colonies?
  1. 15
  2. 18.5
  3. 19
  4. 22
Show answer and solution
Correct answerB. 18.5

Solution walkthrough

  1. The range is the largest value minus the smallest value.
  2. The maximum is and the minimum is , so the range is .
Question 3 of 3Hard
The frequency distribution above summarizes a set of data, where a is a positive integer. How much greater is the mean of the set of data than the median?
  1. 0
  2. 1
  3. 2
  4. 3
Show answer and solution
Correct answerA. 0

Solution walkthrough

  1. Since the frequencies of values less than the middle value, 3, are the same as the frequencies of the values greater than 3, the set of data has a symmetric distribution.
  2. When a set of data has a symmetric distribution, the mean and median values are equal.
  3. Therefore, the mean is 0 greater than the median.

Avoid these traps

Common mistakes on this skill

Finding the median before sorting

The values must be ordered before selecting the middle value or averaging the two middle values.

Treating mean and median as equally sensitive to outliers

Extreme values directly affect the mean but usually have less effect on the median.

Study plan

How to practice this skill in Dolphin

  1. Order the data and count the number of observations.
  2. Use the correct definition for mean or median and keep track of any missing value.
  3. Predict how a changed or added value should move the statistic before finalizing the calculation.
Practice mean and median in Dolphin SAT

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FAQ

Questions about SAT Mean and Median Practice

When is the median more useful than the mean?

The median is often more representative when a distribution is skewed or contains extreme outliers.

How do I find the median with an even number of values?

After sorting, average the two middle values.