SAT Practice Questions: Mean versus Median

By Ron Woldoff

The SAT Math exam will probably contain questions about mean and median, but you may not always have to make calculations. Instead, you may be asked to explain the relationship between the mean and median for a set of numbers.

The following practice questions ask you to explain why the mean and median are similar and different in two separate cases.

Practice questions

  1. An auto dealer’s cars have a mean value of $22,000 and a median value of $25,000. Which of the following situations could explain the difference between the mean and the median?
    A. A few cars are valued much less than the rest.
    B. Many of the cars have values between $22,000 and $25,000.
    C. The cars have values that are close to each other.
    D. A few cars are valued much more than the rest.
  2. The exam scores in a German class have a mean value of 92 and a median value of 92. Which of the following situations could explain the similarity between the mean and the median?
    A. Most students scored below 92.
    B. Most students scored above 92.
    C. The students received extra credit.
    D. The exam scores are evenly spaced out.

Answers and explanations

  1. The correct answer is Choice (A).
    If the car values were evenly spaced apart, the mean and median would be the same. However, if a few cars were valued much lower than the others, these few cars would bring the mean down to a value less than the median.
  2. The correct answer is Choice (D).
    Evenly spaced scores would explain why the mean and the median are the same. If most students scored below 92, that would bring both the mean and the median below 92. If most scored above 92, that would bring them above 92. And if the scores were randomly spread out, the mean and median would be different. Extra credit has no bearing on the similarity between the mean and the median.