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In a set of numbers, if the median is greater than the mean, what can be inferre

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Question: In a set of numbers, if the median is greater than the mean, what can be inferred about the distribution of the numbers?

Options:

  1. The numbers are evenly distributed.
  2. The distribution is skewed to the left.
  3. The distribution is skewed to the right.
  4. The numbers are all equal.

Correct Answer: The distribution is skewed to the left.

Solution: 

If the median is greater than the mean, it indicates that the distribution is skewed to the left, meaning there are a few lower values pulling the mean down.

In a set of numbers, if the median is greater than the mean, what can be inferre

Practice Questions

Q1
In a set of numbers, if the median is greater than the mean, what can be inferred about the distribution of the numbers?
  1. The numbers are evenly distributed.
  2. The distribution is skewed to the left.
  3. The distribution is skewed to the right.
  4. The numbers are all equal.

Questions & Step-by-Step Solutions

In a set of numbers, if the median is greater than the mean, what can be inferred about the distribution of the numbers?
  • Step 1: Understand what the median is. The median is the middle number in a sorted list of numbers.
  • Step 2: Understand what the mean is. The mean is the average of all the numbers in the set.
  • Step 3: Compare the median and the mean. If the median is greater than the mean, it means the middle value is higher than the average value.
  • Step 4: Recognize that when the median is greater than the mean, it suggests that there are some lower values in the set that are pulling the mean down.
  • Step 5: Conclude that the distribution of the numbers is skewed to the left, meaning there are more higher values and a few lower values.
  • Median vs. Mean – Understanding the relationship between median and mean in a data set and how it indicates the skewness of the distribution.
  • Skewness – Recognizing that a left-skewed distribution has a median greater than the mean due to the influence of lower outliers.
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