How to Calculate the Mean, Median, Mode and Range
Mean, median, mode and range are four ways to describe data. The mean is the average, the median is the middle value once sorted, and the mode is the most common. The range is largest − smallest.
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How to Calculate the Mean?
- Add up all the values.
- Divide by how many values there are.
How to Find the Median?
- Put the numbers in order from smallest to largest.
- Find the middle value (or average the two middle values).
How to Find the Mode?
- The mode is the value that appears most often.
- There can be more than one mode, or no mode.
How to Calculate the Range?
- Range = largest value − smallest value.
- A small range means the data is more consistent.
Practice Questions
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Your scores are 3, 5, 9, 5, 8. What is the mean?
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To find the mean, add all the scores and divide by the number of scores: .
These are your scores: 10, 3, 7, 6, 5. What is the range?
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The range is found by subtracting the smallest value from the largest value: .
Here are your scores: 5, 8, 6, 6, 7, 7, 7, 10. What is the mode?
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The mode is the value that occurs most often. Here, 7 appears three times, so it is the mode.
Your scores are 3, 8, 5, 6, 10, 8. What is the median?
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First, sort the scores: 3, 5, 6, 8, 8, 10. Since there are an even number of scores, the median is the average of the two middle values: .
Your scores are: 9, 7, 10, 7, 6, 7, 8. What is the median if the lowest score (6) is removed?
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After removing 6, the scores are 9, 7, 10, 7, 7, 8. Sorted: 7, 7, 7, 8, 9, 10. There are 6 scores, so take the average of the two middle values: .
Here are your scores: 6, 7, 7, 9, 5, 8. If you add another score of 100, how will the mean, median, and mode change?
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The new scores are 5, 6, 7, 7, 8, 9, 100. The mean increases because the total score increases significantly. The middle value remains 7, so the median stays the same. The mode also stays the same since 7 is still the most frequent value.
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Students Also Ask
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The mean shows the average, found by adding the values and dividing by how many there are. The median points to the middle value once the data is sorted. The mode reveals the value that occurs most often. The range gives the spread between the largest and smallest values.
Yes. The mean is also known as the arithmetic mean, and it is what we commonly refer to as the average. You work it out by adding all the values together, then dividing by the total number of values in the set.
When there is an even number of values, the median falls between the two middle values. Sort the values from smallest to largest, find the two in the middle, then take their average. That average is the median for the set.
Yes, a set of data can have more than one mode. The mode is the value that occurs most often, so when two or more values tie for the most occurrences, each of those values is a mode. This is simply a case of ties.
The range tells you the spread of a set of data, found as the difference between the largest and smallest values. A smaller range indicates greater consistency, which means the values are similar. So the range shows at a glance how spread out the values are.
The formula for locating the median is (N + 1) ÷ 2, where N represents the total number of values. It tells you the position of the median once the values are sorted. For example, with 10 values you get 5.5, so the median lies between the 5th and 6th values.