What are mode, median, and range?
Mode, median, and range are three ways to describe a set of numbers. A data set is a group of numbers, such as quiz scores or the ages of students in a class. Each of these measures tells you something different about the data.
- Mode: the number that appears most often in a data set.
- Median: the middle number when the data set is ordered from least to greatest.
- Range: the difference between the greatest number and the least number.
- Data set: 3, 7, 7, 9, 12
- The mode is 7 because it appears twice.
- The median is 7 because it is the middle number.
- The range is 9 because 12 − 3 = 9.
Put the numbers in order from least to greatest before finding the median. To find the range, identify the greatest and least numbers, then subtract the least number from the greatest number. This step helps you avoid mistakes.
How to find the mode
The mode is the value that occurs most frequently in a data set. A data set can have one mode, more than one mode, or no mode at all.
- If one number appears more often than any other, that number is the mode.
- If two or more numbers tie for the most appearances, the data set has more than one mode.
- If every number appears the same number of times, there is no mode.
- Data set: 4, 4, 6, 8, 9 → The mode is 4.
- Data set: 2, 3, 3, 5, 5, 7 → The modes are 3 and 5.
- Data set: 1, 2, 3, 4, 5 → There is no mode.
The mode is the only measure of center that can be used with data that are not numbers, such as favorite colors. For example, if most students choose blue, then blue is the mode.
How to find the median
The median is the middle value in a data set that has been ordered from least to greatest. It splits the data into two equal halves.
- If the data set has an odd number of values, the median is the single middle number.
- If the data set has an even number of values, find the two middle numbers. Add them together and divide by 2 to find their average. This average is the median.
- Odd number of values: 5, 8, 10, 12, 15 → The median is 10.
- Even number of values: 6, 7, 9, 11 → The two middle numbers are 7 and 9. (7 + 9) ÷ 2 = 8. The median is 8.
When a data set has an even number of values, the median may not be one of the numbers in the original set. That is perfectly fine. The median is still a valid measure of the middle of the data.
How to find the range
The range is the difference between the greatest value and the least value in a data set. It shows how spread out the data are.
Use this formula: Range = Greatest value − Least value
- Data set: 12, 15, 18, 22, 30 → Range = 30 − 12 = 18.
- Data set: 4, 9, 9, 14 → Range = 14 − 4 = 10.
- Data set: 100, 105, 110 → Range = 110 − 100 = 10.
A large range means the data are spread far apart. A small range means the data are close together. The range is always a non-negative number because the greatest value is never less than the least value.
Steps for finding mode, median, and range
Follow these steps to find all three measures for any data set:
- Order the data from least to greatest. This is essential for the median and range.
- Find the mode by counting how many times each number appears. The number that appears most often is the mode.
- Find the median by locating the middle value. If there are two middle values, find their average.
- Find the range by subtracting the least value from the greatest value.
Data set: 9, 4, 7, 4, 11, 9, 9
- Step 1: Order the data → 4, 4, 7, 9, 9, 9, 11
- Step 2: Mode → 9 appears three times, so the mode is 9.
- Step 3: Median → There are 7 values, so the middle value is the 4th one. The median is 9.
- Step 4: Range → 11 − 4 = 7.
Always double-check your ordered list. A single out-of-place number can change the median and range.
Using mode, median, and range in real life
People use mode, median, and range every day to understand information. These measures help make decisions in school, sports, business, and science.
- A coach records the points scored in seven games: 12, 15, 15, 18, 20, 22, 25. The mode is 15, the median is 18, and the range is 13.
- A teacher looks at quiz scores: 80, 85, 85, 90, 95. The mode is 85, the median is 85, and the range is 15.
- A store tracks the number of items sold each day: 3, 5, 5, 5, 8, 10. The mode is 5, the median is 5, and the range is 7.
When you read a graph or a chart, look for the mode, median, and range to describe what you see. These three measures give a quick summary of the data.
Common mistakes to avoid
Students often make small errors when finding mode, median, and range. Review these common mistakes so you can avoid them.
- Forgetting to order the data: The median and range require an ordered list.
- Confusing mode with median: The mode is the most frequent number. The median is the middle number.
- Choosing the wrong middle number: Count carefully from both ends when finding the median.
- Subtracting in the wrong order for range: Always subtract the least value from the greatest value.
- Assuming every data set has a mode: Some data sets have no mode at all.
- Incorrect: Data set 8, 3, 5, 3 → Median = 5 (not ordered).
- Correct: Order → 3, 3, 5, 8 → Median = (3 + 5) ÷ 2 = 4.
- Incorrect: Range of 10, 4, 7 → 10 − 7 = 3.
- Correct: Range = 10 − 4 = 6.
Take your time and show your work. Writing the ordered list and the steps for each measure helps you catch mistakes before they happen.
Common Core alignment:
CCSS.MATH.CONTENT.4.OA.C.5 – Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.
CCSS.MATH.CONTENT.4.MD.B.4 – Make a line plot to display a data set of measurements in fractions of a unit. Solve problems involving addition and subtraction of fractions by using information presented in line plots.
Notes for teachers
This resource is designed to provide clear explanations, examples, and practice for learners of different needs and levels of support. It may be used for whole-class instruction, guided practice, independent learning, review, homework, or additional reinforcement at home.