Median Calculator
Median Calculator
The median is the middle value in an ordered data set and is less affected by extreme values than the mean.
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Enter values and select Calculate.
How to Use the Median Calculator
Use this free Median Calculator to find the middle value of a list of numbers. Enter your values separated by commas, then select Calculate. The calculator determines the median after arranging the values in numerical order, so you do not need to sort the list manually.
- Enter two or more numerical values in the input field, separating each value with a comma.
- Include positive numbers, negative numbers or decimals as required by your data.
- Select Calculate to display the median result.
- Select Clear to remove the current values and start a new calculation.
Check that every value is entered correctly and separated by a comma. The median uses the centre position of the sorted data, not the order in which values were originally entered.
What Is the Median?
The median is a measure of central tendency that identifies the middle value in a data set after the values have been arranged from smallest to largest. If the data set contains an odd number of values, the median is the single middle value. If it contains an even number of values, the median is the arithmetic mean of the two middle values.
Unlike the arithmetic mean, the median is generally less affected by unusually high or low values. It is therefore useful when a data set is skewed or contains outliers, such as household incomes, property prices or waiting times.
Median Formula
First, arrange all values in ascending order. Let n represent the number of values.
In the even formula, the two values at the centre are added together and divided by 2. The positions refer to the sorted list, counting the first value as position 1.
Worked Examples
Example 1: Odd number of values
Data: 9, 3, 5, 1, 7
Step 1: Sort the values: 1, 3, 5, 7, 9.
Step 2: There are 5 values, so the middle position is (5 + 1) ÷ 2 = 3.
Answer: The third value is 5. The median is 5.
Example 2: Even number of values
Data: 4, 8, 2, 10
Step 1: Sort the values: 2, 4, 8, 10.
Step 2: The two middle values are 4 and 8.
Step 3: Calculate (4 + 8) ÷ 2 = 6.
Answer: The median is 6.
Median, Mean and Mode: Key Differences
- Median: The middle value after sorting the data.
- Mean: The sum of all values divided by the number of values.
- Mode: The value or values that occur most frequently.
These measures describe the centre of a data set in different ways. The median is often useful when extreme values would pull the mean away from the typical observation. The mode is useful for finding the most frequently occurring value or category.
Practical Uses of the Median
- Income analysis: Compare typical earnings without allowing a small number of very high incomes to dominate the result.
- Real estate: Summarise property prices in an area where a few luxury properties may be outliers.
- Education: Find the middle score in a class or examination data set.
- Business: Review typical order values, delivery times or customer waiting times.
- Research: Describe the centre of numerical data that may be skewed or contain extreme observations.
Frequently Asked Questions About the Median
1. How do I calculate the median?
Arrange the numbers from smallest to largest. If there is an odd number of values, select the middle one. If there is an even number, calculate the average of the two middle values.
2. What is the median of an odd number of values?
It is the single value in the centre of the sorted data set. For example, the median of 2, 5, 8 is 5.
3. What is the median of an even number of values?
It is the average of the two central values after sorting. For example, the median of 2, 4, 8, 10 is (4 + 8) ÷ 2 = 6.
4. Does the data need to be sorted before finding the median?
Yes. The values must be arranged in ascending or descending order to identify the middle position. This calculator sorts the entered values as part of the calculation.
5. Can the median be a decimal?
Yes. When the data set has an even number of values, the average of the two middle values may be a decimal. The original data can also contain decimal values.
6. Is the median affected by outliers?
The median is generally less affected by unusually large or small values than the mean because it depends on the middle position rather than the magnitude of every value.
7. What is the difference between median and average?
Average often refers to the arithmetic mean, which is calculated by adding all values and dividing by their count. The median is the middle value after sorting. They can be different, especially when the data contains outliers.
8. Can I use negative numbers in a median calculation?
Yes. Negative numbers can be included. Arrange all values from the smallest (most negative) to the largest before identifying the middle value or values.
9. What happens if two middle values are different?
When the data set has an even number of values, add the two middle values and divide the total by 2. The median may not be one of the original values.
10. Is this Median Calculator free to use?
Yes. You can use the SRIKAMI Median Calculator online to calculate the median of a numerical data set.
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