Differences between Mean and Median
Mean vs. Median[edit]
In statistics, mean and median are both measures of central tendency used to describe a dataset with a single value.[1] The mean is the arithmetic average, calculated by summing all values and dividing by the count of values.[2] The median is the middle value in a dataset that has been arranged in order of magnitude.[3] While both are used to find the center of a dataset, they have key differences that make them appropriate for different situations.[4]
The primary distinction lies in their sensitivity to outliers, which are values that are significantly different from others in the dataset. The mean is highly affected by outliers because it incorporates every value in its calculation.[5] A single extreme value can significantly pull the mean in its direction. In contrast, the median is less affected by outliers; since it is based on the middle position, extreme high or low values do not alter it as much.[5]
This sensitivity to outliers influences when each measure is best used. The mean is a good measure for datasets with a symmetrical distribution and no significant outliers.[4] However, for skewed data, the median is often considered a better representative of the central location.[3] For example, in right-skewed distributions, like income, a few high earners can inflate the mean, making the median a more accurate representation of a "typical" income.[3] Similarly, in a left-skewed distribution, the mean will be pulled lower than the median.
The calculation process for each also differs. To find the mean, the data does not need to be sorted. For the median, the dataset must first be arranged in ascending or descending order. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
Comparison Table[edit]
| Category | Mean | Median |
|---|---|---|
| Definition | The arithmetic average of all values in a dataset. | The middle value of a dataset when it is sorted in order. |
| Calculation | Sum of all values divided by the number of values.[1] | The middle value of an ordered set; if the set is even, it's the average of the two middle values. |
| Effect of Outliers | Highly sensitive; a single outlier can significantly change the value. | Robust; not significantly affected by extreme outliers. |
| Data Sorting Requirement | Not required. | Data must be arranged in numerical order. |
| Best for Distribution Type | Symmetrical distributions without significant outliers.[4] | Skewed distributions or datasets with outliers.[3] |
| Information Considered | Uses every value in the dataset for its calculation.[3] | Depends only on the middle value(s) in the ordered set. |
| Example with Outlier | In the set {10, 20, 30, 40, 200}, the mean is 60. | In the set {10, 20, 30, 40, 200}, the median is 30. |
In practice, reporting both the mean and the median can provide a more comprehensive understanding of a dataset's distribution. If the mean and median are close in value, the data is likely symmetrical. A significant difference between the two suggests the presence of outliers or a skewed distribution.[3]
References[edit]
- ↑ 1.0 1.1 "khanacademy.org". Retrieved November 18, 2025.
- ↑ "dictionary.com". Retrieved November 18, 2025.
- ↑ 3.0 3.1 3.2 3.3 3.4 3.5 "laerd.com". Retrieved November 18, 2025.
- ↑ 4.0 4.1 4.2 "statology.org". Retrieved November 18, 2025.
- ↑ 5.0 5.1 "statology.org". Retrieved November 18, 2025.
