What is the Difference Between Median and Average (Mean)?
🆚 Go to Comparative Table 🆚The main difference between the median and the average (mean) lies in the way they are calculated and their resistance to outliers. The median is the middle value in a dataset when the values are arranged from smallest to largest, while the average (mean) is the sum of all the values divided by the number of values.
- Median: In a dataset with an even number of values, the median is the average of the two middle values. For example, in the dataset [1, 1, 3, 4, 6, 7], the median is (3 + 4) / 2 = 3.5. In a dataset with an odd number of values, the median is the middle value.
- Average (Mean): The average is calculated by adding all the values in the dataset and dividing the sum by the number of values. For example, the average of [1, 2, 3, 4, 5] is (1 + 2 + 3 + 4 + 5) / 5 = 3.
The median is often more resistant to outliers than the average. In a dataset with extreme values or a skewed distribution, the median can provide a better measure of central tendency than the average. This is because the median is only affected by the values closest to it, making it less sensitive to outliers. In contrast, the average can be significantly influenced by extreme values, leading to a distorted representation of the dataset's central tendency.
In summary, when dealing with a dataset that is fairly uniform or has no outliers, the average can be a suitable measure of central tendency. However, if the dataset is skewed or has outliers, the median can be a more reliable measure of central tendency.
Comparative Table: Median vs Average (Mean)
The difference between the median and the average (mean) can be summarized in the following table:
| Median | Average (Mean) |
|---|---|
| The median is the middle value that separates the lower and higher halves of a number set. | The average is the arithmetic mean of a number set, calculated by adding all the values and dividing by the number of values. |
| The median is helpful when a data set does not follow a normal distribution or has outliers, as it finds the central tendency of a skewed distribution. | Use the average when the data set is fairly uniform. |
| The median is the exact middle value, which separates lower and higher values into two groups. | The average is the sum of all of the values, divided by the number of values. |
In summary, the median and average (mean) are two important measures of central tendency in statistics. The median is the middle value that separates the data into two equal parts, while the average is the sum of all the values divided by the number of values. The median is useful for skewed distributions or datasets with outliers, whereas the average is suitable for uniform datasets.
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