What is the difference between the median and the average? This is a common question in statistics and mathematics, as both measures are used to describe the central tendency of a dataset. While they serve a similar purpose, they are calculated differently and can yield different results, especially when dealing with skewed distributions.
The average, also known as the mean, is calculated by summing all the values in the dataset and dividing by the number of observations. It provides a single value that represents the typical or central value of the dataset. For example, if we have the following dataset: 2, 4, 6, 8, 10, the average would be (2 + 4 + 6 + 8 + 10) / 5 = 6. This means that the average value is 6, and half of the data points are below this value, while the other half are above.
On the other hand, the median is the middle value of a sorted dataset. To find the median, we arrange the data points in ascending or descending order and then select the value that lies in the middle. If the dataset has an odd number of observations, the median is simply the middle value. In our example dataset, the median would be 6, as it is the middle value when the data is sorted in ascending order. However, if we had an even number of observations, such as 2, 4, 6, 8, 10, 12, the median would be the average of the two middle values, which in this case would be (6 + 8) / 2 = 7.
One key difference between the median and the average is their sensitivity to outliers. Since the average is influenced by all the values in the dataset, it can be significantly affected by extreme values or outliers. For instance, if we add an outlier value of 100 to our original dataset, the average would increase to (2 + 4 + 6 + 8 + 10 + 100) / 6 = 19.67. This indicates that the average is pulled towards the outlier, whereas the median remains relatively unchanged at 6.
In contrast, the median is more robust to outliers because it only depends on the middle value(s) of the dataset. This makes it a better measure of central tendency in datasets with skewed distributions or when outliers are present. For example, consider a dataset of house prices: $100,000, $200,000, $300,000, $1,000,000. The average house price would be significantly higher than the median, which would be closer to the middle value of $200,000.
In conclusion, the main difference between the median and the average lies in their calculation methods and sensitivity to outliers. The average is calculated by summing all the values and dividing by the number of observations, while the median is the middle value of a sorted dataset. The average is more sensitive to outliers, whereas the median is more robust and provides a better representation of the central tendency in skewed distributions or datasets with outliers.
