Mathematics
Why Do We Need Both Mean and Median to Understand Data?
Quick fact
A single very high income can pull the mean far above what most people earn, while the median (the middle value) stays almost the same—showing that the mean isn't always the best representation of the 'typical' person.
Why this is interesting
Imagine a neighbourhood where the average salary is reported as $1 million a year. Would you believe it? Probably not, and the reason why lies in the difference between the mean and the median.
Read the full explanation
Understanding Why Do We Need Both Mean and Median to Understand Data?
Think of the mean as the 'fair share' of the total when everything is pooled together. If you have five friends with $10, $20, $30, $40, and $500, the mean is ($10+$20+$30+$40+$500)/5 = $120. That's the amount each person would get if all money was combined and split equally. On the other hand, the median is the middle value when you line everyone up by their money: $10, $20, $30, $40, $500. The middle is $30. The median tells you what the person in the middle has. In this example, the median ($30) gives a much better sense of the 'typical' person's money because it isn't affected by the one person with $500. So, the mean is an arithmetic average, while the median is a positional average.
A deeper explanation
The mean and median are both measures of central tendency—they try to summarize a set with a single 'center'. The mean is calculated by summing all values and dividing by the count. It uses every data point, so it's sensitive to outliers: extreme values pull it toward them. The median is the middle value when data is sorted, so it only depends on the position—it stays the same even if the most extreme values change drastically. This makes the median 'robust' to outliers. The key insight is that comparing the mean and median reveals the shape of the distribution: if they're close, the data is roughly symmetric; if the mean is greater than the median, the data is right-skewed (a few high outliers pull the mean up); if the mean is less, it's left-skewed (a few low outliers drag the mean down). This understanding is vital because it helps us detect that a single number can mislead. For example, national salary reports often use the median because the mean is inflated by billionaires. Both are needed: the mean gives a sense of the total resource pool, while the median gives a sense of the typical experience. Using both gives a fuller picture and helps us ask better questions about the data.