For AI agents: use /llms.txt for the Nakafa content index.
Choose the measure from the data type, the distribution's shape, and the question being asked. The mean changes when extreme values change, the median uses rank without measuring the gaps between values, and the mode identifies only the most frequent value or category.
The table collects that comparison in one place. Every row uses the scores and then the same scores with an extra .
| Measure | What it uses | Value after adding the score |
|---|---|---|
| Mean | Every value in the sum | Moves from down to |
| Median | The middle position of the sorted data | Stays at |
| Mode | The value with the highest frequency | Stays at |
Adding one value does not always change every measure of center. For these data, the mean changes while the median and mode stay the same.
Add every value and divide the sum by how many values there are. Because every value enters the sum, the mean is very sensitive to extreme values, and one unusually large or small value can shift it a long way. For the scores the mean is . Adding the low score gives , so the mean drops by more than one point.
Sort the data and take the value in the middle position. The median depends on the middle position in the ordered data. Changing an endpoint without changing the order or middle values leaves the median unchanged. Adding a new observation can change the middle positions, so recalculate the median. For , the sorted data is with median . Adding the score gives , and the two middle values are both , so the median stays at .
Find the value that appears most often. A single isolated extreme value usually leaves the mode unchanged, and the mode is the only measure here that also works for categories. For the mode is , and it stays after the score is added. If the data is a list of favourite colours such as red, blue, red, green, the mode is red.
Here's a concise guide on when to use each measure:
| Measure | Best Data Type | Extreme-value Influence | When to Use? |
|---|---|---|---|
| Mean | Quantitative (Numbers) | High | When every magnitude should contribute and extreme values do not make the result misleading. |
| Median | Quantitative (Numbers) | Low | When the distribution is skewed or contains unusual tail values and a stable positional center is useful. |
| Mode | Qualitative & Quantitative | Low for one isolated value | When you want to know the most popular value/category or the most frequent occurrence. |
Example Scenarios:
Published: . Updated: .
