What is the Median?
The median is the middle value of a data set when arranged in ascending or descending order. It divides the data into two equal halves.
How to Find the Median:
| Number of values (\(n\)) | Median Position |
|---|---|
| Odd (\(n\)) | Middle value at position \(\frac{n+1}{2}\) |
| Even (\(n\)) | Average of the two middle values at positions \(\frac{n}{2}\) and \(\frac{n}{2}+1\) |
What is the Mode?
The mode is the value that appears most frequently in a data set. A data set can have:
- One mode (unimodal)
- Two modes (bimodal)
- More than two modes (multimodal)
- No mode (if all values occur with same frequency)
Comparison of Measures:
| Measure | Best used when | Advantage | Disadvantage |
|---|---|---|---|
| Mean | Data is symmetrical | Uses all data | Affected by outliers |
| Median | Data has outliers | Not affected by outliers | Doesn't use all data |
| Mode | Data is categorical | Easy to understand | May not be unique |