Median
Definition
The middle value in a sorted dataset. If the dataset has an even number of values, the median is the average of the two middle values.
Why is Median Important?
Median is a foundational mathematical concept used across science, engineering, finance, and everyday problem-solving. From analyzing data sets to optimizing business decisions, this concept provides the analytical framework needed to interpret quantitative information accurately.
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What is the Median?
The median is the middle value in a dataset when the values are sorted in order. If the dataset has an even number of values, the median is the average of the two middle values. The median is a robust measure of central tendency β it is not affected by extreme outliers.
How to Find the Median
| Step | Odd Count Example: {7, 2, 9, 1, 5} | Even Count Example: {3, 7, 1, 9} |
|---|---|---|
| 1. Sort the data | 1, 2, 5, 7, 9 | 1, 3, 7, 9 |
| 2. Find middle position | (5+1)/2 = 3rd value | 2nd and 3rd values |
| 3. Identify median | 5 (the 3rd value) | (3+7)/2 = 5 |
Median vs Mean in Practice
| Dataset | Mean | Median | Better Measure |
|---|---|---|---|
| Salaries: $40K, $45K, $50K, $55K, $500K | $138K | $50K | Median (outlier skews mean) |
| Test scores: 72, 75, 78, 80, 82 | 77.4 | 78 | Either (symmetric data) |
| Home prices in a neighborhood | Skewed high | More typical | Median (real estate standard) |
Where Median is the Standard
- Household income: US Census reports median household income (~$75,000 in 2023)
- Home prices: Real estate uses median price, not average
- Response times: Server performance often reported as median (P50)
- Medical data: Survival times use median due to skewed distributions