Median for a Set of Frequencies

Topics: Median - Statistics

---

(theorem)

When we have data $X$ sorted in classes (groups), the median can also be calculated with:

$$\mathrm{Median}(X)=L_i+\left(\frac{\frac{n}{2}-\sum f_i}{f_{\text{median}}}\right)c$$

…where:

• $L_i$ is the inferior limit of the class (group) that contains the median
• $n$ is the total frequency
• $\sum f_i$ is the sum all frequencies that are less than the median
• $f_{\text{median}}$ is the frequency of the class that contains the median
• $c$ is the length of the interval that contains the median