The Median in Statistics
The median is a measure of central tendency that is often used to summarize a set of data. It represents the middle value in a data set when the values are arranged in order.
How to Calculate the Median
- Order the numbers from smallest to largest.
- If the number of observations (n) is odd, the median is the number at position \( \frac{n+1}{2} \).
- If n is even, the median is the average of the numbers at positions \( \frac{n}{2} \) and \( \frac{n}{2} + 1 \).
For example, in the data set [3, 5, 7], the median is 5, as it is the middle number.
In the data set [3, 5, 7, 9], the median is \( \frac{5 + 7}{2} = 6 \).
Why Use the Median?
The median is especially useful when a data set includes outliers or is not symmetrically distributed, as it is not affected by the extreme values.