Find the median

The median is the middle value of an ordered set of numerical data: when there is an odd number of values, it is the single middle value; when there is an even number, it is the mean of the two middle values. Finding the median requires ordering all values and interpreting it as a measure of center that is less affected by unusually large or small values than the mean; grouped or weighted-data methods are not included.

Detailed Explanation: Find the median

The median is the middle value when a set of numbers is arranged in order from least to greatest.

Order the numbers.
Count the values.
If there is an odd number of values, choose the one middle value.
If there is an even number of values, find the two middle values and calculate their mean.

Example

Find the median of these numbers:

12,\ 5,\ 9,\ 20,\ 7,\ 6

Step 1: Order the numbers from least to greatest.

5,\ 6,\ 7,\ 9,\ 12,\ 20

Step 2: Count the values.

There are $6$ values, so there is an even number of values.

Step 3: Find the two middle values.

The two middle values are $7$ and $9$ .

Step 4: Find their mean.

\frac{7+9}{2}=\frac{16}{2}=8

Therefore, the median is:

\boxed{8}

The median is a useful measure of center because one unusually large or small value usually affects it less than it affects the mean.

Learn by doing: Find the median

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Statistics - Solve for Median

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