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Calculate the median

The median is the center of an ordered numerical data set: after values are arranged from least to greatest, it is the single middle value when the set has an odd number of values, or the mean of the two middle values when it has an even number. This reasoning distinguishes the median from the mean and supports interpreting typical values; it is limited to ungrouped data sets and does not include weighted medians, quartiles, or advanced statistical analysis.

Detailed Explanation: Calculate the median

The median is the middle value in a set of numbers after the numbers are put in order from least to greatest.

  1. Order the numbers.
  2. Count the numbers.
  3. If there is an odd number of values, choose the one middle value.
  4. If there is an even number of values, find the mean of the two middle values.

Example: Find the median of 8,3,5,10,6,8, 3, 5, 10, 6, and 44.

Step 1: Put the numbers in order.

3, 4, 5, 6, 8, 103,\ 4,\ 5,\ 6,\ 8,\ 10

Step 2: Count the values.

There are 66 values, so there are two middle values.

Step 3: Find the two middle values.

The middle values are 55 and 66.

Step 4: Find their mean.

5+62=112=5.5\frac{5+6}{2}=\frac{11}{2}=5.5

So, the median is 5.55.5. Remember to order the numbers first; the median is based on position, not on adding all the numbers together.

Learn by doing: Calculate the median

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    Statistics - Solve for Median

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