Median Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Median.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

The median is the middle value when all data points are arranged in order from smallest to largest. Half the values lie above it and half below. For an even number of values, the median is the average of the two middle values.

If you lined up your whole class by height, the median height is the person standing exactly in the middle. It's not affected by whether the tallest kid is 5'5" or 7 feet - the middle person stays the same.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: The median is the literal middle value once data is sorted. It splits the data set in half and resists being pulled by extreme outliers.

Common stuck point: Students forget to sort the data first. Finding the 'middle' of an unsorted list gives a meaningless answer.

Sense of Study hint: First, arrange all data values in order from smallest to largest. Then, if there is an odd number of values, the median is the middle one. If there is an even number, find the two middle values and average them: Median = (middle1 + middle2) / 2.

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Mean vs Median Mistakes

Worked Examples

Example 1

easy
Find the median of: 12, 5, 8, 3, 15, 7, 10.

Solution

  1. 1
    Step 1: Arrange in order: 3, 5, 7, 8, 10, 12, 15.
  2. 2
    Step 2: There are 7 values (odd), so the median is the middle value at position \frac{7+1}{2} = 4.
  3. 3
    Step 3: The 4th value is 8.

Answer

8
The median is the middle value when data is arranged in order. For an odd number of values, it is the single central value. The median is resistant to outliers, unlike the mean.

Example 2

medium
Find the median of: 4, 9, 2, 7, 11, 6.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Find the median of: 20, 35, 15, 40, 25.

Example 2

medium
The ordered data set is 4, 7, 8, 9, 12, 14, 18. What is the median, and if 30 is added to the set, does the median change?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

mean fair share