Mean vs Median Examples in Statistics

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

Mean and median are both measures of center but respond differently to extreme values (outliers). The mean is pulled toward outliers because it uses every value in its calculation, while the median is resistant to outliers because it depends only on the middle position.

Imagine a room with 10 people earning \50,000 each. Mean and median are both \50,000. Now a billionaire walks in. Mean jumps to \91 million! But median stays around \50,000. Mean is a pushover that gets bullied by extremes; median stands firm.

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: Mean is influenced by every value, including extremes. Median reflects only position. Use median for skewed data; use mean when data is symmetric.

Common stuck point: Students assume the mean is always the better measure. In skewed distributions with outliers, the mean can be far from the typical value.

Sense of Study hint: First, calculate both the mean and the median for your data set. Then check for outliers or skewness. Finally, choose the median when your data has extreme values or is skewed, and the mean when the data is roughly symmetric with no major outliers.

Worked Examples

Example 1

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House prices on a street (in thousands): 200, 210, 190, 205, 195, 800. Calculate the mean and median. Which better represents a typical house price?

Solution

  1. 1
    Step 1: Mean = \frac{200+210+190+205+195+800}{6} = \frac{1800}{6} = 300 thousand.
  2. 2
    Step 2: Ordered: 190, 195, 200, 205, 210, 800. Median = \frac{200+205}{2} = 202.5 thousand.
  3. 3
    Step 3: The mean (300k) is pulled up by the outlier (800k). The median (202.5k) better represents a typical house price.

Answer

Mean = 300\text{k}, Median = 202.5\text{k}. The median is more representative.
Outliers affect the mean but not the median. When data is skewed, the median is often a better measure of centre because it is resistant to extreme values.

Example 2

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Test scores: 78, 82, 79, 81, 80. Calculate both the mean and median. What do you notice?

Practice Problems

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

Example 1

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Salaries at a small company: \30k, \32k, \35k, \33k, \31k, \150k. Should the company report the mean or median salary to represent a typical employee's pay? Justify.

Example 2

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A runner's practice times (in minutes) are 24, 25, 24, 26, 25, 24. Would the mean or the median better describe a typical practice time? Explain.
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Background Knowledge

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

mean fair sharemedian introoutlier detection