Finding the Center: Mean, Median & Mode
Mean, median, and mode are measures of central tendency β different ways to describe the "middle" or "typical" value in a dataset. The mean is the arithmetic average, the median is the middle value when data is ordered, and the mode is the most frequent value. Choosing the right measure depends on the shape of the data and the question being asked.
Components of Mean, Median & Mode
This section covers each measure and when to use it:
- Mean (Average): Add all values and divide by the count. Best for symmetric data without extreme outliers.
- Median: The middle value in an ordered list. Best for skewed data because it resists the pull of outliers.
- Mode: The value that appears most often. Useful for categorical data or identifying the most common outcome.
- Comparing the Three: Understanding when each measure is most appropriate and how outliers affect them differently.
Examples of Mean, Median & Mode
Mean Examples
- Test scores: 85, 90, 78, 92, 85. Mean = (85 + 90 + 78 + 92 + 85) / 5 = 430 / 5 = 86.
- Daily temperatures: 72, 75, 68, 70, 80. Mean = 365 / 5 = 73Β°F.
- A student scores 88, 92, 76, 95, and 84 on five quizzes. The mean is (88 + 92 + 76 + 95 + 84) / 5 = 435 / 5 = 87.
Median Examples
- Data: 3, 7, 9, 12, 15. The middle value is 9 (third of five numbers), so the median is 9.
- Data: 4, 8, 11, 14. With an even count, average the two middle values: (8 + 11) / 2 = 9.5.
- Home prices: $150,000, $180,000, $200,000, $210,000, $950,000. The median is $200,000 β a better measure of a typical home than the mean of $338,000 (pulled up by the outlier).
Mode Examples
- Shoe sizes sold: 8, 9, 10, 9, 11, 9, 10. The mode is 9 because it appears three times.
- Survey responses: red, blue, blue, green, red, blue. The mode is blue (most common answer).
- Test scores: 70, 80, 85, 90, 95. There is no mode because every value appears exactly once.
Comparing the Three Examples
- Data: 2, 3, 3, 4, 100. Mean = 22.4 (pulled by outlier), median = 3, mode = 3. The median and mode better represent the typical value.
- Data: 5, 5, 5, 5, 5. Mean = 5, median = 5, mode = 5. When all values are equal, all three measures agree.
- Salaries at a small company: $40,000, $45,000, $50,000, $55,000, $300,000. The mean is $98,000 but the median of $50,000 better represents a typical employee's pay.