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Calculate and interpret mean, median, and mode as measures of central tendency.
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The sample mean is the sum of all values divided by the number of values:
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Properties of the mean:
The median is the middle value when data is arranged in order.
Properties of the median:
| Situation | Best Measure |
|---|---|
| Symmetric distribution | Mean or Median (approximately equal) |
| Skewed distribution | Median (more representative) |
| Outliers present | Median (resistant) |
| Further calculations needed | Mean (used in standard deviation, regression) |
Used when different values have different weights (e.g., GPA calculation).
Remove a percentage of the highest and lowest values, then calculate the mean. This makes it more resistant to outliers.
AP Tip: The AP exam often tests whether students know that the mean is affected by outliers while the median is not. Be ready to explain which measure is more appropriate in context.