📖Definition
Mean, median, and mode are measures of central tendency - they describe the center of a data set. Mean is the average, median is the middle value when ordered, and mode is the most frequent value.
📐Formula
Mean: add all values and divide by count. Median: arrange in order and find the middle. Mode: find the value that appears most often.
📝Step-by-Step Guide
Calculate the Mean
Add all values together, then divide by the number of values.
Find the Median
Order values from least to greatest. For odd count, median is the middle value. For even count, average the two middle values.
Identify the Mode
Find which value(s) appear most frequently. There can be no mode, one mode, or multiple modes.
Choose the Right Measure
Mean is affected by outliers. Median is better for skewed data. Mode is useful for categorical data.
⚠️Common Mistakes to Avoid
- Forgetting to order data before finding median
- With even numbers, not averaging the two middle values for median
- Confusing mean, median, and mode
- Thinking there must always be a mode
- Letting outliers mislead when using mean
✏️Practice Problems
Find the mode of: 3, 5, 3, 7, 3, 8, 5
Answer: 3
Find the median of: 14, 8, 21, 6, 19, 12
Answer: 13 (average of 12 and 14)
A set of 5 numbers has mean 12 and median 10. The mode is 10. Two numbers are 10. Find all 5 numbers if they are all different except the mode.
Answer: 10, 10, and three other numbers that average to 12
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