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What Is the Mean, Median, Mode?(With Examples)

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.

Grades 6-7Key Stage 3 (Year 7-9)Årskurs 6-7Klasse 6-7

📖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 = Sum of all values / Number of values

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.

Mean = (x₁ + x₂ + ... + xₙ) / n

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

Easy

Find the mode of: 3, 5, 3, 7, 3, 8, 5

Answer: 3

Medium

Find the median of: 14, 8, 21, 6, 19, 12

Answer: 13 (average of 12 and 14)

Hard

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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Worked Examples

How to Find the Mean (Average)easy

Statistics Basics Range Data Analysis Outliers

Curriculum Alignment

CommonCore (6.SP.B.5c)KS3KMK

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