How to Find Mean, Median, Mode, and Range of the Given Data? (+FREE Worksheet!)

The mean, median, mode, and range are four measures that summarize any data set. Together they tell you the center and spread of the numbers, and they appear in nearly every statistics unit in Algebra 1. This guide explains each measure in plain language, with step-by-step examples, two video lessons, and practice problems so you can build real confidence.

What Are Mean, Median, Mode, and Range?

These four measures describe a data set from different angles. The mean is the arithmetic average. The median is the middle value when the data are ordered. The mode is the value that appears most often. The range measures the spread by subtracting the smallest value from the largest. None of them alone tells the whole story — together they give a full picture.

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How to Find Each Measure

Mean (Average)

Add all values in the data set, then divide by the number of values.

Formula: \(\color{blue}{\text{ Mean } = (\text{ sum of all values })}\) ÷ (number of values)

Quick example: Data: 4, 6, 8, 10, 12 → \(\color{blue}{\text{ Sum } = 40}\), \(\color{blue}{\text{ Count } = 5}\) → \(\color{blue}{\text{ Mean } = 40}\) ÷ 5 = 8

Median (Middle Value)

Sort the data from least to greatest. If there is an odd number of values, the median is the middle value. If there is an even number of values, average the two middle values.

Quick example (odd): 3, 7, 9, 11, 15 → Median = 9 (3rd of 5 values)

Quick example (even): 2, 5, 8, 11 → \(\color{blue}{\text{ Median } = (5 + 8)}\) ÷ 2 = 6.5

Mode (Most Frequent Value)

The mode is the value that appears more than once and appears the most. A data set can have no mode, one mode, or multiple modes.

Quick example: 4, 7, 7, 9, 12 → Mode = 7 (appears twice)

Range (Spread)

Subtract the minimum value from the maximum value.

Formula: \(\color{blue}{\text{ Range } = \text{ Maximum } – \text{ Minimum }}\)

Quick example: 3, 7, 7, 10, 13 → \(\color{blue}{\text{ Range } = 13 – 3}\) = 10

Step-by-Step Summary

1. Mean: Add all values → divide by the count.
2. Median: Sort the data → pick the middle value (or average the two middle values for an even count).
3. Mode: Find the value(s) that appear most often.
4. Range: Subtract the smallest value from the largest value.

Watch: Mean, Median, and Mode (Video Lesson)

Math Antics explains each measure clearly with visual examples:

Mean, Median, Mode, and Range – Worked Examples

Example 1: Find the mean, median, mode, and range of: 3, 7, 7, 10, 13

Mean: (\(\color{blue}{3 + 7 + 7 + 10 + 13}\)) ÷ \(\color{blue}{5 = 40}\) ÷ 5 = 8
Median: Data is already ordered. Middle value (3rd of 5) = 7
Mode: 7 appears twice → 7
Range: \(\color{blue}{13 – 3}\) = 10

Example 2: Find the mean, median, mode, and range of: 4, 8, 6, 5, 3, 2, 8, 9, 2, 5

Sorted: 2, 2, 3, 4, 5, 5, 6, 8, 8, 9
Mean: (\(\color{blue}{2+2+3+4+5+5+6+8+8+9}\)) ÷ \(\color{blue}{10 = 52}\) ÷ 10 = 5.2
Median: 10 values → average of 5th and \(\color{blue}{6\text{ th } = (5 + 5)}\) ÷ 2 = 5
Mode: 2, 5, and 8 each appear twice → modes are 2, 5, and 8
Range: \(\color{blue}{9 – 2}\) = 7

Example 3: The ages of players on a team are: 14, 15, 15, 16, 18, 20. Find all four measures.

Mean: (\(\color{blue}{14+15+15+16+18+20}\)) ÷ \(\color{blue}{6 = 98}\) ÷ 6 ≈ 16.3
Median: Average of 3rd and 4th \(\color{blue}{\text{ values } = (15 + 16)}\) ÷ 2 = 15.5
Mode: 15 (appears twice)
Range: \(\color{blue}{20 – 14}\) = 6

Example 4: A data set has no repeated values: 12, 17, 21, 25, 30. What is the mode?

No value appears more than once, so this data set has no mode.

More Practice: Step-by-Step Video Review

Mashup Math walks through mean, median, mode, and range with more examples:

Exercises: Mean, Median, Mode, and Range

Find the mean, median, mode, and range for each data set.

1. 6, 9, 3, 6, 11, 4, 6
2. 22, 18, 25, 22, 30, 18, 22
3. 5, 10, 15, 20, 25
4. 7, 3, 9, 3, 4, 8, 6, 4, 3, 8
5. 100, 85, 92, 88, 76, 100, 95

Answers

1. \(\color{blue}{\text{ Mean } = 45}\) ÷ 7 ≈ 6.4; \(\color{blue}{\text{ Median } = 6}\); \(\color{blue}{\text{ Mode } = 6}\); \(\color{blue}{\text{ Range } = 8}\)
2. \(\color{blue}{\text{ Mean } = 157}\) ÷ 7 ≈ 22.4; \(\color{blue}{\text{ Median } = 22}\); \(\color{blue}{\text{ Mode } = 22}\); \(\color{blue}{\text{ Range } = 12}\)
3. \(\color{blue}{\text{ Mean } = 75}\) ÷ \(\color{blue}{5 = 15}\); \(\color{blue}{\text{ Median } = 15}\); \(\color{blue}{\text{ Mode } = \text{ none }}\); \(\color{blue}{\text{ Range } = 20}\)
4. \(\color{blue}{\text{ Mean } = 55}\) ÷ \(\color{blue}{10 = 5.5}\); \(\color{blue}{\text{ Median } = (4+6)}\) ÷ \(\color{blue}{2 = 5}\); \(\color{blue}{\text{ Mode } = 3}\); \(\color{blue}{\text{ Range } = 6}\)
5. \(\color{blue}{\text{ Mean } = 636}\) ÷ 7 ≈ 90.9; \(\color{blue}{\text{ Median } = 92}\); \(\color{blue}{\text{ Mode } = 100}\); \(\color{blue}{\text{ Range } = 24}\)

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Frequently Asked Questions

What is the difference between mean and median?

The mean is the arithmetic average of all values. The median is the middle value when the data are sorted. The median is less affected by extreme values (outliers) than the mean, so it is often a better measure of center for skewed data sets.

Can a data set have more than one mode?

Yes. If two or more values appear the same maximum number of times, the data set is called bimodal or multimodal. For example, in 2, 2, 5, 5, 9 both 2 and 5 are modes.

How do you find the median with an even number of data values?

Sort the data and identify the two middle values. Add them together and divide by 2. For example, in the sorted data set 3, 7, 11, 15, the two middle values are 7 and 11, so the median is (\(\color{blue}{7 + 11}\)) ÷ \(\color{blue}{2 = 9}\).

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