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

How to find mean, median, mode, and range of the given data, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

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.

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}{6text{ 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 mean, median, mode and range in statistics?

They are four quick ways to describe a data set. The mean is the average (sum ÷ number of values), the median is the middle value once the data is in order, the mode is the value that appears most often, and the range is the largest value minus the smallest. The first three describe the center; the range describes the spread.

How do you calculate the mean, median, mode and range?

Put the data in order first. For 4, 7, 7, 9, 13: the mean is (4 + 7 + 7 + 9 + 13) ÷ 5 = 40 ÷ 5 = 8, the median is the middle value, 7, the mode is 7 because it appears twice, and the range is 13 − 4 = 9. With an even number of values, the median is the average of the two middle numbers.

How do you find mean, median, mode and range of grouped data?

Use each class midpoint as a stand-in value. With classes 0–10 (frequency 3), 10–20 (frequency 5), and 20–30 (frequency 2), the midpoints are 5, 15, and 25, so the estimated mean is (15 + 75 + 50) ÷ 10 = 14. The modal class is 10–20, the median falls in 10–20, and the range is estimated as 30 − 0 = 30.

Are mean, median and mode the same thing?

No. They are all measures of center, but they can give very different answers. For 2, 3, 3, 10, 12, the mean is 30 ÷ 5 = 6, while the median and mode are both 3. The two large values pull the mean up, which is why the median is often a better summary when a data set has outliers.

Is mean, median, mode and range statistics?

Yes. They belong to descriptive statistics, the part of math that summarizes data. Students usually start using them in middle school, especially grade 6, and keep using them in Algebra 1 and statistics courses. They also connect to other measures, such as the interquartile range, which describes the spread of the middle half of the data.

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