Mean (Average)

Learn how to calculate the mean of a data set by adding all values and dividing by the count.

Elementary20 minLesson
Printable worksheet

Definition

The mean (also called the average) is one way to find a typical value in a data set. It represents the "center" of the data.
Formula:
Mean=Sum of all valuesNumber of values\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
Example: Find the mean of 44, 77, and 1010:
Mean=4+7+103=213=7\text{Mean} = \frac{4 + 7 + 10}{3} = \frac{21}{3} = 7
The mean is 77, which is the balance point of the data.

Try it now

What is the mean of 22, 44, and 66?

Worked Examples

A student scored 8585, 9292, 7878, 8888, and 9292 on five tests. What is the mean score?
1

Add all the scores

85+92+78+88+92=43585 + 92 + 78 + 88 + 92 = 435 → Sum = 435435
2

Count how many scores

There are 55 test scores → Count = 55
3

Divide the sum by the count

4355=87\frac{435}{5} = 87 → Mean = 8787

Common Mistakes

Forgetting to count all values

Why it's wrong: When adding a long list of numbers, it's easy to miss one or count incorrectly.

Correct: Always count your values before dividing. Write them out and number them: 1st, 2nd, 3rd...

Dividing by the sum instead of the count

Why it's wrong: Confusing the formula - the divisor should be how many values you have, not their total.

Correct: Remember: Mean = Sum ÷ Count (how many numbers you added)

Thinking the mean must be one of the original values

Why it's wrong: The mean is a calculated value and often falls between the numbers in your data set.

Correct: The mean of 44 and 1010 is 77, which is not in the original data set - and that's okay!

Interactive Visual

Bar Chart

Test scores

Test 1(85)
Test 2(92)
Test 3(78)
Test 4(88)
Test 5(92)

Mean = 87

Dot Plot

Points per game

810121416182022

Each dot is one value (6 values in total).

Mean = 15

Tap a column to count its dots.

Interactive Sandbox

Expression Calculator

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History

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Practice Problems

15 problems
Problem 1 of 15
Easy
What is the mean of 22, 44, and 66?

Why It Matters

The mean is used everywhere to summarize data:
  • School: Your grade point average (GPA) is a mean of your grades
  • Sports: A basketball player's points per game is a mean
  • Weather: The average temperature for a month
  • Science: The average result of repeated experiments
Calculating the mean helps us understand what's "normal" or "typical" in a situation!

Real World Applications

Grade Point Average

Schools calculate your GPA by finding the mean of your grades, often weighted by credits.

Example:

If you earned 9090, 8585, 9292, and 8888 in four subjects, your mean grade is 90+85+92+884=88.75\frac{90+85+92+88}{4} = 88.75.

1Try It Yourself

You have test scores of 8282, 9191, 7878, and 8585.

What is your mean test score?

Step 1: Write the mathematical expression

Calculate: 82+91+78+854\frac{82 + 91 + 78 + 85}{4}

Sports Statistics

Athletes and teams track performance using averages - batting average, points per game, goals per match.

Example:

A soccer player scored 22, 00, 11, 33, 11 goals in 5 matches. Mean = 75=1.4\frac{7}{5} = 1.4 goals per game.

2Try It Yourself

A swimmer's times for 100m freestyle in 4 races were 5858, 5656, 5959, and 5555 seconds.

What is the mean race time?

Step 1: Write the mathematical expression

Calculate the mean of the four times

Key Takeaways

  • 1The mean is found by adding all values and dividing by the count: Mean=SumCount\text{Mean} = \frac{\text{Sum}}{\text{Count}}
  • 2The mean represents a "typical" or "central" value in your data
  • 3The mean can be a decimal, even if all original values are whole numbers
  • 4To find a missing value when you know the mean: multiply mean by count, then subtract the known values

Frequently Asked Questions

They're the same thing! "Average" is the everyday word, while "mean" (specifically "arithmetic mean") is the mathematical term.
They're the same thing! "Average" is the everyday word, while "mean" (specifically "arithmetic mean") is the mathematical term.
No. The mean always falls between the smallest and largest values in your data set (or equals them if all values are the same).
The mean can be misleading when you have extreme values (outliers). For example, if 5 people earn 30,000 dollars and 1 person earns 1,000,000 dollars, the mean salary would be misleadingly high.

Glossary

Mean
The sum of all values divided by the number of values; also called the arithmetic mean or average
Sum
The result of adding numbers together
Data set
A collection of values or observations
Central tendency
A measure that represents the center or typical value of a data set (mean, median, or mode)
Today's challengeOne problem, three tries

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