Mean (Average)

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

Elementary20 minLesson

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:

\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}

Example: Find the mean of

4

7

, and

10

\text{Mean} = \frac{4 + 7 + 10}{3} = \frac{21}{3} = 7

The mean is

7

, which is the balance point of the data.

Try it now

What is the mean of

2

4

, and

6

Worked Examples

A student scored $85$ , $92$ , $78$ , $88$ , and $92$ on five tests. What is the mean score?

Add all the scores

$85 + 92 + 78 + 88 + 92 = 435$ → Sum = $435$

Count how many scores

There are $5$ test scores → Count = $5$

Divide the sum by the count

$\frac{435}{5} = 87$ → Mean = $87$

Answer: The mean test score is $87$ .

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 $4$ and $10$ is $7$ , which is not in the original data set - and that's okay!

Interactive Visual

Bar Chart

A(13%)

B(20%)

C(28%)

D(15%)

E(25%)

Range:to

Click on numbers to select them. Adjust the range to explore different values.

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 $2$ , $4$ , and $6$ ?

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 $90$ , $85$ , $92$ , and $88$ in four subjects, your mean grade is $\frac{90+85+92+88}{4} = 88.75$ .

1Try It Yourself

You have test scores of $82$ , $91$ , $78$ , and $85$ .

What is your mean test score?

Step 1: Write the mathematical expression

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

Sports Statistics

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

Example:

A soccer player scored $2$ , $0$ , $1$ , $3$ , $1$ goals in 5 matches. Mean = $\frac{7}{5} = 1.4$ goals per game.

2Try It Yourself

A swimmer's times for 100m freestyle in 4 races were $58$ , $56$ , $59$ , and $55$ seconds.

What is the mean race time?