Introduction to Mean

The mean, often called the average, is a way to find the central value of a set of numbers. You can think of the mean as the "fair share" value—it is the amount each data point would have if all the values were combined and then shared equally.

How to Calculate the Mean

Calculating the mean takes just two simple steps:

1. Add all the numbers in your data set together to find the total sum.
2. Divide that sum by the number of values in the set.

Example: Find the mean of $85$, $92$, $78$, and $95$.

First, add the numbers together: $85 + 92 + 78 + 95 = 350$

Next, count how many numbers there are (there are $4$ numbers) and divide the sum by that count: $350 \div 4 = 87.5$

The mean is $87.5$.

Understanding Mean as a "Fair Share"

Thinking of the mean as a "fair share" makes it easier to understand what the average represents in real life.

Example: Five friends earned \12$,$$15$,$$8$,$$20$, and$$10$ doing chores. What is the average amount earned?

First, find the total amount of money they earned together: $12 + 15 + 8 + 20 + 10 = 65$

If they decided to pool their money and share it equally among the $5$ friends, you would divide the total by $5$: $65 \div 5 = 13$

The average is **\13$**. This means if everyone got a "fair share," they would each have$$13$.

Finding a Missing Value

Sometimes you know the mean, but you are missing one of the numbers in the data set. You can work backward to find it!

Example: The average score of $4$ tests is $88$. If $3$ of the scores are $85$, $90$, and $82$, what is the $4$th score?

First, find the total number of points needed to get an average of $88$ on $4$ tests. Multiply the mean by the number of tests: $88 \times 4 = 352$ This means the sum of all four tests must be $352$.

Next, add up the $3$ scores you already know: $85 + 90 + 82 = 257$

Finally, subtract the sum of the known scores from the total points needed to find the missing $4$th score: $352 - 257 = 95$

The $4$th score is $95$.