Mean facts for kids

The mean is a type of average in mathematics and statistics. Think of it as finding a central number that represents a group of numbers. There are different kinds of averages, and the mean is one of the most common ones.

The most common type of mean is called the arithmetic mean. You find it by adding up all the numbers in a group and then dividing that total by how many numbers there are.

For example, imagine you have these scores: 1, 2, 2, 100, 100. If you add them all together (1 + 2 + 2 + 100 + 100), you get 205. There are 5 numbers in this group. So, you divide the total (205) by the number of scores (5): 205 / 5 = 41. The arithmetic mean for this group of scores is 41. However, notice that none of the original scores were close to 41. This shows that sometimes the mean alone doesn't tell the whole story about a group of numbers.

How to Calculate the Mean

To find the arithmetic mean of a group of numbers, you follow these simple steps:

• First, add all the numbers together to get a total sum.
• Next, divide that total sum by the count of how many numbers you added.

In math symbols, if you have numbers like X1, X2, X3, and so on, all the way up to XN (where N is the total count of numbers), the sum looks like this:

Then, to find the mean, you divide that sum by N:

This average is often called the sample mean and can be shown with the symbol .

Example of Finding Average Age

Let's look at an example with ages:

• Lucy is 5 years old.
• Tom is 6 years old.
• Emily is 7 years old.

To find their average age:

• Add their ages together:

• The total age is 18.
• There are 3 people, so divide the total by 3:

• The average age of Lucy, Tom, and Emily is 6 years.

Other Ways to Describe Data

The mean is one way to represent a group of numbers with a single value. But there are other useful ways to describe a group of numbers, depending on what information you want to highlight.

• The median is the middle number in a group when the numbers are arranged in order from smallest to largest. Half the numbers are below the median, and half are above it.

* Example: For the scores 1, 10, 50, 100, 100, if you put them in order (they already are!), the number 50 is right in the middle. This means half the scores are less than 50, and half are more than 50. The median can be very helpful when there are some very high or very low numbers that might skew the mean.

• The mode is the number that appears most often in a group of numbers.

* Example: For the scores 1, 2, 2, 100, 200, the number 2 appears twice, which is more than any other number. So, the mode for this group is 2. This tells you the most common score or value.

• The geometric mean is used for numbers that are multiplied together, like growth rates. You multiply all the numbers together and then take the Nth root (where N is the count of numbers).

* Example: For 4, 6, and 9, you multiply them: 4 × 6 × 9 = 216. Since there are three numbers, you find the cube root of 216, which is 6. So, the geometric mean is 6.

• The harmonic mean is often used when you're dealing with rates or speeds. It's calculated by dividing the number of values by the sum of the reciprocals (1 divided by each number).

• The root mean square (RMS) is the square root of the average of the squares of the values. It's often used in physics and engineering, especially for changing values like electrical currents.

When people make many different measurements, they get many different results. These results have a certain distribution, and they tend to center around an "average" value. This average value is what mathematicians call the arithmetic mean.

The term "mean" can also refer to the expected value of a random variable. For a random variable , this is shown as .

Related pages

• Standard deviation

See also

In Spanish: Media (matemáticas) para niños