# Mean Calculator – Calculate Average

Calculate the mean of a number set using the average calculator below.

## What is Mean and Average?

The mean, or *arithmetic mean*, is the average value of a set of numbers. Thus, mean and average are the same thing.

The mean and average are one way to express the middle of a collection of numbers. More specifically, mean is a measure of the central tendency of the group of numbers.

The mean is one of the observations of data used in summary statistics.

## How to Find Mean

To find the mean, start by finding the sum of all of the numbers in the set, then divide the sum by the total count of the numbers.

### Steps to Calculate Mean

- Step 1: count the numbers in the set
- Step 2: add up all the numbers to find the sum
- Step 3: divide the sum by the count

### Mean Formula

You can find the mean using the average formula:

mean = sumcount

Thus, the mean is equal to the sum of the numbers divided by the count of the numbers.

## Example: Calculate the Average

Calculate the mean of the following numbers: [3,1,8,12,22,5]

**Step 1:** count the numbers.

count = 6

**Step 2:** add up the numbers.

sum = 3 + 1 + 8 + 12 + 22 + 5

sum = 51

**Step 3:** divide the sum by the count.

mean = 516

mean = 8.5

The average of the numbers above is **8.5**.

## Mean vs. Median

We briefly touched on summary statistics above. Another common observation of numeric data used in summary statistics is the median.

The median is also a measure of the central tendency of numeric data. The median is the middle value of the data rather than the average value of the data.

The median represents the mid-point of a number set. Half of the numbers in the set are above the median, and half are below it.

So should you use the mean or the median to describe your data? The mean might be beneficial if the average value of the entire set of data is important.

Since the mean considers each value in the data, it might be a more accurate way to describe the central tendency of the data if the majority of the data are in an evenly distributed range.

However, major outliers in the data can skew the mean in one direction. Consider the data: [1,2,3,4,75]

The average value of this data is 17, while the median value is 3.

Since the median only considers the midpoint of the data, it might do a better job of discarding those outliers and reduce the skew. However, there are some cases where those outlier values are important and need to be considered, so the mean might be a better representation of the data in that case.