# Average Calculator

## Calculate arithmetic mean step by step

For the given group of numbers, the calculator will find their average (arithmetic mean), with steps shown.

Related calculators: Geometric Mean Calculator, Harmonic Mean Calculator

### Your Input

**Find the arithmetic mean of $$$1$$$, $$$7$$$, $$$8$$$, $$$1$$$, $$$3$$$, $$$-2$$$, $$$10$$$.**

### Solution

The arithmetic mean of data is given by the formula $$$\mu = \bar{x} = \frac{\sum_{i=1}^{n} x_{i}}{n}$$$, where $$$n$$$ is the number of values and $$$x_i, i=\overline{1..n}$$$ are the values themselves.

Since we have $$$7$$$ points, $$$n = 7$$$.

The sum of the values is $$$1 + 7 + 8 + 1 + 3 - 2 + 10 = 28$$$.

Therefore, the arithmetic mean is $$$\mu = \bar{x} = \frac{28}{7} = 4$$$.