The arithmetic mean of a data set is often referred to as mean of the data set. It is the mathematical average of the data values.

The arithmetic mean of $n$ observations $x_{1},\ x_{2}$, .......$x_{n}$ is given by

$\bar{x}$ = $\frac{x_{1}+x_{2}+......x_{n}}{n}$ or using sigma notation = $\frac{\sum_{i=1}^{n}x_{i}}{n}$

When the data is represented by a frequency distribution where $f1,\ f2,......fn$ are the corresponding frequencies of data values $x_{1},\ x_{2},\ x_{n}$, then the arithmetic mean is computed using the formula

$\bar{x}$ = $\frac{\sum_{i=1}^{n}x_{i}f_{i}}{N}$ where $N$ = $f_{1} + f_{2} + .........+ f_{n}$.

While $\bar{x}$ denotes the mean of sample data the letter ยต is used to represent the population mean.

The value of arithmetic mean is also used in other computations of statistic measures like variance.

Even though the arithmetic mean is easy to compute and based on all data values, it's value is influenced by outliners or extreme values in the data set and hence lead to misinterpretations.

**Example:** The AM $\bar{(x)}$ of the given five numbers $10, 12, 8, 14, 2$ is

$\frac{10+12+8+14+2}{5}$ = $9.2$

→ Read More