Arithmetic Mean or Mean

Arithmatic Mean or Sample Mean:

The mean is simply the average of all the items in a sample. To compute a sample mean, add up all the sample values and divide by the size of the sample.

       We will sometimes make the distinction between the sample mean and the population mean. The population mean (often represented by the Greek letter mu) is simply the average of all the items in a population. Because a population is usually very large, the population mean is usually an unknown constant. 

The formula for the sample mean is:

\[\bar{X}=\frac{\sum{{{x}_{i}}}}{n}\]

       Where $N$ is the number of items in the population. Usually $N$ is very large in the thousands, millions, or sometimes even infinity. The Greek letter sigma indicates that you should add the values together.

       The sample mean (often represented by the symbol $\bar{X}$) is the average of all the items in a sample. The sample mean is a lot easier to compute because the size o f the sample is usually quite manageable. If the sample is chosen carefully, the sample mean is a good estimate of the population mean. The formula for the sample mean is

Sample Mean	Population Mean
\[\bar{x}=\frac{\sum{x}}{n}\]	\[\mu =\frac{\sum{x}}{N}\]

Where $\sum{x}$ - is sum of all data values

                 $N$ - is number of data items in population

                 $n$  - is number of data items in sample

Example: 1  

         The values for seven smokers are: $73, 58, 67, 93, 33, 18$, and $147$. 

Solution: 

         If you added up these values you would get a sum of $489$. Divide that sum by $7$ to get a mean of $69.9$. 

\[\bar{x}=\frac{73+58+67+93+33+18+147}{7}\]

                                                                \[=\frac{489}{7}=69.9\]