# Sample Mean | Population Mean

The average value of a sample or population data is known as the arithmetic mean of that data. The sample mean is the sum of all the values divided by the number of values a sample contains. When the data are based on a series of observations taken as different samples from population, then the mean evaluated is known as sample mean. The sample mean is denoted by $bg_white bar{x}$ and pronounced as “x bar”.

When the given data are comprised of a small number of values then for finding a mean ungrouped data formula will be used. If the given data hold a lot of observations or when finding mean become a problem, then grouped data formula will be used. For grouped data formula, first data are organized in the form of a frequency table.

### Formulas For Sample Mean

1. For ungrouped data

$dpi{100} bg_white fn_jvn bar{x}= frac{x_1 + x_2 + x_3 + x_4.......x_n}{n}= sum frac{x_i}{n}$

2. For grouped Data

$dpi{100} bg_white fn_jvn {color{DarkGreen} bar{x}}= frac{f_1x_1 + f_2x_2 + f_3x_3 + f_4x_4......f_nx_n}{f_1 + f_2 + f_3 + f_4......f_n}= sum frac{f_ix_i}{f_n}$

## Population Mean

When the arithmetic mean of uncut data is evaluated then it is equal to the population mean. Formulas for the sample and population mean are the same. The sample mean differs from the population mean, when the sizes of the samples are very small. The larger the sample size, the more close it will be to the population mean. Population mean is denoted by μ.

### Formulas For The Population Mean

• Formula for ungrouped data

$large dpi{100} bg_white fn_jvn {color{Red} {mu }}= frac{x_1 + x_2 + x_3 + x_4......x_N}{N}$

• Formula for grouped data

$large dpi{100} bg_white fn_jvn {color{Red} {mu }}= frac{f_1x_1 + f_2x_2 + f_3x_3 + f_4x_4......f_Nx_N}{f_1 + f_2 + f_3 + f_4......f_N}$