Mean

• Calculate Mean for grouped and ungrouped data.

For a set of samples consisting individual numbers, $\bar{x} = \dfrac{\Sigma x_i}{N}$
or for a set of samples having frequencies, $\bar{x} = \dfrac{\Sigma w_i x_i}{\Sigma w_i}$

Solved Example:

8-1-01

For the data set, what is the sample mean? $5,\ 5,\ 10,\ 15,\ 20$

Solution:
$\mathrm{Mean} = \dfrac{\Sigma X_i}{N} = \dfrac{5+ 5 + 10 + 15 + 20}{5} = \dfrac{55}{5} = 11$

Solved Example:

8-1-02

In ENGG.tv office, there are 18 employees with various designations. A recent survey about their salaries is tabulated as follows:

Annual Salary Range Number of Employees
\$0 to less than \$20000 5
\$20000 to less than \$40000 7
\$40000 to less than \$60000 4
\$60000 to less than \$80000 2

What is the mean salary of people working in the office of ENGG.tv?

Solution:
$\Sigma f_i x_i = \600000$ $\mathrm{Mean} = \dfrac{\Sigma f_i x_i}{N} = \dfrac{600000}{18} = \33333.3$