<p>Generally, we could find the mean of a data set by using the following formula,</p>
<p style="text-align: center; font-size: 1.125rem"><strong>Mean</strong>, $\bar{x}=\frac{\mathrm{Sum \ of \ data}}{\mathrm{Number \ of \ data}}=\frac{\sum{fx}}{\sum{f}}$</p>
<p class="paragraph-header">Finding Mean of a Frequency Distribution</p>
<p>For a <strong>data set</strong> of ${{x}_{1}}$, ${{x}_{2}}$, ${{x}_{3}}$, …, ${{x}_{n}}$, with the corresponding frequencies  ${{f}_{1}}$, ${{f}_{2}}$, ${{f}_{3}}$ , …, ${{f}_{n}}$ is usually represented in the form of a frequency table below, </p>
<div class="content-block content-block--table"><div class="table-container"><table><colgroup><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"><col style="width: 70px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p>$x$</p></th><th style="text-align: center; --cell-justify: center"><p>${{x}_{1}}$</p></th><th style="text-align: center; --cell-justify: center"><p>${{x}_{2}}$</p></th><th style="text-align: center; --cell-justify: center"><p>${{x}_{3}}$</p></th><th style="text-align: center; --cell-justify: center"><p>…</p></th><th style="text-align: center; --cell-justify: center"><p>${{x}_{n}}$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>$f$</p></td><td style="text-align: center; --cell-justify: center"><p>${{f}_{1}}$</p></td><td style="text-align: center; --cell-justify: center"><p>${{f}_{2}}$</p></td><td style="text-align: center; --cell-justify: center"><p>${{f}_{3}}$</p></td><td style="text-align: center; --cell-justify: center"><p>…</p></td><td style="text-align: center; --cell-justify: center"><p>${{f}_{n}}$</p></td></tr></tbody></table></div></div>
<p>the above equation can be further written as</p>
<p style="text-align: center; font-size: 1.125rem"><strong>Mean</strong>, $\bar{x}$ = $\frac{\sum{fx}}{\sum{f}}=\frac{{{f}_{1}}{{x}_{1}}+{{f}_{2}}{{x}_{2}}+{{f}_{3}}{{x}_{3}}+...+{{f}_{n}}{{x}_{n}}}{{{f}_{1}}+{{f}_{2}}+{{f}_{3}}+...+{{f}_{n}}}$ </p>
<p>The symbol $\sum{{}}$(sigma) is used to denote the sum of multiple terms. </p>
<p class="paragraph-header">Example: Finding Mean of a Frequency Distribution</p>
<p>The monthly salaries of the employees in a company are shown in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table><colgroup><col style="width: 125px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><p>Monthly Salary</p><p>( $ )</p></th><th style="text-align: center; --cell-justify: center"><p>$3100$</p></th><th style="text-align: center; --cell-justify: center"><p>$3200$</p></th><th style="text-align: center; --cell-justify: center"><p>$3300$</p></th><th style="text-align: center; --cell-justify: center"><p>$3400$</p></th><th style="text-align: center; --cell-justify: center"><p>$3500$</p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>Number of employees</p></td><td style="text-align: center; --cell-justify: center"><p>$3$</p></td><td style="text-align: center; --cell-justify: center"><p>$10$</p></td><td style="text-align: center; --cell-justify: center"><p>$18$</p></td><td style="text-align: center; --cell-justify: center"><p>$7$</p></td><td style="text-align: center; --cell-justify: center"><p>$2$</p></td></tr></tbody></table></div></div>
<p>Find the mean monthly salary of the employees. </p>

Generally, we could find the mean of a data set by using the following formula,

**Mean**, $\bar{x}=\frac{\mathrm{Sum \ of \ data}}{\mathrm{Number \ of \ data}}=\frac{\sum{fx}}{\sum{f}}$

For a **data set** of ${{x}_{1}}$, ${{x}_{2}}$, ${{x}_{3}}$, …, ${{x}_{n}}$, with the corresponding frequencies  ${{f}_{1}}$, ${{f}_{2}}$, ${{f}_{3}}$ , …, ${{f}_{n}}$ is usually represented in the form of a frequency table below, 

the above equation can be further written as

**Mean**, $\bar{x}$ = $\frac{\sum{fx}}{\sum{f}}=\frac{{{f}_{1}}{{x}_{1}}+{{f}_{2}}{{x}_{2}}+{{f}_{3}}{{x}_{3}}+...+{{f}_{n}}{{x}_{n}}}{{{f}_{1}}+{{f}_{2}}+{{f}_{3}}+...+{{f}_{n}}}$ 

The symbol $\sum{{}}$(sigma) is used to denote the sum of multiple terms. 

Example: Finding Mean of a Frequency Distribution

The monthly salaries of the employees in a company are shown in the table below.

Finding Mean

Finding Mean

Video Solution: