# Statistics Calculations

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## Statistics Calculation

When processing experimental data, there are many calculations you may have to perform. This page covers some of the common statistical calculations you should be familiar with.

## Mean

Calculating the mean is a good way to determine the average value of a set of data. The equation for mean is:

$\text{mean} = \dfrac{\text{sum}}{\text{n}}$

• $\text{sum}=$ all of the data points added together
• $\text{n}=$ how many values you have measured, or the number of pieces of data

Example: A student records their friends’ heights in the table on the right.

Calculate the mean height of the students.

[3 marks]

$\text{sum of the data} \\ = 165 + 141 + 157 + 169 \\ \, + 154 + 163 \\ = \bold{949} \textbf{ cm}$

$\text{number of pieces of data} = \bold{6}$

$\text{mean}= \dfrac{\text{sum}}{\text{n}}= \dfrac{949}{6}= \bold{158.2} \textbf{ cm}$
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## Range

The range gives you an idea of the spread of the data. It is calculated using the following equation:

$\text{range}=\text{maximum value}-\text{minimum value}$

Example: For the same data in the previous example, calculate the range.

[1 mark]

\text{range} \\ \begin{aligned} &= \text{max value}-\text{min value} \\ &= 169 - 141 \\ &= \bold{28} \textbf{ cm} \end{aligned}

Standard deviation is also used to represent the spread of the data, or the uncertainty in the mean. A large standard deviation means that the data is spread out and the mean has a large uncertainty. A small standard deviation means that the data points are close together and so there is a small uncertainty in the mean. You don’t need to know how to calculate the standard deviation for GCSE.

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## Percentage Increase

Percentage increase is used to compare two data points, usually after some amount of time has passed. You can calculate the percentage increase using the following equation:

$\% \text{ increase}=\dfrac{\text{new value}-\text{old value}}{\text{old value}} \\ \times 100$

Example: A piece of potato is initially measured to have a mass of $9.4 \text{ g}$. After being placed in a beaker of water and left for $2 \text{ hours}$, the mass of the potato is measured to be $12.6 \text{ g}$. Calculate the percentage increase in the mass of the potato.

[2 marks]

\% \text{ increase}\\ \begin{aligned} &= \dfrac{\text{new value}-\text{old value}}{\text{old value}} \times 100 \\ &= \dfrac{\textcolor{7cb447}{12.6} - \textcolor{10a6f3}{9.4}}{\textcolor{10a6f3}{9.4}} \times 100 \\ &= \bold{34.04 \%} \end{aligned}

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@mmerevise

## Statistics Calculations Example Questions

$\text{sum of the data}= 63+47+49+54+61+68+50+46+60+55=\bold{553} \textbf{ s}$

$\text{number of data values} = \bold{10}$

$\text{mean}=\dfrac{\text{sum of the data}}{\text{number of data values}} = \dfrac{553}{10} = \bold{55.3} \textbf{ s}$

Gold Standard Education

\begin{aligned} \text{range} &= \text{maximum value} - \text{minimum value} \\ &= 68-46 \\ &= \bold{22} \textbf{ s} \end{aligned}

Gold Standard Education

\begin{aligned} \% \text{ increase} &= \dfrac{\text{new value}-\text{old value}}{\text{old value}} \times 100 \\ &= \dfrac{56-51}{51} \times 100 \\ &= \bold{ 9.8 \%}\end{aligned}