# Statistics Calculations

## Statistics Calculations Revision

**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{number of pieces of data} = \bold{6}

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

**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]**

**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.

**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]**

## Statistics Calculations Example Questions

**Question 1: **A student records the time it takes some student’s in their class to run a race. The results are in the following table.

Calculate the mean time.

**[3 marks]**

\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}

**Question 2: A **student records the time it takes some student’s in their class to run a race. The results are in the following table.

Calculate the range in the data.

**[1 mark]**

**Question 3: **One student runs a race in 51 \text{ s}. They run the race a second time, but now they are tired so it takes them 56 \text{ s}.

Calculate the percentage increase in the time it took the student to run the race.

**[2 marks]**