# Graphs and Data

## Graphs and Data Revision

**Graphs and Data**

The best way to visually represent data from an experiment is to draw a **graph**. Graphs often give us more insight into our data than just a results table would. It is important to know what type of **graph** to draw, and how to use it.

**Presenting Data**

Before drawing a graph from our **experimental** **data**, we must understand our **data **in more detail and decide what type of visualisation the data requires.

If the **independent variable** is **discrete** (comes in separate categories), then a **bar chart** is the most appropriate to draw. This is because discrete data is not made up of continuous numbers. An example of some **discrete **data is shown below with it’s corresponding** bar chart**.

**Example:**

If we are working with numerical variables, where both are **continuous**, we should draw a **line graph**. This is the graph you will use in most of your experiments. **Continuous data** is numerical data that we can measure. Examples of** continuous data** could be force, rate of reaction, voltage etc. We should plot our data and then draw a line of best fit through it. This is simply a line that goes through or passes near all of the points. An example of some continuous data is shown below with it’s corresponding graph.

**Example:**

**Utilising Graphs**

We can use graphs to extract information from our results. One value we can calculate from our graph is the **gradient**. The gradient will give us the **rate **at which the dependent variable changes with the independent variable.

The **gradient **is given by the change in the y axis divided by the change in the x axis:

\text{Gradient} = \dfrac{\text{Change in y}}{\text{Change in x}}

We can calculate the **gradient **of the Distance-Time graph from the previous box:

- We first should pick 2 points on the line.
- Draw two lines so that the points meet.
- Use these lines to read off the change in the y axis values and the change in the x axis values.
- Calculate your
**gradient**.

The **intercept **of a graph is where the line of best fit meets the axes. We can see in the above example that the **intercept** is at the origin \left(0 ,0\right). We know this is correct because when the time is at 0 seconds, the distance travelled must be 0 metres.

**Extrapolating**

We can use graphs to predict possible data values that aren’t in the results. This is called extrapolation.

We can illustrate this by using **extrapolation** to predict what the distance travelled might be at 7 seconds.

First we must extend our line of best fit until it reaches the value we want to **extrapolate**. This is shown on the diagram with the green segment of the line. Then we just read off the distance value at 7 seconds. The distance travelled is 4.6 metres. Again this is just a prediction because our experiment didn’t include any readings for 7 seconds, so we have **extrapolated**.

## Graphs and Data Example Questions

**Question 1: **State which type of graph/chart should be used to present the following dataset. Give a reason for your answer.

Student |
Number of Televisions in their House |

Romualdo | 1 |

Janine | 5 |

Anneli | 0 |

Fletcher | 2 |

**[2 marks]**

**Bar Chart.**

Because the **independent variable is not a set of continuous numbers** (it is **discrete**).

**Question 2: **Plot a graph using the following results table:

Mass \left(\textbf{kg}\right) |
Force \left(\textbf{N}\right) |

1 | 1.70 |

2 | 3.29 |

3 | 5.07 |

4 | 6.68 |

**[5 marks]**

1 mark for each of the following:

**y-axis correctly labelled, with units.****x-axis correctly labelled, with units.****Appropriate title.****All points plotted correctly.****Line of best fit through points.**

**Question 3: **Calculate the gradient of the graph you drew in Question 2.

**[2 marks]**

Use of \text{Gradient} = \dfrac{\text{Change in y}}{\text{Change in x}}.