# Functional Skills: Scatter Graphs

## Functional Skills: Scatter Graphs Revision

**Scatter Graphs**

We use **scatter graphs **to determine the existence and type of correlation between two variables.

If the graph shows a relationship between the variables, we say they have **correlation**.

There are **4** skills that you need to learn for scatter graphs.

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**Skill 1: Correlation**

If there is a relationship between two variables, we say there is a **correlation**.

There are two types of correlation:

**Positive correlation **â€“ as one variable goes up, the other also goes up.

**Negative correlation **â€“ as one variables goes up, the other goes down.

If the points are randomly spread, we say there is **no correlation**.

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**Skill 2: Drawing Scatter Graphs**

**Example:** The table below shows the results of students’ Maths and English exams out of 100. Plot a scatter graph for this information.

Draw the axes. One should be for the ‘Maths mark’, making sure it goes up to at least 100 and the other should be for the ‘English Mark’, making sure it goes up to at least 100 also. Label the axes.

Then, plot the data as shown on the graph to the right (similar to **plotting coordinates**) e.g. for someone who got 38 on their maths exam and 74 on their English exam, go across to 38 on the x-axis and then up to 74 on the y-axis, and draw a cross or a dot.

**Note:** This graph has a **negative correlation**, because as the Maths mark increases, the English mark decreases.

**Skill 3: Drawing a Line of Best Fit**

A **line of best fit **is a straight line that is used to represent the correlation of the data.

Lines of best fit should go through the middle of all the points, with an equal number of points on either side of the line.

**Note:** Make sure you use a sharp pencil and a ruler when drawing a line of best fit.

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**Skill 4: Using a Line of Best Fit**

If you know one value on a scatter graph, you can use a line of best fit to **predict** the other value.

**Example:** Predict the English mark of someone that scored a mark of 60Â in Maths, using the following scatter graph.

Firstly, we need to draw a line of best fit through the points, as seen previously.

Then, to find the English mark of someone who scored 60 in Maths, go up from 60 on the x-axis until you meet the line of best fit.

Finally, go across to the y-axis and read off the value. Therefore the predicted English mark is \textcolor{red}{50}.

## Functional Skills: Scatter Graphs Example Questions

**Question 1:** For each scatter graph below, state whether or not there is correlation and, if so, state type of correlation.

**[3 marks]**

A: As the values on the x-axis increase, so do the values on the y-axis. Therefore there is a positive correlation.

B: All of the points are randomly scattered. Therefore there is no correlation.

C: As the values on the x-axis increases, the value on the y-axis decreases. Therefore there is a negative correlation.

**Question 2:** John records the temperature of a cup of coffee over time. The results are shown in the table below:

**a)**Â Draw a scatter graph for the data.

**[3 marks]**

**b)** State the type of correlation.

**[1 mark]**

**c)** Estimate the temperature of a cup of coffee after 6 minutes.

**[1 mark]**

**a)** Draw the axes; one should be for the â€˜Timeâ€™ (making sure it goes up to at least 10) and the other for the â€˜Temperatureâ€™ (making sure it goes up to at least 95). Label the axes.

(Since the lowest temperature is 45\degree C, you could start at 40 on the y-axis instead of 0)

Plot the points and mark them with crosses.

**b)** We can see that as the time increases, the temperature decreases. Therefore the correlation is negative.

We can draw a line of best fit to make sure – we need this for part (c) anyway.

**c)** To predict the temperature of a cup of coffee after 6 minutes, go up from 6 on the x-axis until you meet the line of best fit. Then, go across to the y-axis and read off the value.

The predicted temperature of a cup of coffee after 6 minutes is 65\degree C

(allow between 62 \degree C and 68\degree C, because your line of best fit may be slightly different)

**Question 3:** The table below shows the number of hours of revision a group of students spent revising for an exam and the score they achieved:

**a)** Plot these points on the axes below.

**[2 marks]**

**b)** Predict the exam score of a student who completes 22 hours of revision.

**[1 mark]**

**a)** Plot the data points, and mark them with crosses.

**b)** To predict the exam score of a student who completes 22 hours of revision, we need to draw a line of best fit, with an equal number of points on either side of the line.

Then, go up from 22 on the x-axis until you meet the line of best fit. Then, go across to the y-axis and read off the value. So, the predicted score of someone who completes 22 hours of revision is 78

(allow 75 to 81, since your line of fit might be slightly different.)

## Functional Skills: Scatter Graphs Worksheet and Example Questions

### Scatter Graphs L2

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