# Describing Patterns in Scatter Plots

Content Describing Patterns in Scatter Plots
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## Scatter Plot Introduction

A scatter plot is a type of graph that shows the relationship, or association, between two different sets of data, which we call bivariate data. By looking at a scatter plot, we can see patterns such as how the data points cluster, if there are any unusual points (outliers), and whether the relationship is positive, negative, linear, or nonlinear.

## Understanding Scatter Plot

A scatter plot helps us see if there's a link between two variables. For example, it can show if one thing increases, does the other thing tend to increase too? This is a positive association. Or if one decreases as the other increases, that's a negative association. When the points don't show any obvious pattern, we say there's no association. If the points make a straight line, that's a linear association. If they form a curve, it's a nonlinear association.

## Scatter Plot Example

Example Problem:

Create a scatter plot for the following data that shows the number of hours students studied and their test scores:

Hours Studied Test Score
1 50
2 60
3 65
4 70
5 80

Solution:

1. Draw a graph with two axes: horizontal for hours studied and vertical for test scores.
2. Mark each pair of values as a point on the graph.
3. Observe the pattern that the points make.

## Scatter Plot - Guided Practice

How would you plot the point for someone who studied 2 hours and got a score of 60?
What does it mean if most of the points on the scatter plot seem to be rising from left to right?

## Scatter Plot - Your Turn!

Example Problem:

Plot the following data on a scatter plot:

Hours Studied Test Score
1 80
2 78
3 75
4 70
5 65
Construct the scatter plot.
Describe the association.

## Scatter Plot Summary

Scatter plots are a useful way to visualize the relationship between two variables. By plotting bivariate data and analyzing the pattern of points, we can determine if there is an association—whether it's positive, negative, linear, or nonlinear. Understanding scatter plots can help us make predictions and find trends in the data.

## Describing Patterns in Scatter Plots exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Describing Patterns in Scatter Plots.
• ### What is a scatter graph?

Hints

A scatter graph displays a relationship between two sets of data.

If you are not sure, count the number of data categories in each graph.

Data plotted into a scatter graph is given a point for two variables.

For example, person A, weight and height, person B weight and height etc.

Solution

As a scatter graph displays a relationship between two sets of data this is the only one which does that.

You can see the y-axis is ice cream sales and the x-axis is the temperature that day.

• ### Find the correlation.

Hints

Negative correlation means that as one value increases the other value decreases.

An example of this would be, 'as the cakes on the plate decrease, the fuller I would get'.

This is a scatter graph with negative correlation.

The $x$ values increase while the $y$ values decrease.

There are three correct answers here.

Solution

These are all negatively correlated because as one value increases the other decreases.

• miles travelled in the car and the level of petrol in the tank
• sales of winter coats and the temperature of the day
• number of sweets left in the bag and the number of sweets eaten
• ### Find the outlier.

Hints

An outlier is different to the other data points.

On a scatter graph it would not follow the trend of the others and would stand out.

An outlier would look like this on a scatter graph.

Solution

Temperature $26^\circ$C, $50$ ice creams sold

It would not follow the pattern of the others on the scatter graph.

• ### No correlation.

Hints

When a relationship has no correlation it means the two data sets are completely unrelated. They could be easy to spot because they appear a bit silly.

For example, a person's height and the length of time watching TV have no correlation.

The scatter graph looks like this when there is no correlation

We can see there is no pattern to the data.

There are three answers that have no correlation.

Solution

All these are unrelated to each other and do not have correlation.

• Hair length and number of hours on social media
• Height and amount of pets a person has
• Number of illnesses a person has had and number of shoes a person owns
• ### What type of relationship is displayed?

Hints

There are 3 types of correlation.

Decide which is similar to the data displayed above.

• Positive correlation: as the $x$ value increases, the $y$ value increases.
• Negative correlation: as the $x$ value increases, the $y$ value decreases.
• No correlation: the $x$ and $y$ values do not have a relationship.

We can see from this graph that as the $x$ value increases, the $y$ value increases.

Solution

Positive correlation

As the $x$ value increases, the $y$ value increases.

• ### Interpret the scatter graph.

Hints

Go across the $x$ axis to $8$ and go directly up to the cluster of points. Estimate where you think the sales of hot chocolate would be if it fitted the pattern of the others.

Remember, this is an estimate so we are following an imaginary line through the middle of the points to get the best estimate we can.

When you go up to the points from $8$ move left from where you think the vertical line would hit a line going through the middle of the points. Take it across horizontally from there to the $y$ axis to read off the estimate for the amount of hot chocolates sold.

Solution

Estimated answer is $100$ to $120$ hot chocolates sold.

From the graph we can see $100$ is a good estimate but, it is slightly higher so $100$ to $120$ seems fair.