4.2.1 Bivariate Data

Scatter Diagrams

What does bivariate data mean?

Bivariate data is data which is collected on two variables and looks at how one of the factors affects the other
- Each data value from one variable will be paired with a data value from the other variable
- The two variables are often related, but do not have to be

What is a scatter diagram?

A scatter diagram is a way of graphing bivariate data
- One variable will be on the x-axis and the other will be on the y-axis
- The variable that can be controlled in the data collection is known as the independent or explanatory variable and is plotted on the x-axis
- The variable that is measured or discovered in the data collection is known as the dependent or response variable and is plotted on the y-axis
Scatter diagrams can contain outliers that do not follow the trend of the data

Correlation

What is correlation?

Correlation is the how the two variables change in relation to each other
- Correlation could be the result of a causal relationship but this is not always the case
Linear correlation is when the changes are proportional to each other
Perfect linear correlation means that the bivariate data will all lie on a straight line on a scatter diagram
When describing correlation mention
- The type of the correlation
  - Positive correlation is when an increase in one variable results in the other variable increasing
  - Negative correlation is when an increase in one variable results in the other variable decreasing
  - No linear correlation is when the data points don’t appear to follow a trend
- The strength of the correlation
  - Strong linear correlation is when the data points lie close to a straight line
  - Weak linear correlation is when the data points are not close to a straight line
If there is strong linear correlation you can draw a line of best fit (by eye)
- The line of best fit will pass through the mean point $(\bar{x}, \bar{y})$
- If you are asked to draw a line of best fit
  - Plot the mean point
  - Draw a line going through it that follows the trend of the data

What is the difference between correlation and causation?

It is important to be aware that just because correlation exists, it does not mean that the change in one of the variables is causing the change in the other variable
- Correlation does not imply causation!
If a change in one variable causes a change in the other then the two variables are said to have a causal relationship
- Observing correlation between two variables does not always mean that there is a causal relationship
  - There could be underlying factors which is causing the correlation
- Look at the two variables in question and consider the context of the question to decide if there could be a causal relationship
  - If the two variables are temperature and number of ice creams sold at a park then it is likely to be a causal relationship
  - Correlation may exist between global temperatures and the number of monkeys kept as pets in the UK but they are unlikely to have a causal relationship

Worked Example

A teacher is interested in the relationship between the number of hours her students spend on a phone per day and the number of hours they spend on a computer. She takes a sample of nine students and records the results in the table below.

Hours spent on a phone per day	7.6	7.0	8.9	3.0	3.0	7.5	2.1	1.3	5.8
Hours spent on a computer per day	1.7	1.1	0.7	5.8	5.2	1.7	6.9	7.1	3.3

Draw a scatter diagram for the data.

4-2-1-ib-ai-sl-correlation-a-we-solution

Describe the correlation.

4-2-1-ib-ai-sl-correlation-b-we-solution

Draw a line of best fit.

sPCr4WYi_4-2-1-ib-ai-sl-correlation-c-we-solution

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IB DP Maths: AI HL

Revision Notes

4.2.1 Bivariate Data

Scatter Diagrams

What does bivariate data mean?

What is a scatter diagram?

Correlation

What is correlation?

What is the difference between correlation and causation?

Worked Example

Author: Daniel

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