Scatter graphs and correlationIB MYP Maths Standard: Revision notes

A scatter graph shows two variables for the same people or objects, with one point for each pair of values. Put the variable you think causes or controls the other (the independent variable) on the horizontal axis, and the other on the vertical axis. Example: temperature $x$ and drinks sold $y$ give points such as $(18,40)$ and $(33,115)$. Choose scales that fit all the data, label both axes with units, and plot each point as a small cross.

Correlation describes the relationship between the two variables.

• Positive correlation: as $x$ increases, $y$ increases (points slope up to the right).
• Negative correlation: as $x$ increases, $y$ decreases (points slope down to the right).
• No correlation: no pattern, the points are scattered. The correlation is strong when the points lie close to a straight line, and weak when they are more spread out. Always describe it in context, for example 'the hotter the day, the more drinks are sold'.

A line of best fit is a straight line that follows the trend of the points. Draw it with a ruler so that:

• it passes through the middle of the points, with about the same number above and below the line
• it is a single straight line, not joined dot to dot
• it goes through the mean point (mean of $x$, mean of $y$) if you have worked it out. Example: for the speeds $20,30,\dots,70$ and braking distances $8,14,19,25,30,36$ the mean point is $(45,22)$. The line does not have to go through the origin, and an outlier (a point far from the pattern) can be ignored when drawing the line.

To predict $y$ for a given $x$, go up from $x$ to the line, then across to the $y$-axis and read the value. You can also use the equation of the line, $y=mx+c$. Example: the line passes through $(20,45)$ and $(30,100)$. Gradient $=\frac{100-45}{30-20}=5.5$, so each extra 1 °C gives about 5.5 more drinks. At 26 °C: $45+6\times5.5=78$ drinks. A prediction inside the range of the data (interpolation) is usually reliable. A prediction outside the range (extrapolation) is unreliable because the trend may not continue.

Correlation shows that two variables are related, but it does not prove that one causes the other. Ice cream sales and sunburn cases are positively correlated because both rise in hot weather, not because ice cream causes sunburn. A small sample and an outlier can also make a relationship look stronger or weaker than it is. When you evaluate a claim, mention causation, the range of the data and the sample size.