Scatter Diagrams Joan Ridgway

When do we use scatter diagrams? When we look at data, we may want to investigate the relationship between two variables. A good way to compare two variables is to plot them on a scatter diagram. “If someone is good at Maths, are they likely to be good at science too?” “Do taller people have larger feet than shorter people?” “Are taller people better at Maths than shorter people?” “Do people who are good at science have smaller feet?”

Data

“If someone is good at Maths, are they likely to be good at science too?” Comparing Maths Marks with Science Marks This point represents Mohammed, with Maths mark 84 and Science mark 92 This point represents Vicky, with Maths mark 21 and Science mark 34

Correlation There is a correlation between two variables when changes in one variable are linked to changes in the other Correlation can be positive or negative It can be strong, moderate or weak Or there may be no correlation at all

Strong negative correlation x x x x x x x x x x x x x x x x Strong positive correlation x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x Moderate positive correlation x x x x x x x x x x x x x x Weak negative correlation

Comparing Height with Shoe Size “Do taller people have larger feet than shorter people?”

Comparing Heights with Maths Marks “Are taller people better at Maths than shorter people?”

“Do people who are good at science have smaller feet?” Comparing Shoe Sizes with Science Marks

Line of Best Fit If there is correlation on a scatter diagram, whether it is positive or negative, strong, moderate or weak, we can draw a line of best fit. This can be done by eye, or by using the chart wizard on Microsoft Excel. Right-hand click on the actual points, then choose “trend line” (It can also be calculated, but this is more advanced)

Strong negative correlation x x x x x x x x x x x x x x x x Strong positive correlation x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x Moderate positive correlation x x x x x x x x x x x x x x Weak negative correlation

Using the line of best fit Once we have drawn the line of best fit, we can use it to estimate results. By looking at the scatter diagram of Maths and Science marks, we might use the Maths mark to estimate the Science mark of a student who had missed the Science test. If Tom got 40% for Maths, he might have got 45% for Science. If he got 10% for Maths, he might have got 20% for Science.

Gradient and Intercepts Look at the line of best fit, and decide what the gradient, and any intercepts with the graphs axes, tell us about the real situation. We would expect a student who was 148 cm tall to take shoe size 5 For every extra cm in height, we expect an increase of 0.2 in shoe size. For every 5 cm more height there will be an increase of one shoe size

Plot the following pairs of data, and decide what type of correlation there is, if any. 1 2 Draw the line of best fit (the trend line). Think about what the gradient and intercepts tell you about the real situation.