Exercise solution 4, page 710 - GCSE Mathematics for OCR Higher Student Book

⭐ What you need to know:

A) A scatter diagram is used to show the relationship between two sets of data. Each piece of data is plotted as a point with coordinates \((x,y)\). The first value is placed on the horizontal axis and the second value on the vertical axis.

For example, if house numbers are \(2, 4, 6\) and the numbers of residents are \(3, 1, 5\), the points to plot are \((2,3)\), \((4,1)\) and \((6,5)\).

B) To draw the graph correctly, you must choose suitable axes and a sensible scale. The horizontal axis should represent the first variable, and the vertical axis should represent the second variable. Mark equal intervals clearly so that all the data can fit on the graph.

If the horizontal values go from \(2\) to \(14\), you might label the axis in steps of \(2\). If the vertical values go from \(1\) to \(7\), you might label that axis in steps of \(1\).

C) When plotting points, remember that the coordinate \((x,y)\) means move across first, then move up. A common mistake is to reverse the coordinates.

For instance, the point \((8,4)\) means \(8\) across and \(4\) up. It is not the same as \((4,8)\).

D) After plotting the points, you look for a pattern to describe the correlation between the two variables.

If the points tend to rise from left to right, there is positive correlation.
If the points tend to fall from left to right, there is negative correlation.
If the points show no clear pattern, there is no correlation.

This is about the general trend of the points, not whether every point follows the pattern exactly.

E) Correlation does not mean the points must lie exactly on a straight line. In real data, the points are often spread out. You decide the type of correlation by looking at the overall direction of the cloud of points.

For example, if larger values of \(x\) are often matched with larger values of \(y\), that suggests positive correlation, even if some points are higher or lower than expected.

F) A scatter diagram uses pairs of related values. This means each \(x\)-value must stay matched with its own \(y\)-value. You should not sort one row of data without sorting the other in the same way, because that would change the meaning of the points.

For example, if one item has values \(10\) and \(4\), then the point must remain \((10,4)\).