Scatter Graphs

If you are given a table of ‘paired’ data, you can construct a scatter graph

Test scores of 9 people

 Maths 23 43 54 78 92 17 55 66 85 English 34 66 70 75 86 32 69 72 88

We plot a point for each pair of data which corresponds. In this case, each point corresponds to a different person

We can also draw line of best fit through the points.

The line of BEST FIT DOES NOT HAVE TO GO THROUGH THE ORIGIN a)    If you were asked to estimate the English score of someone who achieved 40% in Maths, we could use the line of best fit. From above, you can see the English score is about 53%. This is called INTERPOLATION because our estimation lies WITHIN the data dots. This has been indicated on the diagram

b)    If you were asked to estimate the English score of someone who achieved 10% in Maths then THIS WOULD NOT BE VALID. This would be called EXTRAPOLATION.

This is because we ONLY KNOW THE LINE IS VALID within the data which we have been given

TERMINOLOGY

POSITIVE CORRELATION: the dots go diagonally upwards

The graph above is positively correlated. It suggests that is you are better at Maths then you are better at English.

Other examples would be:

·       Weight and height

·       Temperature and ice-cream sales

·       Time spend revising and exam score

·       Hand size and foot size

NEGATIVE CORRELATION: the dots go diagonally downwards

Examples would include

·       Age and eye-sight

·       Amount of alcohol drunk and coordination

STRENGTH OF CORRELATION

The closer the dots are to a straight line THE STRONGER THE CORRELATION.

A perfectly straight line indicates PERFECT CORRELATION