Scatter Graphs
Wackford Squeers 1
Scatter Graphs Read data from Scatter Graphs, in particular correlation. Draw Scatter Graphs from given data
What is a Scatter Graph?
You create a scatter graph when you plot two sets of data which you think may be related – and the graph should show you if they are, in fact, related For example, in the image on the front of this booklet there are two measures: Height Arm span (how wide they can stretch their arms) The graph is reproduced below
So the first person on the graph has an armspan of around 19cm and a height of 110 cm The remaining results (armspan and height) are plotted similarly We end up with what looks like a ‘mess’ of points
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What we do next is to draw (or try to draw)
A Line of Best Fit This is a line drawn through the dots so that as many dots are on one side of the line as are on the other (or as near as we can draw it!) So we end up with a graph looking like the one on the previous page Finally, we look at the direction of the line (if we have been able to draw one) If the line slopes from bottom left to top right (as with the one in the illustration above we say that the two sets of data have
Positive Correlation This means that they are related – and this makes sense if we think of people’s height and armspan – you would expect taller people to have longer armspans. If the line slopes from top left to bottom right (as in the graph below) we say that the two sets of data have
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Negative Correlation Suppose you were to do a survey of the miles per gallon achieved by a range of cars relative to the size of their engine (as you will do in an exercise at the end of the booklet) you might expect that the larger the size of engine, the lower the miles per gallon the car will do. In such a case we have what is called
Correlation
Negative
Meaning that as one quantity goes up (in this case the size of the engine) another one goes down (the miles per gallon)
No Correlation
An example of a scatter graph where there is no correlation might be colour of eyes plotted against ability in Maths – it is unlikely that the colour of you eyes will be a factor in how good you are at Maths!
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Exercise 1
Below is a table of data relating to the miles per gallon achieved by a car and its size of engine (incm2) Plot the data on a Scatter Diagram Draw a line of best fit through the points What can you say about the performance (mpg) of a car relatd to its engine size (in cm2)? How would you say this in normal English? Mpg 18 23 24 27 28 34 34 35 42 42 42 48 50 Cm3 4800 4000 4900 3900 3200 1990 2400 3400 1100 1400 2500 1100 1800
Plot the points on axes similar to that below: 6000
Size of car engine
5000
4000
3000 2000
1000 10
20
30
40
Miles per gallon
50
60
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Exercise 2
The table below gives the marks achieved by pupils in Maths and Science exams Maths 15 35 34 23 35 27 36 34 23 24 30 40 25 35 20 Science 20 37 35 25 33 30 39 36 27 20 33 35 27 32 28 Draw a scatter graph of the marks cored in the Maths and Science exams Describe the correlation between the marks scored in the two exams
Exercise 3 The table below shows the returns of a postal survey conducted by a polling organization Issued 2000 2500 3000 2800 1400 2100 2000 1800 2400 2600 Returned 480 605 712 683 308 515 492 421 592 624 Construct a Scatter Graph of the surveys and results Draw a line of best fit Describe the correlation between the postal surveys issued and those returned
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