Scatter DiagramsScatter Diagrams

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Joan Ridgway

When do we use scatter diagrams?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?”

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DataDataName Height (cm) Shoe Size Maths Mark (%) Science Mark (%)Adam 172 9 19 22Alex 146 5 38 46Brian 162 8.5 51 54Carl 156 8 49 61

Chan 148 5 55 57Dawn 173 7.5 75 79

Frances 155 7 46 52Georgina 147 4 71 66

Harry 163 8 62 68Ian 184 12 29 31

Jane 149 4.5 60 52Jenny 162 6.5 54 56Kieran 170 10 73 68Lynne 157 6 68 73Michael 156 7.5 57 79

Mohammed 168 9.5 84 92Nasril 153 7 88 82Peter 182 11 63 67

Richard 164 9 64 63Samantha 169 7 51 49

Sarah 153 6.5 73 63Tim 152 6 58 56

Vicky 158 5 21 34Yvonne 150 4.5 65 57

“If someone is good at Maths, are they likely to be good at science too?”

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Maths Marks (%)

Scie

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ks (%

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Comparing Maths Marks with Science MarksComparing 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

CorrelationCorrelation

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

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Strong positive correlation

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Moderate positive correlation

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Weak negative correlation

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Height (cms)

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zes)

Comparing Height with Shoe SizeComparing Height with Shoe Size

“Do taller people have larger feet than shorter people?”

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Height (cm)

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ark

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Comparing Heights with Maths MarksComparing 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 MarksComparing Shoe Sizes with Science Marks

Line of Best FitLine of Best FitIf 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)

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Maths Marks (%)

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ks (%

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Strong negative correlation

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Strong positive correlation

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Moderate positive correlation

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Weak negative correlation

Using the line of best fitUsing the line of best fitOnce 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.

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Maths Marks (%)

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Gradient and InterceptsGradient and InterceptsLook at the line of best fit, and decide what the gradient, and

any intercepts with the graphs axes, tell us about the real situation.

Comparing Height with Shoe Size

y = 0.2x - 20.7

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Height (cms)

Shoe

Size

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ish Si

zes)

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.

Height (cm) Weight (kg)164 58.2152 50.8173 60.3158 56.0177 76.2173 64.2170 68.8168 60.5

Height and weight of students1 2Shoe size

(British sizes)Hand span

(cm)4.5 20.210 21.65 17.39 19.67 21.26 21.2

5.5 19.410 228 19.59 23.75 19.55 20.2

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Shoe size and hand span

Draw the line of best fit (the trend line). Think about what the gradient and intercepts tell you about the real situation.