1. GCSE: Scatter Diagrams
Skipton Girls’ High School
Objectives: Understand the purpose of a scatter diagram, spotting correlation in data, and how to draw a line of best fit.

2. What are Scatter Diagrams?
They display data involving two variables. For example, we might collect compare students’ test performance in English and Maths.
English
Maths 40 55 65 57 41 92 68 80 99 97 75 78 58 67 86 66 72 90
100 32 45

3. How can they help us interpret data?
They can help us identify if there is any relationship between the two variables.
The relationship between two variables is known as correlation. ?
How are English and Maths test scores related?
If someone’s English test score is higher, their Maths score tends to be higher. ?
Schoolboy ErrorTM:
“A higher English score means their Maths score will be higher.”
We call this relationship:
Positive correlation ?

4. Different Types of Correlation
There’s 3 types you should be able to identify.
Weak negative correlation ? ?
Type of correlation:
Weak positive correlation ? ?
strength
type ?
No correlation
Strong positive correlation ? ?

5. Line of best fit
We can add a line of best fit to the scatter diagram. This allows us to estimate one variable’s value given the other.
If a boy gets 50% in his English test, what score might we expect him to get in his Maths test?
65% ?
(I used Excel to generate this trendline.)

6. Line of Best Fit
We can add a line of best fit to the scatter diagram. This allows us to estimate one variable’s value given the other.
Here’s a more interesting question...
Can you come up with an equation that could estimate a Maths Score (y) from an English score (x)?
y = 0.55x ?
The y-intercept seems to be about 39.
We can find the gradient by picking two random points on the line suitably far apart.
(0, 39) and (80, 82)
Change in y is 43
m = = = 0.54 43 80 Δy Δx
Change in x is 80

7. Line of Best Fit y-intercept: 17 ? Gradient: -0.18 ?
Equation of line: x + 17 ?

8. Line of Best Fit y = -0.18x + 17 (-0.18 x 50) + 17 = 8 ?
If someone’s age is 50, how many hours would we therefore expect them to be on the internet?
(-0.18 x 50) + 17 = 8 ?

9. In general, we should be wary of making estimates using values outside the range of our data.
Earnings
£80000
£70000
£60000
£50000
£40000
£30000
£20000
£10000
Estimating for this age is bad because:
The person may have retired. ?
Estimating for this age is bad because:
Children don’t have full-time jobs. ?
Age
When we use our line of best fit to estimate a value inside the range of our data, this is known as: interpolation ?
When we use our line of best fit to estimate a value outside the range of our data, this is known as: extrapolation ?

10. The Dangers of Extrapolation