MathematicsExam code: 0580

Scatter Graphs and Correlation

Statistics

PractiseFlashcards

The three types

  • Correlation describes whether the two quantities tend to change together, and in which direction
  • Positive correlation: both quantities rise together, and the points climb as you read left to right
    • Temperature and the number of cold drinks sold
A scatter diagram showing positive correlation: the crosses climb from the bottom left towards the top right, loosely following a rising trend
Source: Correlation by Save My Exams
  • Negative correlation: one rises while the other falls, and the points descend as you read left to right
    • The age of a car and its value
A scatter diagram showing negative correlation: the crosses fall from the top left towards the bottom right, so one quantity decreases as the other increases
Source: Correlation by Save My Exams
  • Zero correlation: no relationship, and the points form a shapeless cloud
A scatter diagram showing no correlation: the crosses are scattered across the whole grid with no upward or downward trend to them
Source: Correlation by Save My Exams
  • Correlation can also be described as strong or weak, according to how closely the points cluster around a straight line

Describing it in context

  • The standard question asks what type of correlation the diagram shows, for one mark, and the answer is one of those three phrases
  • A follow-up may ask you to describe the relationship, which needs the two quantities named rather than just the word
    • "As the temperature increases, the number of people on the beach increases"
  • Correlation does not prove that one quantity causes the other: both may be driven by something else entirely, and the syllabus asks you to appreciate such restrictions on drawing conclusions

Worked example

Naming and describing correlation

A scatter diagram plots the age of a car in years against its value in pounds. The points fall from the top left towards the bottom right. Name the correlation and describe what it means.

A scatter diagram with age in years from 0 to 10 along the bottom and value in pounds from 0 to 20 000 up the side. Ten crosses fall from the top left, near 17 500 pounds at 1 year, to the bottom right, near 4500 pounds at 9 years. No line is drawn.

Solution:

  • The points descend as you read from left to right, so as one quantity rises the other falls
  • The type is negative correlation
  • Naming it is one mark; describing it is a separate demand and needs both quantities named
  • In context: as the age of a car increases, its value decreases
  • "The points go down" is not a description, because it names neither quantity
  • Note that this shows a relationship only: correlation on its own never establishes that age causes the fall in value

Build on this topic

Check your understanding17 exam questions, marked instantlyTest your recall20 flashcards on the key facts