Mathematics
Grade 9
15 min
Calculate correlation coefficients
Calculate correlation coefficients
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1
Introduction & Learning Objectives
Learning Objectives
Define correlation as a relationship between two sets of data.
Identify positive, negative, and no correlation from simple data sets or visual representations.
Describe the strength of a correlation (strong or weak) based on observed patterns.
Use rational numbers to represent and compare data points in a relationship.
Explain real-world examples of correlated data.
Organize simple data pairs to look for patterns and trends.
Have you ever noticed that the more time you spend practicing a skill, the better you get at it? 🤔 That's a relationship between two things! We call it correlation.
In this lesson, you'll learn how to 'calculate' or determine these kinds of relationships between two sets of numbers, using rational numbers. We...
2
Key Concepts & Vocabulary
TermDefinitionExample
Data SetA collection of information, often numbers, gathered about a topic.A list of students' heights and their shoe sizes is a data set.
Rational NumberA number that can be written as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q$ is not zero. This includes whole numbers, integers, fractions, and decimals.0.5, $\frac{3}{4}$, -2, and 7 are all rational numbers.
CorrelationA relationship or pattern between two sets of data. When we 'calculate correlation coefficients' at this grade level, we are identifying the type and strength of this relationship.There is a correlation between the number of sunny days and the amount of energy generated by solar panels.
Positive CorrelationA type of correlation where as one set of data generally inc...
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Core Formulas
Rule for Identifying Positive Correlation
If, as the values in one data set increase, the values in the other data set also generally increase, then there is a positive correlation.
To 'calculate' a positive correlation, observe if both quantities tend to go up together. Imagine drawing a line through the data points; it would go upwards from left to right.
Rule for Identifying Negative Correlation
If, as the values in one data set increase, the values in the other data set generally decrease, then there is a negative correlation.
To 'calculate' a negative correlation, observe if one quantity goes up while the other goes down. Imagine drawing a line through the data points; it would go downwards from left to right.
Rule for Identifying No Correlation...
2 more steps in this tutorial
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Challenging
A student claims, 'My data shows a weak negative correlation between the number of rainy days per month and the number of people who visit the park.' Their data is: (Jan: 12 days, 300 people), (Feb: 10 days, 350 people), (Mar: 15 days, 250 people), (Apr: 14 days, 400 people). Is their claim correct?
A.Yes, it's a weak negative correlation.
B.No, it's a strong negative correlation.
C.No, it's a positive correlation.
D.No, there is no clear correlation.
Challenging
An ice cream shop owner wants to show a strong positive correlation between the daily high temperature (°F) and the number of scoops sold. Which data set most realistically represents this?
A.(60°, 50), (70°, 55), (80°, 60)
B.(60°, 100), (70°, 50), (80°, 25)
C.(60°, 50), (70°, 150), (80°, 250)
D.(60°, 100), (70°, 10), (80°, 110)
Challenging
A phone's battery percentage is tracked based on hours of active use. Which data set best shows a strong negative correlation for this situation?
A.(1 hour, 90%), (2 hours, 95%), (3 hours, 80%)
B.(1 hour, 90%), (2.5 hours, 65%), (4 hours, 40%)
C.(1 hour, 50%), (2.5 hours, 45%), (4 hours, 42%)
D.(1 hour, 90%), (2.5 hours, 20%), (4 hours, 55%)
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