CAPS Grade 12 Mathematical Literacy: Scatter Plots Revision Notes
Introduction
Scatter plots are a visual way to represent data. They help to understand the relationship between two variables. This is important in various fields like statistics, economics, and social sciences.
Learning Objectives:
– Understand how to create and interpret scatter plots.
– Identify correlation and draw a line of best fit.
– Learn to predict data trends using scatter plots.
Key Points
 Definition and Components of Scatter Plots:
 Scatter plots are graphs that show the relationship between two variables.
 Each data point is plotted as a dot on the graph.

The xaxis and yaxis represent the two variables being compared.

Drawing Scatter Plots:
 Organize data in a table format.
 Plot each pair of values on the graph.

Label the axes appropriately.

Correlation:
 Positive Correlation: As one variable increases, the other also increases.
 Negative Correlation: As one variable increases, the other decreases.

No Correlation: No visible pattern in the data points.

Line of Best Fit (Trend Line):
 A straight line that best represents the data on a scatter plot.
 It minimizes the distance between the line and all the points.
 Can be used to make predictions.
RealWorld Applications
Example:
Consider a student who records the number of hours they studied and their corresponding exam scores:
 Hours Studied  Exam Score (%) 
——————————–
 2  35 
 3  75 
 4  50 
 5  65 
 6  90 
Steps to Create the Scatter Plot:
1. Draw the horizontal (x) and vertical (y) axes.
2. Plot each pair (Hours Studied, Exam Score) on the graph .
3. Draw a line that best fits most of the points.
Interpreting the Scatter Plot:
– Identify if the scatter plot shows a pattern.
– Draw a line of best fit to understand the trend.
– Use the line to predict future scores based on hours studied.
Common Misconceptions and Errors
 Misunderstanding Correlation: Belief that correlation implies causation. While scatter plots show trends, they do not prove one variable causes another.
 Incorrect Axis Labeling: Often, students might mix up the axes. Always ensure the explanatory variable is on the xaxis and the response variable on the yaxis.
 Ignoring Outliers: Not recognizing outliers can skew data interpretation. Identify and understand outliers before drawing conclusions .
Practice and Review
Practice Questions:

Create a scatter plot for the following data set and draw a line of best fit:
 Hours Studied  Exam Score (%) 
——————————–
 1  55 
 3  65 
 4  70 
 6  80 
 8  90  
Interpret the scatter plot:
 Determine the type of correlation.
 Predict the exam score if a student studies for 5 hours.
Solutions:
 Drawing the Scatter Plot: Plot each data point and draw a line that balances the upper and lower points.
 Interpreting the Plot:
 The correlation is positive.
 Using the line of best fit, predict that if a student studies for 5 hours, their score might be around 75%.
Examination Tips:
– Focus on keywords like “correlation,” “trend,” and “line of best fit.”
– Manage your time by first plotting all points before drawing the line of best fit.
Connections and Extensions
 Connections to Other Topics: Scatter plots are related to topics like linear regression and probability.
 RealWorld Implications: Understanding data trends can be useful for market analysis, scientific research, and everyday decisionmaking.
Summary and Quick Review
Summary:
– Scatter plots are used to visualize the relationship between two variables.
– Positive, negative, or no correlation helps interpret the data.
– The line of best fit helps in making predictions based on data trends.
Quick Reference:
– Positive Correlation: (\nearrow)
– Negative Correlation: (\searrow)
– Line of Best Fit: A straight line that best represents the data on a plot.
Additional Resources
 Khan Academy: Video tutorials on scatter plots.
 YouTube: Search for “Scatter plots and correlation” for visual guides.
 BBC Bitesize: Interactive exercises on creating and interpreting scatter plots.
These notes should provide a strong foundation in understanding and working with scatter plots in Mathematical Literacy.
Reference: Study & Master Mathematical Literacy Study Guide Grade 12 .