Maths Literacy Matric Revision: Scatter plots

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

  1. Definition and Components of Scatter Plots:
  2. Scatter plots are graphs that show the relationship between two variables.
  3. Each data point is plotted as a dot on the graph.
  4. The x-axis and y-axis represent the two variables being compared.

  5. Drawing Scatter Plots:

  6. Organize data in a table format.
  7. Plot each pair of values on the graph.
  8. Label the axes appropriately.

  9. Correlation:

  10. Positive Correlation: As one variable increases, the other also increases.
  11. Negative Correlation: As one variable increases, the other decreases.
  12. No Correlation: No visible pattern in the data points.

  13. Line of Best Fit (Trend Line):

  14. A straight line that best represents the data on a scatter plot.
  15. It minimizes the distance between the line and all the points.
  16. Can be used to make predictions.

Real-World 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 x-axis and the response variable on the y-axis.
  • Ignoring Outliers: Not recognizing outliers can skew data interpretation. Identify and understand outliers before drawing conclusions .

Practice and Review

Practice Questions:

  1. 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 |

  2. Interpret the scatter plot:

  3. Determine the type of correlation.
  4. Predict the exam score if a student studies for 5 hours.

Solutions:

  1. Drawing the Scatter Plot: Plot each data point and draw a line that balances the upper and lower points.
  2. Interpreting the Plot:
  3. The correlation is positive.
  4. 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.
  • Real-World Implications: Understanding data trends can be useful for market analysis, scientific research, and everyday decision-making.

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 .

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