Statistics & Scatter Plots
Explore bivariate data, draw scatter plots, identify correlation, and use lines of best fit to make predictions.
Bivariate Data
Bivariate data involves two variables measured on the same set of items. We use scatter plots to display the relationship between these two variables.
Key Terms
Example: Studying hours (x) vs exam score (y). As hours increase, we expect scores to increase — a positive relationship.
Types of Correlation
Correlation describes the strength and direction of a linear relationship between two variables.
Positive Correlation
As x increases, y increases. Points trend upward from left to right.
Negative Correlation
As x increases, y decreases. Points trend downward from left to right.
No Correlation
No clear pattern between x and y. Points are scattered randomly.
Strong Correlation
Points cluster closely around the line of best fit.
Weak Correlation
Points are more spread out from the line of best fit.
Line of Best Fit
A line of best fit (or trend line) is a straight line drawn through the data that best represents the overall trend. It should have roughly equal numbers of points above and below.
Example: Drawing a Line of Best Fit
Step 1: Plot all data points on a scatter plot.
Step 2: Look at the overall direction of the data.
Step 3: Draw a straight line that passes through the middle of the data, with roughly equal points above and below.
Step 4: Use two points on the line to find its equation: y = mx + c.
Warning: Do not use the line of best fit to predict values far outside the data range. This is called extrapolation and can be unreliable.
Knowledge Check
Test your understanding of scatter plots and correlation.
Question 1
What type of data involves two variables measured on the same items?
Question 2
On a scatter plot, which axis should the independent variable be plotted on?
Question 3
A scatter plot shows points trending downward from left to right. What type of correlation is this?
Question 4
Which of these pairs of variables would you most expect to show a positive correlation?
Question 5
A line of best fit has the equation y = 2x + 5. Predict the value of y when x = 8.
Question 6
What is the term for a data point that does not fit the general pattern of a scatter plot?
Question 7
A scatter plot shows points that are closely packed around the trend line. What does this indicate?
Question 8
Using a line of best fit to predict values far outside the range of data is called:
Question 9
A line of best fit passes through (2, 10) and (6, 22). What is the gradient (slope) of the line?
Question 10
A researcher finds a strong positive correlation between hours of sunshine and number of visitors at a beach. Can they conclude that sunshine causes more visitors?
Key Concepts Summary
- ●Bivariate data involves two variables; displayed on a scatter plot.
- ●Correlation can be positive, negative, or none, and strong or weak.
- ●A line of best fit summarises the trend and can be used for predictions.
- ●Interpolation (within data range) is more reliable than extrapolation (outside data range).
- ●Correlation does not imply causation — always consider other factors.