Reading Scatter Plots and Correlations

Scatter plots (also called scatter diagrams or scatter graphs) occasionally appear in UCAT QR. They show the relationship between two numerical variables, with each data point plotted as a dot. While less common than tables or bar charts, scatter plot questions can be straightforward if you understand how to read them and identify patterns.

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Anatomy of a Scatter Plot

A scatter plot has:

• X-axis (horizontal): One variable (e.g., hours of study)
• Y-axis (vertical): Another variable (e.g., exam score)
• Data points: Each dot represents one observation (e.g., one student's hours of study and exam score)
• Optional line of best fit: A straight line drawn through the data to show the overall trend

Reading Individual Data Points

To find the values for a specific data point:

1. Identify the point
2. Read horizontally to the y-axis for the y-value
3. Read vertically down to the x-axis for the x-value

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Types of Correlation

Positive Correlation

As one variable increases, the other tends to increase. Points slope upward from left to right.

Example: Hours of study vs exam score — more study generally leads to higher scores.

Negative Correlation

As one variable increases, the other tends to decrease. Points slope downward from left to right.

Example: Distance from city centre vs property price — properties further from the centre tend to be cheaper.

No Correlation

No discernible pattern. Points are scattered randomly.

Example: Shoe size vs exam score — no meaningful relationship.

Strength of Correlation

Strength	Description
Strong	Points cluster closely around the trend line
Moderate	Points show a clear trend but with some scatter
Weak	A slight trend is visible, but points are widely scattered
None	No trend visible; points appear random

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The Line of Best Fit

A line of best fit (also called a trend line or regression line) is drawn to represent the overall trend in the data.

Using the Line of Best Fit

1. To estimate a y-value for a given x-value: Find x on the horizontal axis, move up to the line, read across to the y-axis.
2. To estimate an x-value for a given y-value: Find y on the vertical axis, move across to the line, read down to the x-axis.
3. To determine the rate of change: Calculate the gradient (rise ÷ run) of the line.

Interpolation vs Extrapolation

• Interpolation (within the data range) is generally reliable
• Extrapolation (beyond the data range) is less reliable — the relationship may not hold outside the observed range

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Identifying Outliers

An outlier is a data point that sits far from the general pattern.

How to Spot Outliers

• Look for points that are clearly separated from the main cluster
• If a line of best fit is drawn, outliers are far above or below the line

Questions About Outliers

• "Which data point is an outlier?" → Identify the point furthest from the trend
• "If the outlier is removed, how does the average change?" → Recalculate the average without that point

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Calculations from Scatter Plots

Reading Specific Values

Question: "What is the exam score of the student who studied for 6 hours?"

Find the data point at x = 6 and read the y-value.

Counting Points in a Region

Question: "How many students scored above 70?"

Count all data points above the y = 70 line.