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Line graphs appear in approximately 1–2 of the 9 QR data sets. They typically show how a quantity changes over time, making them ideal for questions about trends, rates of change, and comparisons between time periods. This lesson covers reading values accurately, identifying trends, interpolating between data points, and comparing multiple lines.
Line graph values are often more precise than bar chart values because the data points are marked (with dots, crosses, or diamonds). If a point falls between gridlines:
| Trend | Description | Visual |
|---|---|---|
| Increasing | Values go up over time | Line slopes upward left to right |
| Decreasing | Values go down over time | Line slopes downward left to right |
| Stable/flat | Values remain roughly constant | Line is roughly horizontal |
| Fluctuating | Values go up and down | Line has peaks and troughs |
The steepness of the line indicates the rate of change:
Example question: "Between which two months was the rate of increase in sales greatest?"
Answer: Find the segment of the line with the steepest upward slope.
If data points are plotted at January, February, March, etc., a question might ask for a value in "mid-February." Assuming a straight line between February and March data points, read the value at the midpoint.
Example: February value = 340, March value = 380.
Mid-February to mid-March value at mid-point = (340 + 380) ÷ 2 = 360.
But if the question asks for "mid-February" specifically, it is the midpoint between the January data point and the February data point.
Extrapolation extends the trend beyond the plotted data. If a line shows a steady increase of 20 per month and the last plotted month is June at 280, an extrapolation to July would give approximately 300.
Caution: UCAT questions that require extrapolation will usually state the assumption (e.g., "If the trend continues at the same rate..."). Without such a statement, do not extrapolate.
Many QR line graphs show two or more lines on the same axes. Questions may ask:
The x-value where two lines meet. At this point, the two quantities are equal.
Read the y-values of both lines at the specified x-value and compare.
Calculate the increase for each line (end value − start value) and compare.
Visually compare the slopes. The steeper line has a greater rate of change.
Formula: Change = Final Value − Initial Value
Example: Sales in January = 200, Sales in June = 350.
Change = 350 − 200 = 150 units increase.
Formula: ((Final − Initial) ÷ Initial) × 100
Example: ((350 − 200) ÷ 200) × 100 = (150 ÷ 200) × 100 = 75% increase
Formula: Total Change ÷ Number of Time Periods
Example: Sales increased by 150 over 5 months.
Average monthly increase = 150 ÷ 5 = 30 per month
Example: "In which month did sales first exceed 300?"
Trace along the line until it crosses the y = 300 level. Read the x-axis value.
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