Multiple Line Graphs — Explained
Detailed Explanation
What information does each line represent?
A multiple line graph shows how two or more series change along a shared horizontal axis, often time. Each plotted point gives a value at a specified horizontal position, and connecting segments help reveal patterns. The legend identifies the series; the vertical axis gives the unit and scale. A line's colour or height is not a complete observation without these labels.
Begin by distinguishing levels from changes. A series can remain above another while growing more slowly. A line can fall while still representing a positive quantity. If the vertical axis shows a growth rate, a downward-sloping positive rate means growth is slowing, not necessarily that the underlying total is shrinking. Read what is plotted before describing a trend.
How can the main comparisons be worked out?
Use an original three-year dataset. Service A handles 80, 100 and 120 thousand applications in Years 1, 2 and 3. Service B handles 90, 95 and 130 thousand. A has equal annual increases of twenty thousand. B increases by five thousand and then thirty-five thousand. A leads in Year 2, but B leads in Years 1 and 3.
Across the full interval, A rises by forty thousand and B by forty thousand. Their absolute increases are equal, but A's proportional increase is 40/80 = 50 per cent while B's is 40/90, about 44.44 per cent. Comparing the starting and ending gaps alone does not describe the intervening Year 2 reversal. A trend summary should identify the period and measure being compared.
What does the slope tell us?
Slope is change in vertical value divided by change in horizontal value. If the time intervals are equal and both series share the same vertical scale, a steeper rising segment represents a larger increase per unit time. If one interval spans one month and another spans three months, compare rates over those durations rather than raw vertical changes.
Suppose output rises from 60 to 90 units over three months, then from 90 to 110 over one month. The first interval adds thirty units, but its average rate is ten units per month. The second adds only twenty units, yet its average rate is twenty per month. A graph with evenly spaced category labels could conceal this distinction if the actual time gaps are unequal. Dates, rather than visual spacing alone, define elapsed time.
When can an intersection be interpreted numerically?
An intersection of two lines on the same axes indicates equal plotted values at that location under the graph's representation. It does not necessarily identify an observed equality between sampled dates. Connecting points with straight lines often implies a visual interpolation; real values between observations could follow a different path. Use linear interpolation numerically only when the question supplies or permits that assumption.
For example, A changes from 100 to 120 and B from 95 to 130 between Years 2 and 3. The gap A minus B changes from 5 to -10. Under linear interpolation, equality occurs one-third of the way through the interval, because the initial gap of 5 closes at a relative rate of 15 per interval. Without that assumption, the exact crossing date cannot be recovered from the two endpoint pairs alone.
How should indices and percentage graphs be read?
An index often assigns a base-period value of 100. If Series X rises from index 100 to 150 and Series Y from 100 to 130, X has grown more proportionally since the base period. This does not prove that X has the larger absolute quantity. X could have started at 200 units and reached 300, while Y started at 1,000 and reached 1,300.
Similarly, two lines showing percentages require denominators before counts can be compared. A 70 per cent pass rate among one hundred candidates represents seventy passes; a 60 per cent rate among two hundred represents one hundred and twenty. The lower line can therefore correspond to the larger count. A chart of rates answers rate questions directly, but it may not contain enough information for a question about the corresponding totals.
What changes when a second vertical axis is used?
A dual-axis chart can place two series with different units or scales in the same plotting area. One line might show rainfall in millimetres and another output in tonnes. Their visual crossing does not mean equal numerical values, and their apparent relative slopes cannot be compared as if the units were the same. Read each series against its assigned axis.
Even with the same unit, separately scaled axes can create a misleading impression of close tracking. Co-movement also does not establish causation. A graph may suggest a relationship worth investigating, but omitted influences, seasonal patterns or changes in measurement can account for the association. In an aptitude answer, distinguish what the displayed data establish from an explanation that would require additional evidence.
How can totals and averages be calculated safely?
For discrete annual quantities, a total over the listed years can be obtained by adding those annual values when they refer to non-overlapping periods and the same unit. For the original example, A's three-year total is 300 thousand and B's is 315 thousand. Averaging their plotted annual counts is also meaningful under that interpretation. Adding monthly cumulative totals would instead count earlier activity repeatedly.
If the line represents a rate measured at particular instants, adding the sampled heights does not directly give a cumulative quantity. Duration and assumptions about the values between samples are needed. Read labels such as 'during the year', 'as at year-end' and 'cumulative to date'. They determine whether summing the points is valid.
What is the final checking routine?
Identify the series, scale, unit and interval; extract the required points; then choose level, difference, ratio or rate of change. Check whether interpolation, aggregation or a causal claim adds an assumption. Use the smallest calculation that answers the actual question, and retain uncertainty when the chart does not determine a unique value.
The strongest reading separates observations from interpretation. A line can show equal total increases with unequal percentage growth, a temporary ranking reversal or a faster rate over a shorter interval. Naming those distinctions makes an answer precise and prevents the visual shape of a graph from replacing the quantities that it represents.