Line graphs and trends

What was the maximum temperature in your city each month of last year? A column of numbers doesn't help much. But plot them , month on the horizontal axis, temperature on the vertical axis , and connect the dots with line segments, and you instantly see the summer peak, the winter dip, and the wobbles in between. That is a line graph, the standard tool for visualising data over time.

Concept

A line graph is a 2-dimensional plot where:

• the horizontal axis records ordered categories (most often time , days, months, years),
• the vertical axis records a measured quantity (temperature, rainfall, marks, population).

For each pair (category, value) you place a point, and then connect adjacent points with straight line segments.

Why line graphs work. The slope between two adjacent points tells the story:

• a steep upward slope says the quantity rose quickly,
• a gentle slope says the change was small,
• a flat segment says no change,
• a downward slope says the value fell.

A two-step process for reading any data graph.

Step 1 , Identify what is given. Notice the title, the axes' labels and scales, the units, and which series of points belongs to which category. If two cities' temperatures are drawn together, use the legend to tell them apart.

Step 2 , Infer and interpret. Look for the highest peak, the lowest dip, the longest steady stretch, the steepest rise and fall. Then ask why , what real-world reason explains that pattern?

Trends to look for.

• Rising trend , values generally increase over time.
• Falling trend , values generally decrease.
• Cyclic / seasonal , a pattern that repeats, like temperature each year.
• Spike or outlier , a single unusually high or low point , often worth investigating.

Multiple lines on one chart. When two series are drawn together (e.g., Kerala's and Punjab's temperatures), the chart makes comparison easy. Which line is higher on average? Which line fluctuates more? Where do they cross?

Choosing the right scale. Always glance at the vertical axis: does it start from $0$? If not, small changes can look exaggerated. A graph that goes from $28^\circ$ to $33^\circ$ on the axis may look very dramatic but represents a swing of only $5^\circ$.

When to use a line graph.

• The horizontal axis is naturally ordered (most often time).
• You want to show change, growth, or comparison of trends.

When a line graph misleads.

• The categories are not ordered (e.g., favourite fruits) , use a bar chart.
• There are very few points , a table or dot plot is clearer.

Worked examples

Example 1. A line graph shows a city's monthly maximum temperature, peaking at $38^\circ$C in June and dipping to $19^\circ$C in January. Describe the trend.

• Rises from January to June, peaks at $38^\circ$ in June, then falls from July to December, reaching about $19^\circ$ in January. This is a typical Indian summer-heavy seasonal pattern.

Example 2. Two line graphs are given side-by-side: Kerala (almost flat, $29-33^\circ$ all year) and Punjab (steep peak in June at $38^\circ$, low of $19^\circ$ in January). Which state has more temperature variation?

• Punjab , its peaks and dips swing much further from the mean.

Example 3. A student's quarterly marks over a year are $60, 65, 72, 80$. Plot and describe.

• Each quarter is higher than the previous , a steady upward trend, gaining $5, 7$, then $8$ marks. The student is improving, and accelerating.

Example 4. A line graph shows daily online lesson attendance for two weeks. The plot rises from $20$ on day $1$ to $45$ on day $5$, drops to $10$ on day $7$ (a Sunday), rises again to $50$ on day $12$. Identify the pattern.

• Weekend dip , attendance falls every Saturday and Sunday and rises during the school week. The cycle repeats weekly.

Try it yourself

1. A line graph rises steadily from January to June, then falls. What real-world quantity could it represent?
2. A line graph stays nearly flat through the year. Describe what that tells you about the underlying quantity.
3. If two lines on the same chart cross at March, what does that mean?
4. A vertical axis runs from $28$ to $33$. Why might this be misleading at a glance?
5. Daily rainfall is given for $10$ days: $0, 5, 12, 3, 0, 0, 18, 25, 7, 0$. Sketch a line graph and find the peak day.
6. Yearly population (in lakhs) of a town: $2, 2.4, 3, 3.5, 4.2$. Describe the growth pattern.
7. Why is a line graph not suitable for showing "students' favourite sports"?
8. In a graph of monthly temperature, the slope between February and March is steepest. What does that tell you?

Activity

Weather diary. For two weeks, note the maximum temperature in your city every day (use the newspaper, a weather app, or just an outdoor thermometer at the same time each day). On the $15$th day, draw a line graph with day-of-month on the horizontal axis and temperature on the vertical. Mark the peak day and the coldest day. Were they part of a longer trend, or one-off changes? Write two sentences interpreting your graph.