12.5 Visualising and Interpreting Data
You already know pictographs, bar graphs, clustered-bar graphs and dot plots. Now we add the sharpest tool for showing change over time: the line graph.
Line graphs
A line graph marks each data point and links consecutive points with straight segments. The horizontal axis usually carries time (months, years), and the vertical axis carries the quantity being tracked. The slope of each segment narrates the story: a steep rise signals a quick increase, a flat segment signals little change, and a downward slope signals a decrease.
Here is a simple two-series line graph comparing the monthly maximum temperature of two regions.
How is a single “monthly maximum” temperature obtained for a whole region? A handful of weather stations across the region log the local temperature each day, and the highest reading recorded in a month becomes that month’s maximum. Knowing how the numbers were gathered helps us judge how far to trust them.
A two-step way to read any graph
Reading a Graph in Two Steps Step 1, Identify what is given. What does each axis show? What scale is used? How are the two series told apart (colour and marker shape, so it still works in black-and-white)?
Step 2, Infer and interpret. Put the trends into words, then turn each observation into a clear conclusion. Finally, let the graph stir up new questions worth chasing.
For the temperature graph above, a careful reading might run:
- Region B climbs steadily from January to a peak near 38\,^\circ\text{C} in June, eases a little through the monsoon, then slides without pause to about 23\,^\circ\text{C} by December. Its lowest monthly maximum, about 19\,^\circ\text{C}, is in January.
- Region A is remarkably flat all year, topping out near 33\,^\circ\text{C} in April and dipping to about 29\,^\circ\text{C} in July. Its summer and winter maxima barely differ.
- In short, Region B swings far more than Region A, getting both colder and hotter than it.
These observations naturally raise questions: Why are the two trends so different? What sets a region’s temperature? Which other regions behave like B?
Math Talk: Crowded Orbits A line graph of the yearly number of objects launched into orbit for the world and a few countries can reveal plenty. When you read one, ask:
- Do the country counts add up to the world count? If not, other countries must be left out.
- For one country, in which year was the jump biggest? (Hunt for the steepest segment, not the tallest point.)
- The graph also guards against over-claiming: “the count rose every year” only holds if no segment tilts downward.
Once you grasp how the data was collected, you can decide how confidently to draw conclusions, and notice bias or gaps.
Why a line graph (and not 52 bars)?
Imagine displaying 13 years of launches for 4 countries as a clustered-column graph: that’s 13 \times 4 = 52 bars jammed side by side, crowded and hard to follow. A line graph stitches the dots into clean trend lines, so the eye can trace change over time in one sweep. That is exactly what line graphs are built for.
Catch the pattern in rain
A bunch of line graphs showing monthly average rainfall for several cities tells a monsoon tale. Cities on the west coast soak up their heaviest rain during June–August from the south-west monsoon. Cities on the east coast peak later, around October–December, under the north-east monsoon. Sorting the line graphs this way makes the geography of rainfall pop out, west-coast lines spike early, east-coast lines spike late.
Figure it Out: Line Graphs
Practice
The table shows the average number of customers entering a shop and buying something over a week. Draw both as line graphs on the same axes.
Mon Tue Wed Thu Fri Sat Sun Entering 16 19 10 14 20 22 35 Buying 10 8 7 11 12 16 26 The table gives the average number of rainy days per month for two cities. (i) How might such data be compiled? (ii) Plot the cities on a line graph (round to whole days). (iii) From a city’s line, read off intermediate monthly values. (iv) Which city sees rain on more days per year? (v) When is each city’s rainy season?
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Coastside 0.1 0 0.1 1.8 6.2 24.1 27.7 24.5 14 8.8 3.9 0.9 Bayport 2.6 1.3 1.9 3.4 2.5 0.4 1 1 1.9 8.1 10.4 7.8 A line graph shows the number of births per month in a country over several years. (i) What do you notice? (ii) Roughly how many births in July of the second year? (iii) What span of time does the graph cover? (iv) Compare January births across three consecutive years. (v) Estimate the total births in the middle year.
- Put days along the horizontal axis and “number of customers” up the vertical axis. Draw two lines, one for entering, one for buying, with different markers or colours. Both rise toward the weekend, peaking on Sunday (35 entering, 26 buying). The buying line stays below the entering line throughout; the gap is the count of visitors who looked but didn’t buy, widest on Sunday (35 - 26 = 9).
- For each month, count the days it rained, averaged over several years. (ii)/(iii) Plot each city’s 12 values, join them, and read intermediate heights straight off a city’s line. (iv) Coastside has the most rainy days per year, its monsoon months alone clear 90 days, while Bayport’s yearly total is far lower. (v) Coastside’s rainy season is June–August (a sharp peak); Bayport’s is October–December (a later, smaller peak), with January–September mostly dry.
- Answers depend on the given graph. General recipe: (i) note rising/falling stretches and any repeating seasonal dips; (ii) read the July point off the vertical scale; (iii) the span runs from the first to the last labelled time on the horizontal axis; (iv) read the three January points and compare their heights; (v) add the twelve monthly values of that year (or estimate 12 \times the average monthly height).