Line graphs: reading change over time

From columns to lines

We already know pictographs, bar graphs, clustered column graphs and dot plots. The chapter shows the monthly maximum temperatures of Kerala and Punjab in 2023 first as a clustered column graph and then with each state’s points joined by lines. Both show the same information, but the line graph makes the change from month to month much easier to follow. Line graphs are mostly used for data over time.

Two steps to read any graph

Step 1: identify what is given. Look at the title, what each axis shows (months across, °C up), the scale, and which colour and marker stands for which state. Different marker shapes help when the graph is printed in black and white, or for readers who find colours hard to tell apart. Ask how the data was collected: a state’s monthly maximum comes from the highest reading at its weather stations. Knowing this shows the data’s scope and limits.

Step 2: infer and interpret. Punjab’s maximum climbs from about 19°C in January to 38°C in June, dips just under 35°C in July, stays flat till September and falls to about 23°C by December. Kerala’s stays almost flat, between about 29°C in July and 33°C in April. So Punjab’s temperature varies far more. Good reading also raises new questions, such as why the two states differ.

Space jam

A line graph of objects launched into space each year shows the world total and the counts for the USA, China and Russia from 2012 to 2024. The world count was around 2,900 in 2023 and 2,800 in 2024, so 2023 was the highest. The three countries do not add up to the world count, so other countries are left out. The USA’s line is steeper from 2022 to 2023 than from 2023 to 2024: the steeper the line, the greater the increase.

Some statements are valid inferences and some are not. The USA launched roughly three quarters of all objects in 2022 to 2024, and China and Russia together launched about 400 in 2024. But the world count did not rise every year, and the graph cannot tell us about Nepal at all. Drawn as a clustered column graph, this data would need 52 columns; the line graph shows the trend far more clearly.

Rain through the year

Monthly average rainfall comes from measuring rain for several years and averaging each month. Graphs for six coastal cities show that Kovalam, Udupi and Mumbai on the west coast get much more rain, peaking from June to August, while Rameswaram on the east coast gets most of its rain from October to December and Chennai peaks in November. Puri, though on the east coast, peaks from July to September. January to March is dry everywhere. The number of days of rain tells a similar story.

Drawing a line graph yourself

To draw one, mark the times on the horizontal axis, choose a scale for the vertical axis, plot each value and join the points. For a shop’s average customers, one line for visitors and one for buyers show that Sunday is the busiest day and that buying follows visiting.

A pattern that repeats

A graph of births in India every month from April 2017 to March 2020 shows a wave that repeats each year: births peak at about 2 million a month from August to October and dip to about 1.4 to 1.5 million around April. A repeating shape like this is easy to spot on a line graph.

Infographics and smooth curves

An infographic tells a story in a picture. One map gives each state a value from −100 (mostly wheat) to +100 (mostly rice) and draws a line between the rice-preferring south and east and the wheat-preferring north-west; overall, India scores +13.48, so rice wins. A line graph of typical sleep by age looks like a smooth curve because its points are very close together: about 9.5 hours at age 6, falling to about 8 hours between 30 and 50, then rising to about 8.5 hours.

Read on: the mean as a balancing point, mean and median from a frequency table, the chapter notes and the NCERT solutions.