Line Graphs

A picture of change

A bar chart compares separate things — cats, dogs, fish — that have no order and no "in between". But lots of data is different: it is one thing measured again and again as time goes by. The temperature every hour. Your height every birthday. A plant, taller each week. Here the readings do have an order, and there really is an in-between: half past two sits between two o'clock and three o'clock.

A line graph is built for exactly this. You plot each reading as a point — time along the bottom, the measured value up the side — and then you join neighbouring points with straight lines. The joined line has a shape, and that shape is the whole prize: at a glance you can see the value rising, falling, holding steady, or climbing to a peak and sliding into a dip.

This overall shape — the story of up, down or steady — is called the trend. A bar chart answers "which is biggest?"; a line graph answers a richer question: "which way is it going?"

sun Scatter five lonely points on a grid and your eye has to hop from one to the next, guessing the pattern. Join them and the pattern is simply drawn for you: the line tilts up when things grow, tilts down when they shrink, and levels off when nothing changes. The slope of each little segment is the change made visible — steep for a fast change, gentle for a slow one. That is why a line graph is the natural picture of a temperature through a day: warming all morning, a peak at midday, cooling into the evening — a single climbing-then-falling line tells the story in one look.

Reading a line graph

Step through this temperature graph: first the two axes, then a point for each reading, then the joining line. Watch how the shape appears only once the points are joined.

Worked example. Reading off the finished graph above:

To read a value, go up from the time to the line, then across to the side axis. At 12{:}00 the temperature is 18^\circ\text{C}.
To read a change, read both values and subtract. From 6{:}00 to 12{:}00 the temperature rose by 18 - 8 = 10^\circ\text{C}.
The peak (the highest point) is 20^\circ\text{C} at 15{:}00. After that the line falls: 20 - 14 = 6^\circ\text{C} cooler by 18{:}00.
The trend in words: warming through the morning, peaking mid-afternoon, then cooling into the evening.

Reading between the points (interpolation). Because the scale is continuous, you can read a time that was never actually measured. Halfway between the 12{:}00 point (18^\circ) and the 15{:}00 point (20^\circ), the line passes through about 19^\circ\text{C} — a fair estimate for 13{:}30. The joining line is our best guess for the in-between moments.

Watching something grow

Time need not be clock time. Any steady, continuous scale works — days, weeks, months. A classic is a plant measured once a week: its height only ever goes up, so the line only ever climbs. A steep stretch of line means a fast-growing week; a flat stretch means it barely grew.

A sunflower is measured every Sunday. Its heights, in centimetres, are:

Week 1: 4 · Week 2: 9 · Week 3: 17 · Week 4: 24 · Week 5: 27

Plotted and joined, the line rises the whole way — an upward trend. But the steepness tells the finer story: the jump from week 2 to week 3 is 17 - 9 = 8\,\text{cm} (the steepest, fastest-growing week), while week 4 to week 5 is only 27 - 24 = 3\,\text{cm} — the line flattens as the sunflower slows down. Total growth over the month: 27 - 4 = 23\,\text{cm}.

Line graph or bar chart?

The two charts answer different questions, so picking the right one matters. Use a line graph when the horizontal axis is a continuous scale — above all time — and the "in between" makes sense: temperature through a day, height over weeks, a price over months. Use a frequency bar chart when the horizontal axis is separate categories with no order and no in-between: favourite fruit, eye colour, type of pet. You would never join the top of the "cat" bar to the top of the "dog" bar — there is nothing halfway between a cat and a dog!

Only join points when the in-between makes sense. A line graph promises that halfway along a segment is a real halfway value. That is true for temperature over time, but nonsense for categories — so join for continuous data, and never for a bar chart's separate bars.
Check the scale before you read a value. If the side axis ticks go up in 2s (or 5s, or 10s), a point one square above the 10 tick reads 12, not 11. Read the line against the axis, not by how high it "looks".
The trend is the shape, not a single point. One dip in a mostly-rising line does not make the trend "falling". Step back and read the overall direction.

Try it: a graph that changes

Here is a fresh week of daily readings. Press Play to plot the points and draw the joining line, then read the trend from its shape — is it mostly rising, mostly falling, or just wobbling along level? Read the highest and lowest points off the side axis, and work out the change from the first day to the last. Press Refresh for a brand-new week.