Tales by Dots and Lines · Lesson 8 of 13
Reading and Drawing Line Graphs
“Read axes and legends, describe change over time, and construct a two-series line graph.”
• Identify the variables, units, scale, and legend of a line graph. • Read values and compare variation across time. • Construct a line graph from a two-series table. • Explain what joined points do and do not show.
A list of twelve monthly temperatures gives individual numbers, but it can take time to see the year’s pattern. A line graph puts time along one axis and the measured quantity along the other. Connected points help your eyes follow rises, falls, and flatter periods.
Before interpreting a pattern, identify what each point actually represents. A monthly maximum, a monthly total, and a monthly average are different measurements. A graph can be drawn neatly and still be misunderstood if its labels are skipped.
Line Graphs
A line graph plots pairs of values, usually an ordered time and a measured quantity. Points belonging to the same series are joined in time order. The horizontal axis commonly shows time, and the vertical axis shows the quantity with its unit.
A two-series graph needs a legend. Different colours help, but different point shapes or line patterns make the series distinguishable when colours are hard to see. Equal numerical intervals on an axis should have equal spacing.
A connected set of observations measured for the same quantity or group across the displayed times.
Temperature
The following redraw shows the chapter’s temperature pattern for Kerala and Punjab. Values are rounded visual readings, so use them for approximate comparisons. The label describes monthly maximum temperature; it does not give the temperature at every place or on every day.
Kerala’s values remain in a fairly narrow band through the year. Punjab’s values rise strongly towards the middle of the year and fall afterwards. We can describe these visible differences without assuming that the graph alone explains their causes.
Problem
Identify the main features of the temperature graph.
- 1.The horizontal axis lists January through December in order.
- 2.The vertical axis is temperature in degrees Celsius, labelled from 0 to 40.
- 3.The two series are Kerala and Punjab, identified by different colours and point shapes.
- 4.Each point is a monthly maximum-temperature value in the displayed dataset, not a daily reading.
Identify, Then Interpret
Use two passes. First identify the title, population or place, period, axes, units, scale, and series. Then interpret: locate peaks, compare values at the same time, describe changes within a series, and summarise the overall pattern.
Questions about how the data was collected come next. Which stations contributed? How was a state-level value assembled? Were all places measured in the same way? Metadata about collection helps us understand the scope and limits of the graph. A title alone may not answer these questions.
Problem
Which series varies more across the year, and approximately how much?
- 1.Read Punjab’s lowest value as about 19°C in January and its highest as about 38°C in June.
- 2.The difference is about 38 − 19 = 19°C.
- 3.Kerala ranges roughly from 29°C to 33°C, a difference of about 4°C.
- 4.Punjab shows greater variation in the displayed monthly maxima. This does not give the daily minimum temperatures.
Drawing from a Table
A shop records daily visitors and daily purchasers. The two counts share the same unit, people, and the same seven days, so they can use one set of axes. Keep days in order, choose a scale that reaches the largest count, and plot each series separately before joining its points.
| Day | Visitors | Purchasers |
|---|---|---|
| Mon | 16 | 10 |
| Tue | 19 | 8 |
| Wed | 10 | 7 |
| Thu | 14 | 11 |
| Fri | 20 | 12 |
| Sat | 22 | 16 |
| Sun | 35 | 26 |
Problem
Explain a suitable construction method for the table.
- 1.Draw seven equally spaced day positions on the horizontal axis.
- 2.Use a vertical scale from 0 to 40 people, with equal intervals such as 10 people.
- 3.Plot the visitor points: Monday at 16, Tuesday at 19, and so on. Join them in day order.
- 4.Plot and join the purchaser points using a different shape or line pattern.
- 5.Add a clear title, the vertical unit, and a legend. Check Sunday’s points at 35 and 26 against the table.
Problem
Find the largest visitor–purchaser gap and the largest day-to-day increase in visitors.
- 1.Subtract purchasers from visitors for each day: 6, 11, 3, 3, 8, 6, 9.
- 2.The largest gap is 11 people on Tuesday.
- 3.Visitor changes are +3, −9, +4, +6, +2, and +13.
- 4.The largest increase is 13 visitors from Saturday to Sunday. A high value and a large increase answer different questions.
What the Joining Line Means
The line between Monday and Tuesday makes the direction of change visible. It does not mean the shop literally had fractional daily visitors at every point along that segment. Only the plotted observations are recorded daily counts.
A straight segment may support an estimate between observations in some measurement settings, but it is not proof of what happened there. Likewise, a line crossing another line between two days does not establish an observed equality on a recorded day. Always connect your claim to the times actually measured.
Make Your Own Time Graph
Collect one manageable quantity for five consecutive days, such as the number of pages you read.
- Define the quantity and use the same counting rule each day.
- Make a table with dates and values.
- Choose a scale and plot the points in time order.
- Write one observation about a value and one about a change.
Your title, dates, and unit should allow another person to read the graph without asking what the numbers mean. If a day is missing, show that honestly instead of inventing a count.
Quiz
What must a graph’s vertical axis label tell you?
Which series has greater yearly variation in the displayed temperature graph?
How many purchasers are recorded on Thursday?
What is the visitor increase from Saturday to Sunday?
Why use different shapes as well as colours for two series?
A number such as 20 is meaningful only when the measured quantity and unit are clear.
Practice Problems
- Find the visitor–purchaser gap on Friday.
- Find the total number of purchasers during the week.
- Describe Punjab’s approximate change from January to June.
- Choose a suitable vertical scale for daily values 4, 9, 11, 6, 13.
- Two lines cross halfway between Tuesday and Wednesday. Does that prove the recorded Tuesday counts were equal?
- Explain why the highest point and steepest upward segment need not occur together.
Step 1: Friday has 20 visitors and 12 purchasers. Step 2: The difference is 20 − 12 = 8 people.
Key Takeaways
• Read labels, units, scale, time period, and legend before interpreting a graph. • Line graphs make change across ordered time easier to follow. • Compare values at the same time and changes over the same duration. • Plot accurately from a table and distinguish every series. • Joined segments do not create extra observed data.