What this chapter is about
This chapter introduces you to the world of representing data visually using dots and lines. When we collect information about things around us — like temperatures over a week, runs scored in cricket matches, or prices of vegetables — we can tell a story through pictures called graphs. Instead of looking at long lists of numbers, graphs let us see patterns, compare values, and understand changes at a glance.
At this stage, you learn to read and draw different types of graphs: pictographs, bar graphs, double bar graphs, and especially line graphs. A line graph connects data points with straight lines and is very useful when data changes over time — like how your height increases year by year, or how the temperature rises and falls during a day.
After studying this chapter, you should be able to read information from graphs, draw your own graphs on paper, choose the right type of graph for a situation, and understand what the dots and lines are telling you about the data.
Key ideas
- A graph is a picture that shows numerical information in a way that is easy to understand and compare.
- A bar graph uses rectangular bars of equal width to represent different values; the height of each bar shows the size of that value.
- A double bar graph shows two sets of related data side by side, making comparison easy — for example, comparing boys and girls in each class of a school.
- A line graph uses points connected by straight lines to show how data changes, usually over time; the horizontal axis often shows time and the vertical axis shows the quantity being measured.
- On any graph, the horizontal axis (going left to right) and the vertical axis (going up and down) must be labelled clearly so readers know what is being shown.
- The scale is the value each small division represents on an axis; choosing a good scale makes the graph easy to read without being too large or too small.
- Line graphs are especially useful for showing trends — whether something is increasing, decreasing, or staying the same over a period.
- When data points are connected by lines, the steeper the line, the faster the change between those two points.
Formulas and facts to remember
- Scale rule: If 1 cm on the axis represents 10 units, then a value of 45 is plotted at 4.5 cm from the origin.
- Reading a point: Locate the point, then read its horizontal position (x-value) and vertical position (y-value) from the axes.
- Bar width: In a bar graph, all bars must have the same width; only heights differ.
- Choosing scale: Pick a scale so the largest value fits comfortably on your paper — divide the largest value by the space available.
- Trend direction: If the line goes upward from left to right, values are increasing; if it goes downward, values are decreasing; if flat, values are constant.
- Double bar graph spacing: Keep the two bars for each category touching or close together, with a gap before the next category.
Worked examples
Example 1: Drawing a line graph for temperature
The temperature (in °C) recorded at noon on five days of a week was: Monday 28, Tuesday 30, Wednesday 32, Thursday 29, Friday 31.
Step 1: Draw the horizontal axis and label it "Day". Mark Monday to Friday at equal intervals.
Step 2: Draw the vertical axis and label it "Temperature (°C)". Since values range from 28 to 32, choose a scale starting at 26, going up to 34, with each 1 cm representing 2°C.
Step 3: Plot each point — Monday at height 28, Tuesday at 30, and so on.
Step 4: Connect the points with straight lines in order from Monday to Friday.
The line graph shows temperature rose from Monday to Wednesday, dropped on Thursday, then rose again on Friday.
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Example 2: Reading a double bar graph
A double bar graph shows the number of students who passed in Maths and Science in three sections: Section A (Maths 35, Science 32), Section B (Maths 40, Science 38), Section C (Maths 28, Science 30).
Question: In which section did more students pass in Science than in Maths?
Solution: Compare the two bars for each section. In Section A, Maths (35) is more than Science (32). In Section B, Maths (40) is more than Science (38). In Section C, Science (30) is more than Maths (28).
Answer: Section C.
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Example 3: Choosing a scale
Ravi wants to draw a bar graph for the runs scored by five batsmen: 120, 85, 150, 95, 130. His graph paper is 15 cm tall.
Step 1: The highest value is 150. To fit this in 15 cm, he can use 1 cm = 10 runs (since 150 ÷ 10 = 15 cm).
Step 2: Now 120 runs = 12 cm, 85 runs = 8.5 cm, and so on.
This scale makes the graph neat and easy to read.
Common mistakes
- Forgetting to label the axes → always write what each axis represents and include units.
- Using unequal gaps between categories on the horizontal axis → keep spacing uniform.
- Connecting points in a bar graph → bar graphs use separate bars, not lines; lines are for line graphs.
- Choosing a scale that makes all bars almost the same height → pick a scale that starts near zero so differences are visible.
- Joining points in random order in a line graph → always connect points in the correct sequence (usually left to right by time).
Quick revision
- A bar graph uses bars; a line graph uses dots connected by lines.
- Line graphs show change over time; steeper lines mean faster change.
- Always label both axes and mention the scale you used.
- Double bar graphs compare two related sets of data side by side.
- Choose a scale so your largest value fits comfortably on the paper.
- Read graphs carefully — look at both axes before answering questions.