Schooling · Class 8 · Mathematics · Tales by Dots and Lines · Chapter on a page
CBSE Class 8 · Mathematics · NCERT Ganita Prakash Part-II
Tales by Dots and Lines: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- graph
- bar graph
- double bar graph
- line graph
- horizontal axis
- scale
- trends
- Formulas and facts
- Scale rule
- Reading a point
- Bar width
- Choosing scale
- Trend direction
- Double bar graph spacing
- Watch out for
- Forgetting to label the axes
- Using unequal gaps between…
- Connecting points in a bar graph
- Choosing a scale that makes all bars…
- Joining points in random order in a…
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.
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.
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.