Data Handling & Probability (VI–VIII) • Topic 2 of 4

Bar Graphs, Pie Charts & Histograms

Once data is tabled, it is pictured — and CTET cares that you match the right chart to the right data. A bar graph uses bars of equal width with gaps between them to compare separate (discrete, categorical) categories such as favourite sports or pupils per class; the bar height shows the frequency. A double bar graph compares two data sets side by side (boys vs girls, this year vs last). A histogram looks similar but is for continuous, grouped data (class intervals) and so has NO gaps between bars — the bars touch, because the intervals are continuous. This 'gap vs no-gap' distinction is a favourite CTET test point and a common student confusion. A pie chart (circle graph) shows how a whole is divided into parts, so it suits data expressed as parts of a total; each sector's angle is (value ÷ total) × 360°, and all the sectors add to 360°. Children's typical errors: leaving gaps in a histogram or removing them from a bar graph, reading the wrong axis, and forgetting that pie-chart sectors must sum to the whole (360° or 100%). NCERT places histograms and pie charts in Class 8 precisely because they need the prior ideas of grouped data and proportion.

✅ Solved examples

1. A school has 720 students. In a pie chart, the sector for students who walk to school has an angle of 90°. How many students walk to school?
Fraction of the circle = 90 ÷ 360 = 1/4. So walkers = 1/4 × 720 = 180 students.
2. In a budget pie chart, food takes ₹4,500 out of a total monthly spend of ₹18,000. What is the angle of the 'food' sector?
Angle = (value ÷ total) × 360° = (4500 ÷ 18000) × 360° = 0.25 × 360° = 90°.
3. A student draws a graph of continuous marks data (intervals 0–10, 10–20, …) and leaves gaps between the bars. What is the error, and what should it be?
Continuous grouped data must be shown as a histogram, where bars touch with no gaps (the class intervals are continuous). Gaps belong to a bar graph, which is for discrete categories. The bars should be drawn adjacent.
4. Which representation best suits the data 'percentage of a family's income spent on rent, food, savings and other'?
A pie chart. The data are parts of one whole (total income = 100%), and a pie chart shows each part as a sector of the whole circle.

✏️ Practice — try these, take hints as needed

1. A pie chart represents 60 books. The 'fiction' sector has an angle of 120°. How many fiction books are there?
Fraction = 120 ÷ 360 = 1/3.
Multiply the fraction by 60.
20 books
2. The key visual difference between a bar graph and a histogram is:
One is for discrete categories, the other for continuous intervals.
Think about the gaps between bars.
A bar graph has gaps between bars (discrete data); a histogram has no gaps — bars touch (continuous grouped data)
3. In a pie chart of 1,080 voters, a candidate's sector is 60°. How many voters does that represent?
Fraction = 60 ÷ 360 = 1/6.
1/6 of 1,080.
180 voters
4. All the sector angles of a correctly drawn pie chart must add up to what?
It is a full circle.
Or 100% of the whole.
360 degrees

📝 Topic test — 8 questions

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