Pie Chart & Histogram — REET Maths Notes
Pie charts and histograms test how well you can read and build visual data in REET Maths. This page covers the sector-angle formula, the histogram-vs-bar-graph difference, and fully solved REET 2024 questions.
- 2 questions in REET 2024
- Class 8 level
- 6 min read
How REET asks this topic
REET 2024 carried one question that tested the concept directly — in a histogram, what is the height of each bar proportional to (answer: frequency) — and a second question where you had to find the total amount from one given slice of a pie chart (savings at 15% = ₹3,000) and then work out the value of a different slice (food at 25%). So expect both concept-based and calculation-based questions from this topic.
What Is a Pie Chart
A pie chart shows the different parts of a data set as sectors (slices) of a circle, where each sector's angle is proportional to that part's share of the whole. The formula for finding any item's angle is: sector angle = (value of that item ÷ total value) × 360°.
Steps to draw a pie chart: first find the total of all items, then work out each item's angle using the formula above, and finally use a compass and protractor to mark the sectors on the circle. The angles of all sectors must always add up to 360°.
Example: Pie Chart of a Class Survey
| Favourite Sport | Percentage | Angle |
|---|---|---|
| Cricket | 40% | 144° |
| Football | 25% | 90° |
| Kabaddi | 20% | 72° |
| Others | 15% | 54° |
Check: 40+25+20+15=100%, and 144+90+72+54=360° — both totals must come out right.
Solved Example (Based on REET 2024)
In a pie chart, a family's monthly savings are shown as 15%, which equals ₹3,000. Total monthly amount = 3,000 × 100/15 = ₹20,000. Spending on food is 25%, so food expense = 25% of 20,000 = ₹5,000. Note that ₹20,000 is the total amount, not the food expense — this is the mistake students make most often.
Histogram vs Bar Graph
Histogram
Type of dataContinuous class-interval data
Gap between barsNo gap (bars are adjacent)
Meaning of widthEqual to the class interval, meaningful
What height is proportional toFrequency (when class intervals are equal)
Bar Graph
Type of dataDiscrete categorical data
Gap between barsUsually has a gap
Meaning of widthArbitrary, no particular meaning
What height is proportional toFrequency or value
In a histogram with equal class intervals, bar height is directly proportional to frequency — this is exactly what REET 2024 asked.[Source 1]
Caution with unequal class intervals
If a histogram's class intervals are not equal, bar height is not taken as equal to the frequency directly — instead, height is decided by 'frequency density' (frequency ÷ width of the class interval), so that each bar's area stays proportional to that class's actual frequency.
Frequency Polygon
A frequency polygon is another diagram linked to the histogram — it's drawn by joining the midpoints of the tops of each bar with straight lines. It can also be drawn directly, without a histogram, by plotting class marks against frequency.
This diagram is especially useful for comparing data from two or more groups, because several polygons can be drawn on the same graph at once, whereas viewing multiple histograms together is difficult.
When to Use a Pie Chart, When a Histogram
- Suited to a pie chart
- When you need to show the proportion of different parts of a total — such as a budget, vote share, or market share.
- Suited to a histogram
- When you need to show the distribution of data grouped into continuous class intervals — such as students' marks or age groups.
How to Teach This to Children
Classroom activity
Have Class 8 students run a survey in class (say, favourite sport or fruit), collect the data, then build the pie chart themselves with a compass and protractor — this makes the sector-angle formula click in a hands-on way.
Teaching aids
Show students how folding round pieces of coloured paper, or drawing histograms on graph paper, makes clear why bars in a histogram never have gaps while bars in a bar graph can.
Common misconception
Children often assume every slice of a pie chart must be the same size, or treat histograms and bar graphs as the same thing (forgetting the gap difference). Clear up both misconceptions with worked examples.
Assessment idea
Have students build both a pie chart and a histogram from the same survey data they collected, then compare which diagram works better in which situation.
Cross-subject link
In Social Studies class, build pie charts from real data like census figures or crop production, to show students that reading data isn't a skill confined to maths alone.
Memory trick / exam tip
To convert a percentage directly into an angle (in degrees), multiply the percentage by 3.6 (because 360÷100=3.6) — for example, 25% → 25×3.6=90°, 20% → 20×3.6=72°. This trick is much faster than working out '100% of the total = 360°' each time.
REET 2024 Questions (with Solutions)
Question 92
In a histogram, the heights of the rectangles belong to those classes :
- Aबारम्बारताओं के व्युत्क्रमानुपाती
- Bबारम्बारताओं के समानुपाती
- Cवर्ग-अन्तराल के समानुपाती
- Dवर्ग-अन्तराल के व्युत्क्रमानुपाती
Explanation
आयतचित्र (histogram) में प्रत्येक वर्ग के लिए एक आयत बनाया जाता है जिसकी चौड़ाई वर्ग-अन्तराल के बराबर होती है। समान वर्ग-अन्तराल होने पर आयतों की ऊँचाई उन वर्गों की बारम्बारताओं (frequencies) के समानुपाती होती है। जिस वर्ग की बारम्बारता अधिक, उसका आयत उतना ही ऊँचा होता है, इसलिए (B) सही है।
Question 97
The given pie chart shows the savings and expenditure on various items of a family in a month. If the monthly savings of family is Rs. 3,000, then the expenditure of food will be
Figure: Pie chart of a family's monthly budget: Food 25 percent, Clothes 10 percent, Savings 15 percent, Others 20 percent, Transport 5 percent, Rent 10 percent, Education 15 percent. Diagram added and verified: savings of Rs 3000 at 15 percent gives a total of Rs 20000, so food at 25 percent is Rs 5000, matching the stored answer.
- A2,500 रुपये
- B3,000 रुपये
- C5,000 रुपये
- D20,000 रुपये
Explanation
पाई चार्ट में बचत 15% है, जो 3,000 रुपये के बराबर है। अतः कुल मासिक राशि = 3,000 × 100/15 = 20,000 रुपये। भोजन पर व्यय 25% है, इसलिए भोजन पर व्यय = 20,000 का 25% = 5,000 रुपये। 20,000 रुपये कुल राशि है, भोजन का व्यय नहीं।
Practice Questions
Question 1
A complete circle in a pie chart measures how many degrees?
- A180°
- B270°
- C360°
- D100°
Explanation
The complete angle of any circle is always 360°.
Question 2
If an item's value is 25% of the total, what will its angle be in the pie chart?
- A60°
- B75°
- C90°
- D100°
Explanation
25% × 360° = 90° (or 25×3.6=90).
Question 3
In a histogram, between adjacent rectangles there is usually:
- Aगैप (space) होता है
- Bकोई गैप नहीं होता
- Cसदैव बराबर ऊँचाई होती है
- Dसदैव त्रिभुजाकार आकार होता है
Explanation
A histogram represents continuous class-interval data, so there is no gap between its bars.
Question 4
The main difference between a bar graph and a histogram is:
- Aबार ग्राफ असंतत श्रेणीगत आँकड़ों हेतु, आयतचित्र संतत वर्ग-अंतराल आँकड़ों हेतु प्रयुक्त होता है
- Bदोनों बिल्कुल समान हैं
- Cआयतचित्र केवल वृत्त में बनता है
- Dबार ग्राफ में गैप कभी नहीं होता
Explanation
A bar graph is used for categorical (discrete) data while a histogram is used for continuous class-interval data — this is the fundamental difference.
Question 5
In a pie chart, an item's angle is 72°. What percentage of the total does it represent?
- A15%
- B20%
- C25%
- D30%
Explanation
Percentage = (72÷360)×100 = 20%.
Question 6
In a family's monthly budget pie chart, 'education' expense is shown as 18%. If the family's total monthly income is ₹25,000, what is the expense on education?
- A₹3,500
- B₹4,000
- C₹4,500
- D₹5,000
Explanation
18% of 25,000 = 25,000×18/100 = ₹4,500.
Question 7
In a pie chart, four items A, B, C, D have angles 90°, 120°, 60°, and the rest respectively. What is the angle of D?
- A60°
- B80°
- C90°
- D100°
Explanation
Total angle = 360°; A+B+C = 90+120+60 = 270°; D = 360−270 = 90°.
Question 8
In a histogram, the width of a rectangle is equal to:
- Aबारंबारता
- Bवर्ग-अंतराल (class interval)
- Cमाध्य
- Dसंचयी बारंबारता
Explanation
In a histogram, each bar's width equals the class interval of that class.
Question 9
In a histogram with equal class intervals, the height of a rectangle is proportional to:
- Aवर्ग-अंतराल
- Bबारंबारता
- Cसंचयी बारंबारता
- Dमाध्यिका
Explanation
When class intervals are equal, a bar's height is directly proportional to that class's frequency.
Question 10
Which is the most suitable activity to teach Class 8 students how to draw a pie chart?
- Aकक्षा में सर्वेक्षण (जैसे पसंदीदा खेल) कराकर परकार व चांदे से स्वयं पाई चार्ट बनवाना
- Bकेवल पाठ्यपुस्तक में बना चार्ट दिखाना
- Cबिना गणना के अनुमान से सेक्टर बनवाना
- Dयह गतिविधि केवल शिक्षक द्वारा करना
Explanation
Collecting data through a survey and then working out the calculations themselves to build a pie chart helps students deeply learn both the sector-angle formula and the construction process.
Frequently Asked Questions
How many questions come from pie chart-histogram in REET?+
REET 2024 carried 1–2 questions from this topic in the maths section — one concept-based, one calculation-based.
How do you find the sector angle in a pie chart?+
Formula: sector angle = (value of that item ÷ total value) × 360°. Quick method: multiply the percentage by 3.6.
What's the main difference between a histogram and a bar graph?+
A histogram is built for continuous class-interval data with no gaps between bars, while a bar graph is built for discrete categorical data and can have gaps.
In a histogram with equal class intervals, what is height proportional to?+
Frequency — the higher the frequency, the taller the bar.
What is a frequency polygon?+
It's a diagram made by joining the midpoints of the tops of a histogram's bars with straight lines, useful for comparing data across multiple groups.
How is height decided in a histogram with unequal class intervals?+
In that case, height isn't taken directly as frequency but as frequency density (frequency ÷ width of the class interval).
What should the angles of all sectors in a pie chart add up to?+
They must always add up to exactly 360°, since a pie chart represents the full circle.
Can a pie chart show negative values?+
No, a pie chart only shows proportions of positive values as sectors, since a circle's angle or area cannot be negative.
Read Next
Official Sources
Change Log
- 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked