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Pie charts look easy until you have to draw one from a table of 120 survey answers, or read one where the slices are labelled only in degrees. This post covers the method the new NCERT Class 8 book uses, a full worked example, how to read a pie chart backwards, when not to use one, and where chance and probability have moved.
Where is data handling in the new Class 8 NCERT books?
The older NCERT book had Chapter 4, Data Handling, according to its contents page. In the new books the same ideas are spread out:
Pie charts: section 3.5, "A Slice of the Pie", in Ganita Prakash Part II, Chapter 3, part of proportional reasoning.
Mean, median and line graphs: Chapter 5, "Tales by Dots and Lines", in Ganita Prakash Part II.
Chance and probability: Chapter 7, "The Mathematics of Maybe: Introduction to Probability", in the new Class 9 book, Ganita Manjari Part I. Its introduction says the chapter covers randomness and empirical and theoretical probability.
Ask your teacher which edition your class uses, since some schools change books at different times.
How do you draw a pie chart?
The book's rule: the angle of each slice is proportional to its count, and the whole circle is 360°. So you share 360° in the ratio of the data. Its example shares 360° among grades A to E in the ratio 12 : 10 : 8 : 6 : 4, which simplifies to 6 : 5 : 4 : 3 : 2, giving 108°, 90°, 72°, 54° and 36°.
Worked example. 120 students were asked how they come to school: bus 45, walk 30, bicycle 25, car 20.
Check the total: 45 + 30 + 25 + 20 = 120
Degrees per student: 360 ÷ 120 = 3°
Angles: bus 45 × 3 = 135°, walk 30 × 3 = 90°, bicycle 25 × 3 = 75°, car 20 × 3 = 60°
Check: 135 + 90 + 75 + 60 = 360°
Draw a circle and one radius. With a protractor, mark 135° from the radius, then 90° from the new line, and so on. Label each slice.
As percentages, the slices are bus 37.5%, walk 25%, bicycle about 20.8% and car about 16.7%. Those add to 100% once you allow for rounding.
How do you read a pie chart backwards?
Turn the angle into a fraction of 360°.
A 72° slice in a survey of 250 people: 72 ÷ 360 = 1/5, so 250 ÷ 5 = 50 people.
A slice that is 25% of the whole: 25% of 360° = 90°.
When is a pie chart the wrong choice?
Use a pie chart only when the slices are parts of one whole. A week of daily temperatures is not parts of a whole; it is change over time, so it belongs on a line graph, which Chapter 5 teaches.
When the data are parts of a whole, a pie chart works well. In a series of experiments, Spence and Lewandowsky (1991) found little to choose between pie and bar charts for judging proportions. The pie chart had a slight advantage when the judgement was complicated, and both beat a table.
What does "chance" mean, and where has it gone?
In the new books, probability is a Class 9 topic, but the core idea is easy to preview. When all outcomes are equally likely, the probability of an event is the number of favourable outcomes divided by the total number of outcomes.
A fair die has 6 equally likely outcomes. Three are even (2, 4, 6), so the probability of an even number is 3/6 = 1/2.
If you toss a coin 20 times, you may not get exactly 10 heads. The fraction you observe is an experimental probability, and it tends to settle near 1/2 as you toss more.
Our guide to probability in Class 10 goes further.
Which mistakes come up most often?
Using counts as degrees. A slice for 45 students is not 45°.
Skipping the totals check. Count the data before you calculate.
Comparing slices across two pies with different totals. 40% of 50 people is 20, while 30% of 200 people is 60. The smaller slice can stand for more people.
Rounding each angle separately and ending at 359° or 361°. Adjust the largest slice by a degree and say so.
Trusting the mean when one value is extreme. For 4, 5, 6 and 25, the mean is 40 ÷ 4 = 10, but the median is 5.5. Chapter 5 treats the mean as a balancing point and shows how adding one value can shift the median.
A five-day practice routine
Day 1: Survey 20 to 30 people at home or in class about one question, such as favourite fruit.
Day 2: Turn your data into angles and draw the pie chart. Run both totals checks.
Day 3: Read three pie charts backwards, from angles to counts, using made-up totals.
Day 4: Track one quantity for a week, such as minutes of reading, and draw a line graph instead.
Day 5: Roll a die 30 times and record how often an even number comes up. Compare your fraction with 1/2.
Pie charts rest on direct proportion; our guide to direct and inverse proportion in Class 8 covers it. If a term such as median or experimental probability is still unclear, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing.
Today, ask five family members one question, then draw your first pie chart from their answers.
