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Smart Charts - Pie Charts

Grade 5CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

A Pie Chart, also known as a circle graph, is a way of showing data using a circle divided into 'slices'. The entire circle represents the whole amount or the total frequency of the data collected.

The size of each slice represents its share of the total. Visually, a larger slice indicates a higher value, while a smaller slice indicates a lower value. If you see a slice that looks like a perfect 'L' shape starting from the center, it usually represents a quarter or 14\frac{1}{4} of the total.

In a Pie Chart, a straight line passing through the center (the diameter) divides the circle into two equal parts. Each part represents exactly half or 12\frac{1}{2} of the total data.

If a circle is divided by two perpendicular lines (lines crossing at a 9090^{\circ} angle) through the center, it creates four equal sections. Each of these sections is called a 'quarter' and represents 14\frac{1}{4} of the whole.

We can find the exact number for any slice by multiplying the fraction it represents by the total number. For example, if a chart represents 2020 children and the 'Apples' slice is 12\frac{1}{2} of the circle, the number of children who like apples is 1010.

The sum of all the slices in a Pie Chart always adds up to the whole. In terms of fractions, the sum of all parts is equal to 11. Visually, there are no gaps or overlaps between the slices.

Pie Charts are very useful for comparing parts of a group to the whole group at a single glance, such as comparing the number of students who walk to school versus those who take the bus.

📐Formulae

Value of a slice=Fraction of the slice×Total Value\text{Value of a slice} = \text{Fraction of the slice} \times \text{Total Value}

Fraction of a slice=Value of the sliceTotal Value\text{Fraction of a slice} = \frac{\text{Value of the slice}}{\text{Total Value}}

Total Value=Sum of all slice values\text{Total Value} = \text{Sum of all slice values}

Sum of all fractions in a pie chart=1\text{Sum of all fractions in a pie chart} = 1

💡Examples

Problem 1:

A class of 4040 students was asked about their favorite fruit. The Pie Chart shows that 12\frac{1}{2} of the students like Mangoes, 14\frac{1}{4} like Apples, and 14\frac{1}{4} like Bananas. Calculate the number of students for each fruit.

Solution:

  1. Total students = 4040. \n2. Students who like Mangoes = 12×40=20\frac{1}{2} \times 40 = 20 students. \n3. Students who like Apples = 14×40=10\frac{1}{4} \times 40 = 10 students. \n4. Students who like Bananas = 14×40=10\frac{1}{4} \times 40 = 10 students. \nCheck: 20+10+10=4020 + 10 + 10 = 40.

Explanation:

To find the number of students, multiply the total count by the fraction represented by each slice of the pie chart.

Problem 2:

In a library of 200200 books, a Pie Chart shows that Science books occupy 15\frac{1}{5} of the chart. How many Science books are there in the library?

Solution:

  1. Total number of books = 200200. \n2. Fraction of Science books = 15\frac{1}{5}. \n3. Number of Science books = 15×200\frac{1}{5} \times 200. \n4. Calculation: 200÷5=40200 \div 5 = 40. \nSo, there are 4040 Science books.

Explanation:

Divide the total value by the denominator of the fraction to find the value represented by that specific part of the pie chart.