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Describing Charts and Graphs

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A graphical representation of data and information offers a quick and simple way to understand the features. It is more effective than presenting the data in the form of tables. There are many ways to represent the data graphically such as bar graph, double bar graph, pictograph, line graph, linear graph, histogram, etc.

A pie chart is a type of graph that represents the data in a circular graph. The slices of pie show the relative size of the data. Let’s understand what is a circle graph or a pie chart and how is it read and drawn using examples.

## What is a Circle Graph or a Pie Chart?

A pie chart or a “pie graph” or “circle chart”, is a pictorial representation of data in the form of a circular chart or pie where the slices of the pie show the size of the data. It divides the circular region into sectors or sections to illustrate the numerical values or data. Each sector denotes a proportionate part of the whole. To find out the composition of something, the pie chart is better than other graphs like a bar graph, line plot, histogram, etc.

In a pie chart, the arc length of each slice and consequently the area and central angle it forms in a pie chart is proportional to the quantity it represents. It is the best tool to compare discrete data.

## Uses of Pie Chart

Whenever the data has to be represented visually as a fractional part of a whole, we use pie charts. It is used to compare the data and to visualize which data looks smaller/greater than the other. These are some of the uses of a pie chart.

- In a business, it is used to compare the growth areas such as profit and loss.
- In school, pie charts are used to show the time allotted to each section, the grades of students in a form of percentages, etc.
- Pie charts are used in comparing the relative size of data of people owning the same vehicles, similar houses, etc.
- They are used to represent the marketing and sales data for the comparison of brands.

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## How to Interpret a Pie Chart

To read or interpret a pie chart, we see if the given chart is given in percentages or in numbers, or without any value.

- If the values in a pie chart are given in percentages, the following formula is used

Convert each value in percent into simple numbers using the formula $\text{Value} = \frac{\text{Value in percent}}{100} \times {\text{Total}}$.

- If the values in a pie chart are given in numbers, the following steps are used

**Step 1:** Add all the values to get the Total.

**Step 2:** Convert each value in into percents using the formula $\text{Percent} = \frac{\text{Value in number}}{\text{Total}} \times 100$.

- If the pie chart is without any values, then compute measure each angle and get the percent proportion of the data using the formula

$\frac{\text{Angle measurement}}{360} \times 100$.

### Examples

Let’s consider some examples to understand how pie charts are interpreted

**Ex 1:** Pie chart with values in percentages.

Consider the following pie chart, showing the distribution of items in an inventory. If the inventory has a total of 500 items, we want to know the count of each item.

Number of Item A = $\frac {17}{100} \times 500 = 85$

Number of Item B = $\frac {33}{100} \times 500 = 165$

Number of Item C = $\frac {50}{100} \times 500 = 250$

Total number of items = $85 + 165 + 250 = 500$.

**Ex 2:** Pie chart with values in numbers.

Consider the following pie chart, showing the distribution of favourite fruit among 50 children. We want to know the fraction of each item in percent.

Total number of children = $5 + 15 + 10 + 20 = 50$

Fraction of children liking banana = $\frac {5}{50} =\frac {1}{10}$ or $\frac {1}{10} \times 100 = 10%$.

Fraction of children liking apple = $\frac {15}{50} =\frac {3}{10}$ or $\frac {3}{10} \times 100 = 30%$.

Fraction of children liking grapes = $\frac {10}{50} =\frac {1}{5}$ or $\frac {1}{5} \times 100 = 20%$.

Fraction of children liking mango = $\frac {20}{50} =\frac {2}{5}$ or $\frac {2}{10} \times 100 = 40%$.

**Note:** The total of all percent = $10 + 30 + 20 + 40 = 100%$.

**Ex 3:** Pie chart without any values.

A group of 600 children was asked about their favourite colour. The data collected is represented in the following pie chart. We want to know the number of children liking each of the colours.

The first step is to measure the angle of each of the sectors of a pie chart.

The angle of the Blue sector = $150^{\circ}$

The angle of the Red sector = $45^{\circ}$

The angle of the Green sector = $60^{\circ}$

The angle of the Orange sector = $105^{\circ}$

Therefore, the distribution of favourite colours among 600 children is

Blue = $\frac {150}{360} \times 600 = 250$

Red = $\frac {45}{360} \times 600 = 75$

Green = $\frac {60}{360} \times 600 = 100$

Orange = $\frac {105}{360} \times 600 = 175$

## How to Draw a Pie Chart

The following steps are used to draw a pie chart by using the above-mentioned formulas, we can convert the data into angles of the sectors of a pie chart.

**Step 1:** Write all the data into a table and add up all the values to get a total.

**Step 2:** To find the values in the form of a percentage divide each value by the total and multiply by 100.

**Step 3:** To find how many degrees for each pie sector we need, we take a full circle of $360^{\circ}$ and use the formula: $\frac{\text{Frequency}}{\text{Total Frequency}} \times 360^{\circ}$.

**Step 4:** Once all the degrees for creating a pie chart are calculated, draw a circle (pie chart) using the calculated measurements with the help of a protractor.

### Examples

Let’s consider an example to understand how a pie chart is drawn.

**Ex 1:** The monthly income of a family is ₹28,800. The monthly expenditure of the family on various items is given below.

Monthly income of a family = ₹$28,800$

Monthly expenses of a family are

Rent = ₹$8,000$

Food = ₹$10,800$

Clothing = ₹$5,600$

Education = ₹$3,600$

Savings = ₹$800$

The measure of angles of sectors corresponding to expenses are

Rent = $\frac{8,000}{28,800} \times 360 = 100^{\circ}$

Food = $\frac{10,800}{28,800} \times 360 = 135^{\circ}$

Clothing = $\frac{5,600}{28,800} \times 360 = 70^{\circ}$

Education = $\frac{3,600}{28,800} \times 360 = 45^{\circ}$

Savings = $\frac{800}{28,800} \times 360 = 10^{\circ}$

## Advantages and Limitations of a Pie Chart

Given below are the advantages of a pie chart which are the reasons for the widespread application of pie charts in different fields. There are a few limitations in pie charts. These are also listed below.

## Practice Problems

**1.** There are 900 creatures in a zoo as per the list given below:

Represent the above data with a pie chart.

**2.** Various modes of transport used by 1260 students in a given school are given below:

Represent the above data with a pie chart.

**3.** The data given below shows the number of hours spent by a schoolboy on different activities on a working day.

Represent the above data with a pie chart.

## FAQs

### What is a pie chart with an example?

A pie chart is a pictorial representation of data in the form of a circular chart or pie where the slices of the pie show the size of the data. A list of numerical variables along with categorical variables is needed to represent data in the form of a pie chart.

### Why is a pie chart used?

Pie charts are often used to represent sample data—with data points belonging to a combination of different categories. Each of these categories is represented as a “slice of the pie.” The size of each slice is directly proportional to the number of data points that belong to a particular category.

**How do you calculate angles for a pie chart?**

To find how many degrees for each pie sector we need, we take a full circle of $360^{\circ}$ and use the formula: $\frac{\text{Frequency}}{\text{Total Frequency}} \times 360^{\circ}$.

## Conclusion

In this article, we learned what is a circle graph or a pie chart. A pie chart also known as a “pie graph or “circle chart”, is a pictorial representation of data in the form of a circular chart or pie where the slices of the pie show the size of the data. The main advantage of a pie chart is easy to understand and comparison of component items in the chart easily.