Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars are proportional to the measure of data.

The types of bar charts are as follows:

1. Vertical bar chart
2. Horizontal bar chart

Apart from the vertical and horizontal bar graph, the two different types of bar charts are:

• Grouped Bar Graph
• Stacked Bar Graph

Properties of Bar Graph

Some of the important properties of a bar graph are as follows:

• All the bars should have a common base.
• Each column in the bar graph should have equal width.
• The height of the bar should correspond to the data value.
• The distance between each bar should be the same.

How to Draw a Bar Graph?

In order to visually represent the data using the bar graph, we need to follow the steps given below.

• Step 1: First, decide the title of the bar graph.
• Step 2: Draw the horizontal axis and vertical axis. (For example, Types of Pets)
• Step 3: Now, label the horizontal axis.
• Step 4: Write the names on the horizontal axis, such as Cat, Dog, Rabbit, Hamster.
• Step 5: Now, label the vertical axis. (For example, Number of Pets)
• Step 6: Finalise the scale range for the given data.
• Step 7: Finally, draw the bar graph that should represent each category of the pet with their respective numbers.

Bar Graph Solved Examples

To understand the above types of bar graphs, consider the following examples:

Example 1:

In a firm of 400 employees, the percentage of monthly salary saved by each employee is given in the following table. Represent it through a bar graph.

Solution:

The given data can be represented as

This can also be represented using a horizontal bar graph as follows:

Example 2:

A cosmetic company manufactures 4 different shades of lipstick. The sale for 6 months is shown in the table. Represent it using bar charts.

Solution:

The graph given below depicts the following data

Example 3:

The variation of temperature in a region during a year is given as follows. Depict it through the graph (bar).

Solution:

As the temperature in the given table has negative values, it is more convenient to represent such data through a horizontal bar graph.

A pie chart is a graphical representation technique that displays data in a circular-shaped graph.

Formula

The pie chart is an important type of data representation. It contains different segments and sectors in which each segment and sector of a pie chart forms a specific portion of the total(percentage). The sum of all the data is equal to 360°.

The total value of the pie is always 100%.

To work out with the percentage for a pie chart, follow the steps given below:

• Categorize the data
• Calculate the total
• Divide the categories
• Convert into percentages
• Finally, calculate the degrees

Therefore, the pie chart formula is given as

(Given Data/Total value of Data) × 360°

How to Create a Pie Chart?

Imagine a teacher surveys her class on the basis of favourite Sports of students:

Football	Hockey	Cricket	Basketball	Badminton
10	5	5	10	10

The data above can be represented by a pie chart as following and by using the circle graph formula, i.e. the pie chart formula given below. It makes the size of the portion easy to understand.

Step 1: First, Enter the data into the table.

Football	Hockey	Cricket	Basketball	Badminton
10	5	5	10	10

Step 2: Add all the values in the table to get the total.

I.e. Total students are 40 in this case.

Step 3: Next, divide each value by the total and multiply by 100 to get a per cent:

Football	Hockey	Cricket	Basketball	Badminton
(10/40) × 100 =25%	(5/ 40) × 100 =12.5%	(5/40) ×100 =12.5%	(10/ 40) ×100 =25%	(10/40)× 100 =25%

Step 4: Next to know how many degrees for each “pie sector” we need, we will take a full circle of 360° and follow the calculations below:

The central angle of each component = (Value of each component/sum of values of all the components)✕360°

Football	Hockey	Cricket	Basketball	Badminton
(10/ 40)× 360° =90°	(5 / 40) × 360° =45°	(5/40) × 360° =45°	(10/ 40)× 360° =90°	(10/ 40) × 360° =90°

Now you can draw a pie chart.

Step 5: Draw a circle and use the protractor to measure the degree of each sector.

 Favorite Sports of students %

Question: The percentages of various cops cultivated in a village of particular distinct are given in the following table.

Items	Wheat	Pulses	Jowar	Groundnuts	Vegetables	Total
Percentage of cops	125/3	125/6	25/2	50/3	25/3	100

Represent this information using a pie-chart.

Solution:

The central angle = (component value/100) × 360°

The central angle for each category is calculated as follows

Items	Percentage of cops	Central angle
Wheat	125/3	[(125/3)/100] × 360° = 150°
Pulses	125/6	[(125/6)/100] × 360° = 75°
Jowar	25/2	[(25/2)/100] × 360° = 45°
Groundnuts	50/3	[(50/3)/100] × 360° = 60°
Vegetables	25/3	[(25/3)/100] × 360° = 30°
Total	100	360°

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 3: Choose the largest central angle. Construct a sector of a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in the clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in the clockwise direction in descending order of magnitudes of their central angles.

Step 5: Shade the sectors obtained by different colours and label them as shown in the figure below.

Question:

The pie-chart shows the marks obtained by a student in an examination. If the student secures 440 marks in all, calculate the marks in each of the given subjects.

Solution:

The given pie chart shows the marks obtained in the form of degrees.

Given, total marks obtained = 440

i.e. 360 degrees = 440 marks

Now, we can calculate the marks obtained in each subject as follows.

Marks secured in mathematics = (central angle of maths/ 360°) × Total score secured

= (108°/ 360°) × 440 = 132 marks

Marks secured in science = (central angle of science / 360°) × Total score secured

= (81°/ 360°) × 440 = 99 marks

Marks secured in English = (central angle of English/ 360°) × Total score secured

= (72°/ 360°) × 440 = 88 marks

Marks secured in Hindi = (central angle of Hindi / 360°) × Total score secured

= (54°/ 360°) × 440 = 66 marks

Marks secured in social science = (central angle of social science / 360°) × Total score secured

= (45°/ 360°) × 440 = 55 marks

This can be tabulated as:

Subject	Mathematics	Science	English	Hindi	Social science	Total
Marks	132	99	88	66	55	440

A line graph is a unique graph which is commonly used in statistics. It represents the change in a quantity with respect to another quantity. For example, the price of different flavours of chocolates varies, which we can represent with the help of this graph. This variation is usually plotted in a two-dimensional XY plane. If the relation including any two measures can be expressed utilizing a straight line in a graph, then such graphs are called linear graphs. Thus, the line graph is also called a linear graph.

The following are the types of the line graph. They are:

1. Simple Line Graph: Only one line is plotted on the graph.
2. Multiple Line Graph: More than one line is plotted on the same set of axes. A multiple line graph can effectively compare similar items over the same period of time.
3. Compound Line Graph: If information can be subdivided into two or more types of data. This type of line graph is called a compound line graph. Lines are drawn to show the component part of a total. The top line shows the total and line below shows part of the total. The distance between every two lines shows the size of each part.

Vertical Line Graph

Vertical line graphs are graphs in which a vertical line extends from each data point down to the horizontal axis. Vertical line graph sometimes also called a column graph. A line parallel to the y-axis is called a vertical line.

Horizontal Line Graph

Horizontal line graphs are graphs in which a horizontal line extends from each data point parallel to the earth. Horizontal line graph sometimes also called a row graph. A line parallel to the x-axis is called a vertical line.

Example Questions on Line Graph:

The birth and death rates of a particular city are given below. Study the chart carefully and answer the given questions.

Question 1:

Calculate the average number of births in the city between 2001 to 2005.

a. 3.2 billion

b. 2.8 million

c. 4.4 million

d. 4 million

Solution:

From the graph, calculate the values of total births between 2001 to 2005. Then find the average of them.

So, average births = (3.5 + 4 + 5 + 3 + 6.5)/ 5 = 4.4.

Therefore, the average births between 2001 to 2005 is 4.4 million (since units are in millions).

Hence, option (c) is the answer.

Question 2:

By what percent (approx.) did the number of births increased in 2005 from the previous year?

a. 180

b. 150

c. 90

d. 117

Solution:

At first, the increase in births has to be calculated.

So, Increase in deaths in 2005 from 2004 = 6.5 – 3 = 3.5 million.

Now, percentage increase = (3.5 / 3) × 100 = 116.66 %.

As the closest option is 117 %, the answer will be option (d).

Question 3:

Calculate the difference between the number of deaths and the number of births over the years.

a. 5 million

b. 6 million

c. 1 billion

d. 3 million

Solution:

First, the total deaths and births over the years have to be calculated.

So, total deaths over the years = 27 and,

Total births over the years = 22

Now, the difference will be = 27 – 22 = 5.

Hence, the correct answer will be an option (a) i.e. 5 million.

Question 4:

In which year the percentage increase in birth rate over the previous year was the maximum?

a. 2001

b. 2002

c. 2003

d. 2004

e. 2005

Solution:

For this question, one can either calculate the percentage increase in each of the years or can just approximate to arrive at the right answer.

General Method:

To calculate percentage increase every year, one can use the following formula:

For a certain year, percentage increase or decrease = (difference of values from previous year/ value in that year) × 100.

So, for 2002, percentage increase in = (4 – 3.5) × 100 = 50 %.

Similarly, for 2003, percentage increase = 100 %.

For, 2004, percentage increase = 200 % (decrease).

And for 2005, percentage increase is = 350 %.

It can be seen that the percentage increase was highest in 2005 and so, option (e) is the correct answer.

Shortcut Method:

From the diagram, check where the slope of the line graph is the highest. First, ignore 2004 as it saw a decline in the birth rate. Now, it can be easily seen that, in 2005, the line graph took a sharp turn upwards. So, 2005 had to be the year when the percentage increase in birth rate over the previous year was the maximum.