A bar graph is a pictorial representation of the numerical data by a number of bars of uniform width erected horizontally or
vertically with equal spacing between them.

Initially, data used to be represented pictorially through pictographs in which picture symbols were used to represent a certain number of items and then each
observation was shown by drawing the proportional number of pictures. But the method of drawing pictographs was time consuming and so it did not turn out to be very useful.

However bar graphs are simple to draw, convenient to read and provide for easy comparison of the given data.

Bar graph c\onsist of rectangles of equal width and varying heights depending upon the numerical data. Also, the distance between each pair of consecutive rectangles is
kept the same.

To construct a bar graph, we follow the steps given below:

**Step 1:** On a squared/graph sheet, draw two mutually perpendicular lines, called the horizontal and vertical axes.

**Step 2:** Mark along the horizontal axes, at equal gaps, the quantity which is non-numeric, e.g., days, states, months, subjects, etc.

Mark along the vertical axis the numerical data that varies, by choosing a suitable scale, e.g., marks, heights, rainfall, etc

**Step 3:** Draw bars of equal width along the horizontal axis and heights, if it is a vertical bar. Arrange the bars, keeping the distance in between the two consecutive bars the
same.

There are three types of bar graph. They are :-

**1. Simple Bar Graph.
2. Double Bar Graph.
3. Divided Bar Graph.**

Example 1:

The marks obtained by Stella in her annual examination are shown below:

Subject | Science | Social Studies | Mathematics | Statistics | English |

Marks Obtained | 30 |
50 |
60 |
40 |
20 |

**Solution****:**

Example 2:

Different modes of travel to school, used by fifty students from a certain locality,are given below. Draw a bar graph to represent the following data.

Example 1**:**

** ** Here is a bar graph showing the marks obtained by James his half-yearly examination in five different subjects.

Study the bar graph and answer the following questions:

(i) Name the subject in which he scored the highest marks.

(ii) How many marks did he score in Statistics?

(iii) In how many subjects did he score more than 50% marks?

(iv) Name the subject in which he scored the lowest marks.

Solution:

(i) Mathematics.

(ii) 40%

(iii) One, Mathematics.

(iv) English

Example 2:

Here is a bar graph showing rainfall (in cm) in a city during the last six months of the

year 2005.

Study the bar graph and answer the following questions:

(i) In which month was the rainfall the lowest?

(ii) In which month was therainfall the highest?

(iii) What was the total of the rainfall in six months?

Solution:

(i) November

(ii) August and September

(iii) 185 cm.

(i) In Bar Graph Worksheet take the width of all bars(rectangles)of the Bar Graph equal.

(ii)Space between consecutive bars of the Bar Graph Worksheet should be equal.

(iii)The height (or length) of a bar of Bar Graph Worksheet is equal( or proportional) to the frequency of the corresponding variate(observation).

(iv) The width of bars has no significance. In fact, the width of the bars of Bar Graph Worksheet is shown simply to make the

representation more eye-catching.