- Category: Mathematics

**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, are known as bar graphs (also known as bar charts). **

The concept of a bar graph is covered in this article. The key concepts that are included here are bar graph definition, bar graph examples, bar graph types along with some sample questions on bar graphs. Before knowing about the bar graphs, it is important to know what statistics is. The collection, presentation, analysis, organization and interpretation of observations or data is known as statistics. The statistical data can be represented by various methods such as tables, bar graph, pie charts, histograms, frequency polygons etc.

**In the upcoming discussion, the collection of data through a bar graph is discussed.**

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, are known as bar graphs (also known as bar charts). The bars drawn are of uniform width and the variable quantity is represented on one of the axes. Also, the measure of the variable is depicted on the other axes. The heights or the lengths of the bars denote the value of the variable and these graphs are also used to compare certain quantities. The frequency distribution tables can be easily represented using bar charts which simplify the calculations and understanding of data.

The types of bar charts are as follows:

- Vertical bar chart
- Horizontal bar chart
- Range bar chart

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.

Savings (in percentage) | Number of Employees(Frequency) |

20 | 105 |

30 | 199 |

40 | 29 |

50 | 73 |

Total | 400 |

Solution: The given data can be represented as

This can be also 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.

Month | Sales (in units) | |||

Shade 1 | Shade 2 | Shade 3 | Shade 4 | |

January | 4500 | 1600 | 4400 | 3245 |

February | 2870 | 5645 | 5675 | 6754 |

March | 3985 | 8900 | 9768 | 7786 |

April | 6855 | 8976 | 9008 | 8965 |

May | 3200 | 5678 | 5643 | 7865 |

June | 3456 | 4555 | 2233 | 6547 |

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 graph (bar).

Month |
Temperature |

January | -6°C |

February | -3.5°C |

March | -2.7°C |

April | 4°C |

May | 6°C |

June | 12°C |

July | 15°C |

August | 8°C |

September | 7.9°C |

October | 6.4°C |

November | 3.1°C |

December | -2.5°C< |

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

**Question:**

*A school conducted a survey to know the favourite sports of the students. The table below shows the results of this survey.*

Name of the Sport |
Total Number of Students |

Cricket | 45 |

Football | 53 |

Basketball | 99 |

Volleyball | 44 |

Chess | 66 |

Table Tennis | 22 |

Badminton | 37 |

From this data,

1. Draw a graph representing the sports and the total number of students.

2. Calculate the range of the graph.

3. Which sport is the most preferred one?

4. Which two sports are almost equally preferred?

5. List the sports in ascending order.

To learn more about statistics, we suggest you to refer NCERT solutions for Data collection method. To refer CT’s NCERT solutions for Graphs, click here – Introduction to Graphs