#### notes

The representation then becomes easier to understand than the actual data. We shall study the following graphical representations in this section.

(A)Bar graphs

(B) Histograms of uniform width, and of varying widths

(C) Frequency polygons

**(A) Bar graphs:**

A bar graph is a pictorial representation of data in which usually bars of uniform width are drawn with equal spacing between them on one axis (say, the x-axis), depicting the variable. The values of the variable are shown on the other axis (say, the y-axis) and the heights of the bars depend on the values of the variable.**Steps in the process:**

1. Decide on a title for your graph.

2. Draw the vertical and horizontal axes.

3.Label the horizontal axes.

4. Write the names of pets where the bars will be.

5. Label the vertical axes.

6. Decide on the scale. Explain that you should consider the least and the greatest number shown on the graph. Discuss what range of numbers should be shown on this bar graph.

7. Draw a bar to show the total for each item.

**(B) Histograms :**

There are no gaps in between consecutive rectangles, the resultant graph appears like a solid figure. This is called a histogram, which is a graphical representation of a grouped frequency distribution with continuous classes. Also, unlike a bar graph, the width of the bar plays a significant role in its construction.

**(C) Frequency polygons: **

There is yet another visual way of representing quantitative data and its frequencies. This is a polygon. In frequency polygon are join the midpoints of the upper sides of the adjacent rectangles of this histogram by means of line segments. Although, there exists no class preceding the lowest class and no class succeeding the highest class, addition of the two class intervals with zero frequency enables us to make the area of the frequency polygon the same as the area of the histogram.

Frequency polygons can also be drawn independently without drawing histograms. The mid-points of the class-intervals used in the data. These mid-points of the class-intervals are called class-marks.

To find the class-mark of a class interval, we find the sum of the upper limit and lower limit of a class and divide it by 2. Thus,**Class-mark = `("Upper limit + Lower limit")/2`**

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#### Related QuestionsVIEW ALL [61]

The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:-

Length (in mm) |
Number of leaves |

118 - 126 | 3 |

127 - 135 | 5 |

136 - 144 | 9 |

145 - 153 | 12 |

154 - 162 | 5 |

163 - 171 | 4 |

172 - 180 | 2 |

(i) Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]

(ii) Is there any other suitable graphical representation for the same data?

(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

A random survey of the number of children of various age groups playing in a park was found as follows:-

Age (in years) |
Number of children |

1 - 2 | 5 |

2 - 3 | 3 |

3 - 5 | 6 |

5 - 7 | 12 |

7 - 10 | 9 |

10 - 15 | 10 |

15 - 17 | 4 |

Draw a histogram to represent the data above.

The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below.

Section |
Number of girls per thousand boys |

Scheduled Caste (SC) | 940 |

Scheduled Tribe (ST) | 970 |

Non SC/ST | 920 |

Backward districts | 950 |

Non-backward districts | 920 |

Rural | 930 |

Urban | 910 |

(i) Represent the information above by a bar graph.

(ii) In the classroom discuss what conclusions can be arrived at from the graph.