#### Topics

##### Number Systems

##### Number Systems

##### Algebra

##### Polynomials

##### Linear Equations in Two Variables

##### Algebraic Expressions

##### Algebraic Identities

##### Coordinate Geometry

##### Geometry

##### Introduction to Euclid’S Geometry

##### Lines and Angles

##### Triangles

##### Quadrilaterals

- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Angle Sum Property of a Quadrilateral
- Types of Quadrilaterals
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Another Condition for a Quadrilateral to Be a Parallelogram
- The Mid-point Theorem
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram

##### Area

##### Circles

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Angle Subtended by a Chord at a Point
- Perpendicular from the Centre to a Chord
- Circles Passing Through One, Two, Three Points
- Equal Chords and Their Distances from the Centre
- Angle Subtended by an Arc of a Circle
- Cyclic Quadrilateral

##### Constructions

##### Mensuration

##### Areas - Heron’S Formula

##### Surface Areas and Volumes

##### Statistics and Probability

##### Statistics

##### Probability

#### description

- Bar graph
- Pie graph
- Histogram

#### 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`**

#### Shaalaa.com | Graphical Representation of Data

#### Related QuestionsVIEW ALL [62]

The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:-

Number of balls |
Team A |
Team B |

1 - 6 | 2 | 5 |

7 - 12 | 1 | 6 |

13 - 18 | 8 | 2 |

19 - 24 | 9 | 10 |

25 - 30 | 4 | 5 |

31 - 36 | 5 | 6 |

37 - 42 | 6 | 3 |

43 - 48 | 10 | 4 |

49 - 54 | 6 | 8 |

55 - 60 | 2 | 10 |

Represent the data of both the teams on the same graph by frequency polygons.

[**Hint** :- First make the class intervals continuous.]

100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:-

Number of letters |
Number of surnames |

1 - 4 | 6 |

4 - 6 | 30 |

6 - 8 | 44 |

8 - 12 | 16 |

12 - 20 | 4 |

(i) Draw a histogram to depict the given information.

(ii) Write the class interval in which the maximum number of surnames lie.

A survey conducted by an organisation for the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures (in %):-

S.No. |
Causes |
Female fatality rate (%) |

1 | Reproductive health conditions | 31.8 |

2 | Neuropsychiatric conditions | 25.4 |

3 | Injuries | 12.4 |

4 | Cardiovascular conditions | 4.3 |

5 | Respiratory conditions | 4.1 |

6 | Other causes | 22.0 |

(i) Represent the information given above graphically.

(ii) Which condition is the major cause of women’s ill health and death worldwide?

(iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.

The following table gives the life times of 400 neon lamps:-

Life time (in hours) |
Number of lamps |

300 - 400 | 14 |

400 - 500 | 56 |

500 - 600 | 60 |

600 - 700 | 86 |

700 - 800 | 74 |

800 - 900 | 62 |

900 - 1000 | 48 |

(i) Represent the given information with the help of a histogram.

(ii) How many lamps have a life time of more than 700 hours?