#### Question

The marks obtained by 100 students in a Mathematics test are given below:

Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |

No. of students |
3 | 7 | 12 | 17 | 23 | 14 | 9 | 6 | 5 | 4 |

Draw an ogive for the given distribution on a graph sheet.

Use a scale of 2 cm = 10 units on both axes.

Use the ogive to estimate the:

1) Median.

2) Lower quartile.

3) A number of students who obtained more than 85% marks in the test.

4) A number of students who did not pass in the test if the pass percentage was 35.

#### Solution

Draw the cumulative frequency table.

Marks | Number of Students (Frequency) | Cumulative Frequency |

0-10 | 3 | 3 |

10-20 | 7 | 10 |

20-30 | 12 | 22 |

30-40 | 17 | 39 |

40-50 | 23 | 62 |

50-60 | 14 | 76 |

60-70 | 9 | 85 |

70-80 | 6 | 91 |

80-90 | 5 | 96 |

90-100 | 4 | 100 |

Scale: On x-axis, 1 unit = 10 marks, On y-axis, 1 unit = 10 students

1) Median = `(N/2)^"th" term = (100/2)^"th" term = 50^"th term"`

Draw a horizontal line through mark 50 on the y-axis. The, draw a vertical line from the point it cuts on the graph. The point this line touches the x-axis is the median. Thus, median = 45

2) Lower quartile = `(N/4)^"th" term = (100/4)^"th" term = 25^"th term"`

Draw a horizontal line through mark 25 on the y-axis. The, draw a vertical line from the point it cuts on the graph. The point this line touches the x-axis is the lower quartile

Thus, lower quartile = 31

3) Draw a vertical line through mark 85 on the x-axis. Then, draw a horizontal line from the point it cuts on the graph.

The point where this line touches the y-axis is the number of students who obtained less than 85% marks =93

Thus, number of students who obtained more than 85% marks =100 – 93 = 7

4) Draw a vertical line through mark 35 on the x-axis. The, draw a horizontal line from the point it cuts on the graph.

The point where this line touches the y-axis is the number of students who obtained less than 35% marks = 21