Sum

Use graph paper for this question.

The marks obtained by 120 students in an English 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 | 5 | 9 | 16 |
22 |
26 | 18 |
11 |
6 | 4 | 3 |

Draw the ogive and hence, estimate:

(i) the median marks.

(ii) the number of students who did not pass the test if the pass percentage was 50.

(iii) the upper quartile marks.

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#### Solution

C.I |
Marks lessthan |
No.ofstudents |
Cumulativefrequency |

0-10 | 10 | 5 | 5 |

10-20 | 20 | 9 | 14 |

20-30 | 30 | 16 | 30 |

30-40 | 40 | 22 | 52 |

40-50 | 50 | 26 | 78 |

50-60 | 60 | 18 | 96 |

60-70 | 70 | 11 | 107 |

70-80 | 80 | 6 | 113 |

80-90 | 90 | 4 | 117 |

90-100 | 100 | 3 | 120 |

i. No.of students =120

∴ Median = 60th term through marks of 60 draw a line parallel to x - axis which meets the curve at A. From A draw perpendicular to x-axis, which meets it at A . From A draw a perpendicular to x-axis which

meets it at B.

ii. The upper quartile marks `(Q_3 ) = 3/4 n^(th)` term

`= 3^(th)/4 xx 120= 90^(th) ` term

draw a line parallel to x-axis which meets the 1 curve at C. From C draw perpendicular to x-axis which meets it at D.

Concept: Graphical Representation of Ogives

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