# Two sections of Class IX having 30 students each appeared for the mathematics olympiad. The marks obtained by them are shown below:

46 31 74 68 42 54 14 61 83 48 37 26 8 64 57 93 72 53 59 38 16 88 75 56 46 66 45 61 54 27 27 44 63 58 43 81 64 67 36 49 50 76 38 47 55 77 62 53 40 71 60 58 45 42 34 46 40 59 42 29

Construct a group frequency distribution of the data above using the classes 0-9, 10-19 etc., and hence find the number of students who secured more than 49 marks.

**Solution:**

Given, the data represents the marks obtained by two sections of Class IX having 30 students each who appeared for the mathematics olympiad.

We have to construct the group __frequency distribution__ of the data above using the classes 0-9, 10-19, etc

Class interval | Marks obtained by students | Number of students |

0 - 9 | 8 | 1 |

10 - 19 | 14, 16 | 2 |

20 - 29 | 26, 27, 27, 29 | 4 |

30 - 39 | 31, 38, 37, 36, 38, 34 | 6 |

40 - 49 | 46,42,48,46,45,47,44,43,49,40,45,42,46,40,42 | 16 |

50 - 59 | 54,57,53,59,56,54,58,50,55,53,58,59 | 12 |

60 - 69 | 68,61,64,66,61,63,64,67,62,60 | 10 |

70 - 79 | 74,72,75,76,77,71 | 6 |

80 - 89 | 83,88,81 | 3 |

90 - 99 | 93 | 1 |

The group frequency distribution of the data above is

Class | Tally Marks | Frequency |

0 - 9 | | | 1 |

10 - 19 | | | | 2 |

20 - 29 | | | | | | 4 |

30 - 39 | 6 | |

40 - 49 | 16 | |

50 - 59 | 12 | |

60 - 69 | 10 | |

70 - 79 | 6 | |

80 - 89 | | | | | 3 |

90 - 99 | | | 1 |

Total frequency = 1 + 2 + 4 + 6 + 16 + 12 + 10 + 6 + 3 + 1= 60

We have to find the number of students who secured more than 49 marks

From the frequency distribution table,

Number of students who secured more than 49 marks = 12 + 10 + 6 + 3 + 1

= 22 + 10

= 32

Therefore, the number of students who scored more than 49 marks is 32.

**✦ Try This: **Two sections of Class IV having 30 students each appeared for the mathematics olympiad. The marks obtained by them are shown below:

45 32 75 69 43 55 13 62 84 49 38 27 7 63 58 94 73 55 58 39 17 89 74 54 47 66 46 60 53 25 25 45 65 57 45 83 64 66 35 48 50 76 38 42 55 77 61 53 40 70 60 59 44 43 33 44 41 58 43 8. Construct the group frequency distribution of the data above using the classes 0-9, 10-19 etc., and hence find the number of students who secured more than 89 marks.

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 14

**NCERT Exemplar Class 9 Maths Exercise 14.4 Sample Problem 2**

## Two sections of Class IX having 30 students each appeared for the mathematics olympiad. The marks obtained by them are shown below: 46 31 74 68 42 54 14 61 83 48 37 26 8 64 57 93 72 53 59 38 16 88 75 56 46 66 45 61 54 27 27 44 63 58 43 81 64 67 36 49 50 76 38 47 55 77 62 53 40 71 60 58 45 42 34 46 40 59 42 29. Construct a group frequency distribution of the data above using the classes 0-9, 10-19 etc., and hence find the number of students who secured more than 49 marks.

**Summary:**

Two sections of Class IX having 30 students each appeared for the mathematics olympiad. The marks obtained by them are shown below: 46 31 74 68 42 54 14 61 83 48 37 26 8 64 57 93 72 53 59 38 16 88 75 56 46 66 45 61 54 27 27 44 63 58 43 81 64 67 36 49 50 76 38 47 55 77 62 53 40 71 60 58 45 42 34 46 40 59 42 29. The group frequency distribution of the data above using the classes 0-9, 10-19 etc.,is shown above and hence the number of students who secured more than 49 marks is 32

**☛ Related Questions:**

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