TOPICS

Exercise - 14.4

Statistics

**Question-1 :-** The following distribution gives the daily income of 50 workers of a factory.
Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Daily income (in Rs.)(upper class limits) | Number of workers | Cumulative Frequency (cf) |

Less than 120 | 12 | 12 |

Less than 140 | 14 | 12 + 14 = 26 |

Less than 160 | 8 | 26 + 8 = 34 |

Less than 180 | 6 | 34 + 6 = 40 |

Less than 200 | 10 | 40 + 10 = 50 |

Total | n = 50 |

**Question-2 :-** During the medical check-up of 35 students of a class, their weights were recorded as follows:
Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Weight (in kg)(upper class limits) | Number of students (cf) |

Less than 38 | 0 |

Less than 40 | 3 |

Less than 42 | 5 |

Less than 44 | 9 |

Less than 46 | 14 |

Less than 48 | 28 |

Less than 50 | 32 |

Less than 52 | 35 |

Weight (in kg)(upper class limits) | Number of students | Cumulative Frequency (cf) |

Less than 38 | 0 | 0 |

38 - 40 | 3 - 0 = 3 | 3 |

40 - 42 | 5 - 3 = 2 | 5 |

42 - 44 | 9 - 5 = 4 | 9 |

44 - 46 | 14 - 9 = 5 | 14 |

46 - 48 | 28 - 14 = 14 | 28 |

48 - 50 | 32 - 28 = 4 | 32 |

50 - 52 | 35 - 32 = 3 | 35 |

Total | n = 35 |

**Question-3 :-** The following table gives production yield per hectare of wheat of 100 farms of a village.
Change the distribution to a more than type distribution, and draw its ogive.

Production yeild (lower class limits) | Number of farms | Cumulative Frequency (cf) |

Less than 120 | 2 | 100 |

Less than 140 | 8 | 100 - 2 = 98 |

Less than 160 | 12 | 98 - 8 = 90 |

Less than 180 | 24 | 90 - 12 = 78 |

Less than 200 | 38 | 78 - 24 = 54 |

Less than 200 | 16 | 54 - 38 = 16 |

Total | n = 100 |

CLASSES