Jharkhand Board JAC Class 10 Maths Solutions Chapter 14 Statistics Ex 14.4 Textbook Exercise Questions and Answers.

## JAC Board Class 10 Maths Solutions Chapter 14 Statistics Exercise 14.4

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.

Solution:

Question 2.

During the medical check-up of 35 students of a class, their weights were recorded as follows:

Weight (in kg) | No. of students |

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 |

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.

Solution:

Weight (in kg) | Frequency | Cumulative frequency |

36 – 38 | 0 | 0 |

38 – 40 | 3 | 3 |

40 – 42 | 2 | 5 |

42 – 44 | 4 | 9 |

44 – 46 | 5 | 14 = cf |

46 – 48 | 14 = f | 28 |

48 – 50 | 4 | 32 |

50 – 52 | 3 | 35 |

n = 35 |

\(\frac{\mathrm{n}}{2}=\frac{35}{2}=17.5\)

Plot the points (38, 0) (40, 3) (42, 5) (44, 9) (46, 14) (48, 28) (50, 32) (52, 35)

Median = l + \(\left[\frac{\frac{\mathrm{n}}{2}-\mathrm{cf}}{\mathrm{f}}\right]\) × h

= 46 + \(\left[\frac{17.5-14}{14}\right]\) × 2

= 46 + \(\frac{3.5 \times 2}{14}\)

= 46 + 0.5= 46.5.

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.

Solution:

Production yield (in kg/hec) | Number of farms | c.f. |

More than 50 | 2 | 100 |

More than 55 | 8 | 98 |

More than 60 | 12 | 90 |

More than 65 | 24 | 78 |

More than 70 | 38 | 54 |

More than 75 | 16 | 16 |

∴ Co-ordinate points are (50, 100), (55, 98), (60, 90), (65, 78), (70, 54) and (75, 16).