#### Question

The daily wages of 80 workers in a project are given below.

Wages (in Rs.) |
400-450 | 450-500 | 500-550 | 550-600 | 600-650 | 650-700 | 700-750 |

No. of Workers |
2 | 6 | 12 | 18 | 24 | 13 | 5 |

Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs.

50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:

1) the median wage of the workers

2) the lower quartile wage of workers

3) the numbers of workers who earn more than Rs. 625 daily

#### Solution

The cumulative frequency table of the given distribution is as follows:

Wages in Rs |
Upper Limit |
No. of workers |
Cumulative frequency |

400-450 | 450 | 2 | 2 |

450-500 | 500 | 6 | 8 |

500-550 | 550 | 12 | 20 |

550-600 | 600 | 18 | 38 |

600-650 | 650 | 24 | 62 |

650-700 | 700 | 13 | 75 |

700-750 | 750 | 5 | 80 |

The ogive is as follows:

Number of workers = n = 80

1) Median = (n/2)th term = 40th term

Through mark 40 on the Y-axis, draw a horizontal line which meets the curve at point A.

Through point A, on the curve draw a vertical line which meets the X-axis at point B

The value of point B on the X-axis is the median, which is 605.

2) Lower quartile `(Q_1) = (80/4)th` term = 20th term = 550

3) Through mark of 625 on X-axis, draw a verticle line which meets the graph at point C.

Then through point C, draw a horizontal line which meets the Y-axis at the mark of 50.

Thus, the number of workers that earn more than Rs. 625 daily = 80-50 = 30