#### Question

The monthly income of a group of 320 employees in a company is given below:

Monthly Income |
No. of Employees |

6000-7000 | 20 |

7000-8000 | 45 |

8000-9000 | 65 |

9000-10000 | 95 |

10000-11000 | 60 |

11000-12000 | 30 |

12000-13000 | 5 |

Draw an ogive the given distribution on a graph sheet taking 2 cm = Rs. 1000 on one axis and 2 cm = 50 employees on the other axis. From the graph determine:

(1) the median wage

(2) the number of employees whose income is below Rs. 8500.

(3) if the salary of a senior employee is above Rs. 11,500, find the number of senior employees in the company.

(4) the upper quartile.

#### Solution 1

Monthly |
No. of Employees |
c.f. |

6000 - 7000 | 20 | 20 |

7000 - 8000 | 45 | 65 |

8000 - 9000 | 65 | 130 |

9000 - 10000 | 95 | 225 |

10000 - 11000 | 60 | 285 |

11000 - 12000 | 30 | 315 |

12000 - 13000 | 5 | 320 |

(i) From the graph, the median wage = 160·5 (appro.)

(ii) The number of employees whose income is below ₹8500 = 90 (appro.)

(iii) The number of senior employees whose salary is above ₹ 11500 = 20 (appro.)

(iv) The upper quartile Q_{3} = 240 (appro.)

#### Solution 2

Monthly Income |
No. of Employees |
c.f. |

6000-7000 | 20 | 20 |

7000-8000 | 45 | 65 |

8000-9000 | 65 | 130 |

9000-10000 | 95 | 225 |

10000-11000 | 60 | 285 |

11000-12000 | 30 | 315 |

12000-13000 | 5 | 320 |

Here, n = 320

1) Media = `n/2` th term = 160 th term

From the graph, the corresponding x coordinate is 9400

median wage = 9400 approx

2) The number of employees whose income is below Rs. 8500 = 95 (approx.)

3) The number of senior employees whose salary is above Rs. 11500 = 320 – 305 = 15 (approx.)

4) The upper quartile `Q_3 = ((3n)/4)^"th"` term = 240 th term

From the graph, the corresponding x co-ordinate is 10,300 (approx.)