**Question:**

The weekly wages (in Rs.) of 30 workers in a factory are given:

830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840

Mark a frequency table with intervals as 800-810, 810-820 and so on, using tally marks. Also, draw a histogram and answer the following questions:

(i) Which group has the maximum number of workers?

(ii) How many workers earn Rs 850 and more?

(iii) How many workers earn less than Rs 850?

**Solution:**

The frequency table with intervals $800-820,810-820, \ldots 890-900$ is given below:

Wage (in Rs) | Tally Wage | Frequency | Tally marks |

800 |
804, 808, 806 | 3 | III |

810 |
810, 812 | 2 | II |

820 |
820 | 1 | I |

830 |
830, 835, 835, 836, 832, 833, 835, 835, 836 | 9 | |

840 |
845, 845, 840, 840, 840 | 5 | |

850 |
855 | 1 | I |

860 |
869, 860, 868 | 3 | III |

870 |
878 | 1 | I |

880 |
885 | 1 | I |

890 |
890, 898, 890, 890 | 4 | IIII |

The class limits are represented along the *x-*axis and the frequencies along the *y-*axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is shown below:

(i) The group that has the maximum number of workers is represented as the highest rectangle. It is in the interval $830-840$.

(ii) The number of workers who earn Rs 850 or more can be calculated from frequency table in the following manner:

$1+3+1+1+4=10$

(iii) The number of workers who earn less than Rs 850 can be calculated from frequency table in the following manner:

$3+2+1+9+5=20$