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# The frequency distribution table of agriculture holdings in a village is given below:

Area of land (in hectares): | 1-3 | 3-5 | 5-7 | 7-9 | 9-11 | 11-13 |

Number of families: | 20 | 45 | 80 | 55 | 40 | 12 |

Given:

The frequency distribution table of agriculture holdings in a village is given.

To do:

We have to find the modal agriculture holdings of the village.

Solution:

The frequency of the given data is as given below.

Area of land (in hectares)($x_i$): | Number of families$(f_i$): |

1-3 | 20 |

3-5 | 45 |

5-7 | 80 |

7-9 | 55 |

9-11 | 40 |

11-13 | 12 |

We observe that the class interval of 5-7 has the maximum frequency(80).

Therefore, it is the modal class.

Here,

$l=5, h=2, f=80, f_1=45, f_2=55$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=5+\frac{80-45}{2 \times 80-45-55} \times 2$

$=5+\frac{35}{160-100} \times2$

$=5+\frac{70}{60}$

$=5+1.16$

$=6.16$

**The modal agriculture holdings of the village is 6.2 hectares.**

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