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# The frequency distribution table of agricultural 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

Find the modal agricultural holdings of the village

**Solution:**

Given, the above data represents the frequency distribution of agricultural holdings in a village.

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

Area of land (in hectares) | Number of families |

1 - 3 | 20 |

3 - 5 | 45 |

5 - 7 | 80 |

7 - 9 | 55 |

9 - 11 | 40 |

11 - 13 | 12 |

Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)]h

Where, l is the lower limit of the modal class

f₁ is the frequency of the modal class

f₀ is the frequency preceding the modal class

f₂ is the frequency succeeding the modal class

h is the class size

From the table,

Maximum frequency = 80

This frequency lies in the class 5-7

l = 5

h = 2

f₁ = 80

f₀ = 45

f₂ = 55

Now, f₁ - f₀ = 80 - 45 = 35

2f₁ - f₀ - f₂ = 2(80) - 45 - 55

= 160 - 100

= 60

[(f₁ - f₀)/(2f₁ - f₀ - f₂)] = 35/60

= 7/12

Now, mode = 5 + (7/12)2

= 5 + (14/12)

= 5 + 7/6

= 5 + 1.17

= 6.17

= 6.2

Therefore, the mode of the given data is 6.2

**✦ Try This: **The frequency distribution table of agricultural 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 | 25 | 49 | 90 | 85 | 60 | 32 |

Find the modal agricultural holdings of the village.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 14

**NCERT Exemplar Class 10 Maths Exercise 13.3 Sample Problem 4**

## The frequency distribution table of agricultural 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. Find the modal agricultural holdings of the village

**Summary:**

The modal agricultural holdings of the village is 6.2 hectares

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