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# The monthly income of 100 families are given as below

Income (in Rs) Number of families

0 - 5000 8

5000 - 10000 26

10000 - 15000 41

15000 - 20000 16

20000 - 25000 3

25000 - 30000 3

30000 - 35000 2

35000 - 40000 1

Calculate the modal income

**Solution:**

Given, the monthly income of 100 families.

We have to find the modal income.

Income (in Rs) |
Number of families |

0 - 5000 |
8 |

5000 - 10000 |
26 |

10000 - 15000 |
41 |

15000 - 20000 |
16 |

20000 - 25000 |
3 |

25000 - 30000 |
3 |

30000 - 35000 |
2 |

35000 - 40000 |
1 |

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 = 41

This frequency lies in the class 10000 - 15000

l = 10000

h = 5000

f₁ = 41

f₀ = 26

f₂ = 16

Now, f₁ - f₀ = 41 - 26 = 15

2f₁ - f₀ - f₂ = 2(41) - 26 - 16

= 82 - 42

= 40

[(f₁ - f₀)/(2f₁ - f₀ - f₂)] = 15/40

= 3/8

Now, mode = 10000 + (3/8)(5000)

= 10000 + (15000/8)

= 10000 + 1875

= 11875

Therefore, the modal income is 11875.

**✦ Try This: **The monthly income of 100 families are given as below:

Income (in Rs) | Number of families |

0 - 5000 | 7 |

5000 - 10000 | 25 |

10000 - 15000 | 47 |

15000 - 20000 | 15 |

20000 - 25000 | 2 |

25000 - 30000 | 6 |

30000 - 35000 | 1 |

35000 - 40000 | 6 |

Calculate the modal income.

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

**NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 17**

## The monthly income of 100 families are given as below: Income (in Rs) Number of families 0 - 5000 8 5000 - 10000 26 10000 - 15000 41 15000 - 20000 16 20000 - 25000 3 25000 - 30000 3 30000 - 35000 2 35000 - 40000 1. Calculate the modal income

**Summary:**

The modal income of 100 families is 11875

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