Sum

For the following data of daily expenditure of families (in ₹), compute the expenditure below which 75% of families include their expenditure.

Daily expenditure (in ₹) |
350 | 450 | 550 | 650 | 750 |

No. of families |
16 | 19 | 24 | 28 | 13 |

Advertisement Remove all ads

#### Solution

To find the expenditure below which 75% of families have their expenditure, we have to find Q_{3}.

We construct the less than cumulative frequency table as given below:

Daily expenditure (in ₹) |
No. of families (f) |
Less than cumulative frequency(c.f.) |

350 | 16 | 16 |

450 | 19 | 35 |

550 | 24 | 59 |

650 | 28 | 87 ← Q_{3} |

750 | 13 | 100 |

Total |
100 |

Here, n = 100

Q_{3 }= value of 3 `(("n" + 1)/4)^"th"`observation

= value of `3((100+1)/4)^"th"`observation

= value of (3 × 25.25)^{th} observation

= value of (75.75)^{th} observation

Cumulative frequency which is just greater than (or equal to) 75.75 is 87.

∴ Q_{3} = 650

∴ The expenditure below which 75% of families include their expenditure is 650.

Concept: Quartiles

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads