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

Question

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 |

Answer 1

To find the expenditure below which 75% of families have their expenditure, we have to find Q3.

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 Q3 |
| 750 | 13 | 100 |
| Total | 100** | |

Here, n = 100

Q3 = 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.
Q3 = 650
The expenditure below which 75% of families include their expenditure is 650.