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

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

#### Solution

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.

Concept: Quartiles
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