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.