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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
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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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