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in Economics by (70.4k points)
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The distribution of amount paid by 200 customers coming for snacks at a restaurant on a particular day is given below:

Amount (₹) 0 - 50 50 - 100 100 - 150 150 - 200 200 - 250
No. of customers 25 40 80 30 25

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Amount paid ₹ No. of customers f Cumulative frequency cf
0-50 25 25
50- 100 40 65
100-150 80 145
150-200 30 175
200 – 250 25 200
Total n = 200 -

First Quartile:

Q1 Class = Class that Includes \(\left(\frac{n}{4}\right)\)th observation

= Class that includes \(\left(\frac{200}{4}\right)\) = 50th observation

Referring to column cf

Q1 class = 50 – 100

Now, Q1 = L + \(\frac{\left(\frac{n}{4}\right)-c f}{f}\) × c

Putting L = 50: \(\left(\frac{n}{4}\right)\) = 50: cf = 25: f = 40 and c = 50 In the formula,

Third Quartile:

Q3 Class = Class that Includes 3 \(\left(\frac{n}{4}\right)\)th observation

= Class that Includes 3 (50)th = 150th observation

Referring to column cf. Q3 class = 150 – 200

Now. Q3 = L + \(\frac{3\left(\frac{n}{4}\right)-c f}{f}\) × c

Putting L = 150: 3 \(\left(\frac{n}{4}\right)\) = 150: cf = 145; f = 30 and c = 50 in the formula.

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