Calculate Q3 for the following data. Sales (in lakhs ₹) 10-20 20-30 30-40 40-50 50-60 60-70 No. of firms 20 30 70 48 32 50 - Economics

QUESTION

Calculate Q₃ for the following data.

Sales (in lakhs ₹)	10-20	20-30	30-40	40-50	50-60	60-70
No. of firms	20	30	70	48	32	50

SOLUTION

Sales (in lakhs Rs)	Number of firms	cf
10-20	20	20
20-30	30	50
30-40	70	120
40-50	48	168
50-60	32	200
60-70	50	250
	N = 250

Q₃= Size of 3${\displaystyle {\left(\frac{n}{4}\right)}^{\text{th observation}}}$

= Size of 3${\displaystyle {\left(\frac{250}{4}\right)}^{\text{th observation}}}$

= Size of 3${\displaystyle {\left(62.5\right)}^{\text{th observation}}}$

= Size of 187.5^{th observation}

= Size of 187.5^{th observation} lies in cf 200

Hence, quartile class is 50-60

L = 50, F = 32, CF = 168, N = 250, H = 10

Q₃ = 1+${\displaystyle \frac{(\frac{3n}{4}-cf)}{f}\times h}$

Q₃ = 50+${\displaystyle \frac{\frac{3\left(250\right)}{4}-168}{32}\times 10}$

Q₃ = 50+${\displaystyle \frac{\left(582\right)}{32}\times 10}$

Q₃ = 50+${\displaystyle \frac{\left(5820\right)}{32}\times 10}$

Q₃ = 50+181.875

Q₃ = 50+181.875

Q₃ = 231.875

Q₃ = 231.875