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 Qfor 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${\left(\frac{n}{4}\right)}^{\text{th observation}}$

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

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

= Size of 187.5th observation

= Size of 187.5th observation lies in cf 200

Hence, quartile class is 50-60

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

Q3 = 1+$\frac{\left(\frac{3n}{4}-cf\right)}{f}×h$

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

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

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

Q3 = 50+181.875

Q3 = 50+181.875

Q3 = 231.875

Q3 = 231.875