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 ₹)10-2020-3030-4040-5050-6060-70
No. of firms203070483250


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(n4)th observation

= Size of 3(2504)th observation

= Size of 3(62.5)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+(3n4-cf)f×h

Q3 = 50+3(250)4-16832×10

Q3 = 50+(582)32×10

Q3 = 50+(5820)32×10

Q3 = 50+181.875

Q3 = 50+181.875

Q3 = 231.875

Q3 = 231.875