My Cart
Your Cart 0

    Your cart is empty.

  • Total (Amount) ₹0.00
NCERT · Class 11 · Statistics

Chapter 7: Index Numbers

Practice each question, then open the answer or worked solution.

Textbook exercises

22 questions
Q21Written answer

Given the following data—

YearCPI of industrial workers (1982 = 100)CPI of agricultural labourers (1986–87 = 100)WPI (1993–94 = 100)
1995–96313234121.6
1996–97342256127.2
1997–98366264132.8
1998–99414293140.7
1999–00428306145.3
2000–01444306155.7
2001–02463309161.3
2002–03482319166.8
2003–04500331175.9

(i) Comment on the relative values of the index numbers.

(ii) Are they comparable?

Show solutionHide solution
Worked solution
ANSWER (i) Comment on the relative values: All three index numbers rise steadily over the period, showing a continuous increase in prices (inflation). The CPI of industrial workers is the highest throughout, rising from 313 to 500 — an increase of about 60% over the period — reflecting a sharp rise in their cost of living. The CPI of agricultural labourers rises from 234 to 331 (about 41%), a slower increase. The WPI rises from 121.6 to 175.9 (about 45%). Thus the cost of living of industrial workers rose faster than that of agricultural labourers, while wholesale prices rose moderately. (ii) Are they comparable? No, they are not directly comparable. The three indices have different base years (1982, 1986–87 and 1993–94) and cover different baskets of goods and different categories (industrial workers, agricultural labourers, and wholesale prices in general). Because the bases and baskets differ, their absolute values cannot be compared side by side; we can only compare the trend or rate of change within each series, not the level of one against another. To compare them properly they must first be converted to a common base year.
Q22Written answer

The monthly expenditure (Rs.) of a family on some important items and the Goods and Services Tax (GST) rates applicable to these items is as follows: Calculate the average tax rate as far as this family is concerned.

ItemMonthly Expense (Rs)GST Rate %
Cereals15000
Eggs2500
Fish, Meat2500
Medicines505
Biogas505
Transport1005
Butter5012
Babool1012
Tomato Ketchup4012
Biscuits7518
Cakes, Pastries2518
Branded Garments10018
Vacuum Cleaner, Car100028
Show solutionHide solution
Worked solution
ANSWER The average GST rate is a weighted average, where the weights are the shares of expenditure on each category and the variable is the GST rate. Group the items by their common GST rate and add up the expenditure in each group.
Category (GST slab)Expenditure / Weight (w)GST Rate (x)wx
Category 1 (0%): Cereals, Eggs, Fish & Meat20000.000
Category 2 (5%): Medicines, Biogas, Transport2000.0510
Category 3 (12%): Butter, Babool, Tomato Ketchup1000.1212
Category 4 (18%): Biscuits, Cakes/Pastries, Branded Garments2000.1836
Category 5 (28%): Vacuum Cleaner, Car10000.28280
Total3500338
Average GST rate = Σwx / Σw = 338 / 3500 = 0.0966. The average tax (GST) rate for this family is 0.0966, i.e. about 9.66 per cent.