Skip to content
Worked Examples · Example 7
Q.

Calculate the price index using weighted average of relatives method for the food consupltion in a student hostel in a month. Use data of year 1997 as base year for calculations.

CommodityWeightPrice per unit 1997Price per unit 2001
Rice14 quintals90120
Wheat20 kg3046
Pulses35 kg2234
Milk15 litre5090
Sikkim CbseNCERTSubjective· 3mImportance★★★★★est
18% · 7/40 Questions
🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Weight each price relative R=pnp0×100R=\dfrac{p_n}{p_0}\times100 by its base-period value p0Q0p_0 Q_0: P01=∑(p0Q0)R∑p0Q0=∑pnQ0∑p0Q0×100=51403380×100≈152.07P_{01}=\dfrac{\sum (p_0 Q_0)R}{\sum p_0 Q_0}=\dfrac{\sum p_n Q_0}{\sum p_0 Q_0}\times100=\dfrac{5140}{3380}\times100\approx 152.07.

R=pnp0×100,P01=∑(p0Q0) R∑p0Q0=∑pnQ0∑p0Q0×100R=\frac{p_n}{p_0}\times100,\qquad P_{01}=\frac{\sum (p_0 Q_0)\,R}{\sum p_0 Q_0}=\frac{\sum p_n Q_0}{\sum p_0 Q_0}\times100

where the weight is the base-period value p0Q0p_0 Q_0 (base price × base quantity), p0p_0 = 1997 price and pnp_n = 2001 price.

  1. Form the value weight p0Q0p_0 Q_0 and the weighted relative (pnp0)p0Q0=pnQ0\left(\frac{p_n}{p_0}\right)p_0 Q_0 = p_n Q_0 for each commodity.
CommodityQ0Q_0p0p_0 (1997)pnp_n (2001)Value weight p0Q0p_0 Q_0(pnp0)p0Q0=pnQ0\left(\frac{p_n}{p_0}\right)p_0 Q_0 = p_n Q_0
Rice14901201260126016801680
Wheat203046600600920920
Pulses35223477077011901190
Milk15509075075013501350
Total∑p0Q0=3380\sum p_0 Q_0 = 338051405140

Unlock everything free for 14 days

  • Full step-by-step solutions
  • Concept-first explanations
  • Methods, shortcuts & mistakes
  • PYQ mapping + timed mock tests

Full access for 14 days. No credit card required.