Index Numbers and Time Based Data

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An index number is a measure of change in a group of related variables over two different situations with respect to time, geographical location, or other characteristics. It tracks the movement in th

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Relative Index Number for time period n = In = (pn/p0) × 100 Where: - pn = price in current period n - p0 = price in base period 0 For quantity index: In = (Qn/Q0) × 100 The base period always has

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Simple Aggregative Index = (Σpn/Σp0) × 100 Σp0 = 3.20 + 1.70 + 148.10 = ₹153.00 Σpn = 3.80 + 2.10 + 149.50 = ₹155.40 Index = (155.40/153.00) × 100 = 101.57 This shows prices increased by only 1.57%

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1. Heavily influenced by commodities with large unit prices 2. Commodities with lower unit prices get dominated by high-priced items 3. High unit prices become 'concealed weights' causing bias 4. Uses

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Laspeyres' Index uses base period quantities as weights. Developed by French economist Laspeyres in 1871. Formula: InLa = (Σpn × Q0)/(Σp0 × Q0) × 100 Where: - pn = current period prices - p0 = base

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Paasche's Index uses current period quantities as weights. Developed by German statistician Paasche in 1874. Formula: InPa = (Σpn × Qn)/(Σp0 × Qn) × 100 Differences from Laspeyres: 1. Uses current p

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Fisher's Ideal Index is the geometric mean of Laspeyres' and Paasche's indices. Formula: InF = √[(Σp1Q0/Σp0Q0) × (Σp1Q1/Σp0Q1)] × 100 It's called 'ideal' because: 1. It satisfies both time-reversal

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Time Reversal Test checks if an index method works regardless of which period is chosen as base. Test: P01 × P10 = 1 Where P01 = index for period 1 with base 0 P10 = index for period 0 with base 1 I