Find Laspeyre's, Paasche's and Fisher's index numbers for the year 2024 with base year 2023 from the data about price and consumption of food items given below : | Item | Unit | Price 2024 (₹) | Quantity 2024 | Price 2023 (₹) | Quantity 2023 | |---|---|---|---|---|---| | Rice | 20 kg. | 800 | 1.5 kg. | 780 | 1 kg. | | Milk | Litre | 44 | 10 Litre | 40 | 12 Litre | | Bread | kg. | 50 | 1.5 kg. | 45 | 2 kg. | | Banana | Dozen | 36 | 1.5 Dozen | 30 | 2 Dozen |

> > [!TLDR] > From the weighted totals: Laspeyre $= \tfrac{1500}{1410}\times 100 = 106.38$, Paasche $= \tfrac{1769}{1682.5}\times 100 = 105.14$, Fisher $= \sqrt{106.38\times 105.14} = 105.76$. > > GSEB Class-12 Statistics, Index Number (weighted index numbers): > > Here $0 = 2023$ (base) and $1 = 2024$ (current). Using the prices and quantities: > > | Item | $p_0$ | $q_0$ | $p_1$ | $q_1$ | $p_1 q_0$ | $p_0 q_0$ | $p_1 q_1$ | $p_0 q_1$ | > |---|---|---|---|---|---|---|---|---| > | Rice | 780 | 1 | 800 | 1.5 | 800 | 780 | 1200 | 1170 | > | Milk | 40 | 12 | 44 | 10 | 528 | 480 | 440 | 400 | > | Bread | 45 | 2 | 50 | 1.5 | 100 | 90 | 75 | 67.5 | > | Banana | 30 | 2 | 36 | 1.5 | 72 | 60 | 54 | 45 | > | **Total** | | | | | **1500** | **1410** | **1769** | **1682.5** | > > **Laspeyre's index** (base-year quantities as weights): > $$P_{01}^{L} = \frac{\Sigma p_1 q_0}{\Sigma p_0 q_0} \times 100 = \frac{1500}{1410} \times 100 = 106.38$$ > …

Find Laspeyre's, Paasche's and Fisher's index numbers for the year 2024 with base year 2023 from the data abou

Question 38 of 45

Find Laspeyre's, Paasche's and Fisher's index numbers for the year 2024 with base year 2023 from the data about price and consumption of food items given below :

Item	Unit	Price 2024 (₹)	Quantity 2024	Price 2023 (₹)	Quantity 2023
Rice	20 kg.	800	1.5 kg.	780	1 kg.
Milk	Litre	44	10 Litre	40	12 Litre
Bread	kg.	50	1.5 kg.	45	2 kg.
Banana	Dozen	36	1.5 Dozen	30	2 Dozen

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2025Subjective· 5mImportance★★★★★

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From the weighted totals: Laspeyre $= \tfrac{1500}{1410}\times 100 = 106.38$ , Paasche $= \tfrac{1769}{1682.5}\times 100 = 105.14$ , Fisher $= \sqrt{106.38\times 105.14} = 105.76$ .

GSEB Class-12 Statistics, Index Number (weighted index numbers):

Here $0 = 2023$ (base) and $1 = 2024$ (current). Using the prices and quantities:

Item	$p_0$	$q_0$	$p_1$	$q_1$	$p_1 q_0$	$p_0 q_0$	$p_1 q_1$	$p_0 q_1$
Rice	780	1	800	1.5	800	780	1200	1170
Milk	40	12	44	10	528	480	440	400
Bread	45	2	50	1.5	100	90	75	67.5
Banana	30	2	36	1.5	72	60	54	45
Total					1500	1410	1769	1682.5

Laspeyre's index (base-year quantities as weights):

$P_{01}^{L} = \frac{\Sigma p_1 q_0}{\Sigma p_0 q_0} \times 100 = \frac{1500}{1410} \times 100 = 106.38$

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