Compute the Laspeyre's, Paasche's and Fisher's index numbers for the year 2019 from the data given below: | Items | Quantity Year 2018 | Quantity Year 2019 | Price Year 2018 | Price Year 2019 | |---|---|---|---|---| | A | 25 kg | 32 kg | 42 | 45 | | B | 15 litre | 20 litre | 28 | 30 | | C | 10 pieces | 20 pieces | 30 | 36 | | D | 8 meter | 15 meter | 20 | 25 | | E | 30 litre | 36 litre | 60 | 65 |

> > [!TLDR] > Laspeyre $= \frac{\sum p_1q_0}{\sum p_0q_0}\times100 = 109.52$; Paasche $= \frac{\sum p_1q_1}{\sum p_0q_1}\times100 = 110.29$; Fisher $= \sqrt{L\times P} = 109.90$. > > Let subscript 0 = 2018 (base), 1 = 2019 (current). Compute the products: > > | Item | $q_0$ | $q_1$ | $p_0$ | $p_1$ | $p_1q_0$ | $p_0q_0$ | $p_1q_1$ | $p_0q_1$ | > |---|---|---|---|---|---|---|---|---| > | A | 25 | 32 | 42 | 45 | 1125 | 1050 | 1440 | 1344 | > | B | 15 | 20 | 28 | 30 | 450 | 420 | 600 | 560 | > | C | 10 | 20 | 30 | 36 | 360 | 300 | 720 | 600 | > | D | 8 | 15 | 20 | 25 | 200 | 160 | 375 | 300 | > | E | 30 | 36 | 60 | 65 | 1950 | 1800 | 2340 | 2160 | > | **Total** | | | | | **4085** | **3730** | **5475** | **4964** | > > **Laspeyre's index (base-year weights):** > $$P_{01}^{L} = \frac{\sum p_1 q_0}{\sum p_0 q_0}\times 100 = \frac{4085}{3730}\times 100 = 109.52$$ > …

Compute the Laspeyre's, Paasche's and Fisher's ind – Class 12 Statistics

Question 19 of 45

Compute the Laspeyre's, Paasche's and Fisher's index numbers for the year 2019 from the data given below:

Items	Quantity Year 2018	Quantity Year 2019	Price Year 2018	Price Year 2019
A	25 kg	32 kg	42	45
B	15 litre	20 litre	28	30
C	10 pieces	20 pieces	30	36
D	8 meter	15 meter	20	25
E	30 litre	36 litre	60	65

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2020Subjective· 5mImportance★★★★★

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Laspeyre $= \frac{\sum p_1q_0}{\sum p_0q_0}\times100 = 109.52$ ; Paasche $= \frac{\sum p_1q_1}{\sum p_0q_1}\times100 = 110.29$ ; Fisher $= \sqrt{L\times P} = 109.90$ .

Let subscript 0 = 2018 (base), 1 = 2019 (current). Compute the products:

Item	$q_0$	$q_1$	$p_0$	$p_1$	$p_1q_0$	$p_0q_0$	$p_1q_1$	$p_0q_1$
A	25	32	42	45	1125	1050	1440	1344
B	15	20	28	30	450	420	600	560
C	10	20	30	36	360	300	720	600
D	8	15	20	25	200	160	375	300
E	30	36	60	65	1950	1800	2340	2160
Total					4085	3730	5475	4964

Laspeyre's index (base-year weights):

$P_{01}^{L} = \frac{\sum p_1 q_0}{\sum p_0 q_0}\times 100 = \frac{4085}{3730}\times 100 = 109.52$

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