Compute Laspeyre's, Paasche's and Fisher's index number for the year 2021 from the data given below. | Item | Quantity Year 2021 | Quantity Year 2020 | Price (₹) Year 2021 | Price (₹) Year 2020 | |---|---|---|---|---| | A | 25 kg | 32 kg | 42 | 45 | | B | 15 litre | 20 litre | 28 | 30 | | C | 10 pieces | 20 pieces | 30 | 36 | | D | 8 metre | 15 metre | 20 | 25 | | E | 30 litre | 36 litre | 60 | 65 |

> > [!TLDR] > With base 2020, current 2021: $\Sigma p_0q_0=5475,\ \Sigma p_1q_0=4964,\ \Sigma p_0q_1=4085,\ \Sigma p_1q_1=3730$. Laspeyre $\approx90.67$, Paasche $\approx91.31$, Fisher $\approx\mathbf{90.99}$. > > **Notation:** $p_0,q_0$ = 2020 (base) price & quantity; $p_1,q_1$ = 2021 (current) price & quantity. > > **Working table:** > > | Item | $q_0$ | $q_1$ | $p_0$ | $p_1$ | $p_0q_0$ | $p_1q_0$ | $p_0q_1$ | $p_1q_1$ | > |---|---|---|---|---|---|---|---|---| > | A | 32 | 25 | 45 | 42 | 1440 | 1344 | 1125 | 1050 | > | B | 20 | 15 | 30 | 28 | 600 | 560 | 450 | 420 | > | C | 20 | 10 | 36 | 30 | 720 | 600 | 360 | 300 | > | D | 15 | 8 | 25 | 20 | 375 | 300 | 200 | 160 | > | E | 36 | 30 | 65 | 60 | 2340 | 2160 | 1950 | 1800 | > | **Total** | | | | | **5475** | **4964** | **4085** | **3730** | > > **Laspeyre's index (base-year weights):** > $$P_{01}^{L}=\frac{\Sigma p_1q_0}{\Sigma p_0q_0}\times100=\frac{4964}{5475}\times100=90.67.$$ > …

Compute Laspeyre's, Paasche's and Fisher's index n – Class 12 Statistics

Question 26 of 45

Compute Laspeyre's, Paasche's and Fisher's index number for the year 2021 from the data given below.

Item	Quantity Year 2021	Quantity Year 2020	Price (₹) Year 2021	Price (₹) Year 2020
A	25 kg	32 kg	42	45
B	15 litre	20 litre	28	30
C	10 pieces	20 pieces	30	36
D	8 metre	15 metre	20	25
E	30 litre	36 litre	60	65

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2022Subjective· 5mImportance★★★★★

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With base 2020, current 2021: $\Sigma p_0q_0=5475,\ \Sigma p_1q_0=4964,\ \Sigma p_0q_1=4085,\ \Sigma p_1q_1=3730$ . Laspeyre $\approx90.67$ , Paasche $\approx91.31$ , Fisher $\approx\mathbf{90.99}$ .

Notation: $p_0,q_0$ = 2020 (base) price & quantity; $p_1,q_1$ = 2021 (current) price & quantity.

Working table:

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

Laspeyre's index (base-year weights):

$P_{01}^{L}=\frac{\Sigma p_1q_0}{\Sigma p_0q_0}\times100=\frac{4964}{5475}\times100=90.67.$

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