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 | 32 | 42 | 45 | | B | 15 | 20 | 28 | 30 | | C | 10 | 20 | 30 | 36 | | D | 8 | 15 | 20 | 25 | | E | 30 | 36 | 60 | 65 |

> > [!TLDR] > $\sum p_1q_0=4085,\ \sum p_0q_0=3730,\ \sum p_1q_1=5475,\ \sum p_0q_1=4964$; $L=109.52,\ P=110.29,\ F=\sqrt{LP}=109.90$. > > With base year 2018 ($p_0,q_0$) and current year 2019 ($p_1,q_1$): > > | 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 quantity weights): > $$P_{01}^{L}=\frac{\sum p_1q_0}{\sum p_0q_0}\times100=\frac{4085}{3730}\times100=109.52.$$ > …

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

Question 31 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	32	42	45
B	15	20	28	30
C	10	20	30	36
D	8	15	20	25
E	30	36	60	65

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2023Subjective· 5mImportance★★★★★

69% · 31/45 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 →

$\sum p_1q_0=4085,\ \sum p_0q_0=3730,\ \sum p_1q_1=5475,\ \sum p_0q_1=4964$ ; $L=109.52,\ P=110.29,\ F=\sqrt{LP}=109.90$ .

With base year 2018 ( $p_0,q_0$ ) and current year 2019 ( $p_1,q_1$ ):

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 quantity weights):

$P_{01}^{L}=\frac{\sum p_1q_0}{\sum p_0q_0}\times100=\frac{4085}{3730}\times100=109.52.$

…

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

←Previous questionQ16 — The data about per unit price and weights for four different items in …→Next questionQ18 — Which prices are considered in the construction of the cost of living …

🎓Unlock everything free for 14 days

Unlock everything free for 14 days