Answer to Question #228249 in Statistics and Probability for Himanshu

Question

2(a) Construct Laspeyres, Paasche and Fisher indices from the following data:

Item 2018 2019

Price (Rs.) Expenditure (Rs.) Price (Rs.) Expenditure (Rs.)

A 10 60 15 75

B 12 120 15 150

C 18 90 27 81

D 8 40 12 48

2(b) Fit a straight line trend to the following data and estimate the expected profit for the year

2022. What is the average annual change in profit?

Year 2013 2014 2015 2016 2017 2018 2019

Profit (in lacs of Rs.) 60 72 75 65 80 85 95

Answer 1

Laspeyres index

$\frac{\sum P_1Q_1}{\sum P_0Q_0}*100$

Paasche index

$\frac{\sum P_1Q_1}{\sum P_0Q_1}*100$

Fisher index

$\sqrt\frac{\sum P_1Q_0}{\sum PQ_0}*\frac{\sum P_1Q_1}{\sum P_0Q_1}*100\\ =\sqrt{L*P}$

P_O, P₁ = Initial price and current price respectively

Q_O, Q₁= Initial quantity and current quantity respectively

Laspeyres index

$L=\frac{\sum P_1Q_1}{\sum P_0Q_0}*100\\ L=\frac{15*6+15*10+27*5+5*12}{10*6+12*10+18*5}*100\\ L=140.32$

Paasche index

$L=\frac{\sum P_1Q_1}{\sum P_0Q_1}*100\\ L=\frac{15*5+15*10+27*3+12*4}{10*5+12*10+18*3+8*4}*100\\ L=138.28$

Fisher index

$F=\sqrt\frac{\sum P_1Q_0}{\sum PQ_0}*\frac{\sum P_1Q_1}{\sum P_0Q_1}*100\\ F=\sqrt{L*P}\\ F=\sqrt{140.322*138.28}\\ F=139.2972$