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## Karnataka 2nd PUC Statistics Question Bank Chapter 2 Index Number

Section – A

### 2nd PUC Statistics Index Number One Mark Questions and Answers

Question 1.

What is an index number?

Answer:

“Index numbers are statistical devices designed to measure the relative changes in the level of a phenomenon with respect to time, geographical location or other characteristics such as income, profession, etc”

Question 2.

Why index numbers are known “economic barometers”?

Answer:

Index numbers measures the pulses of an economy and act as barometers to find the variations or fluctuations in economic conditions of a country.

Question 3.

Define price relative.

Answer:

Price relative is the price of the current year (p_{1})expressed as the percentage of the price in the base year (p_{0}).

Question 4.

What is value of index number for the base year?

Answer:

100.

Question 5.

If price during the current year is triple the price during the base year, what is the index number?

Answer:

Question 6.

If the current year price index is 175, what would you conclude?

Answer:

The prices have increased by 75% in the Current year when compared to base year

Question 7.

Ilf the general price level goes up by 80% between 2000 & 2012, what is the index number for 2012 with base 2000?

Answer:

The price increased by 180% in the current year 2012 than base year 2000.

Question 8.

If the quantity index number for current year is 80, then what would you conclude?

Answer:

Quantity has decreased by 20% in the current year than base year.

Question 9.

Mention one characteristic of index numbers.

Answer:

Index numbers are specialised type of averages

Question 10.

Mention one use of index numbers.

Answer:

Trends and tendencies can be calculated by using index numbers.

Question 11.

Mention one limitation of index numbers.

Answer:

Since index numbers are based on the sample data, they are only approximate indicators.

Question 12.

(a) What is meant by price index number?

(b) What is meant by quantity index number?

(c) What is meant by value index number?

Answer:

(a) The price index numbers study general change in the prices of articles in the current period as compared to that of the base period.

(b) Quantity index number measure the relative change in the volume of goods manufactured or produced consumed or distributed.

(c) Value index numbers measure the relative change in the total money value of production.

Question 13.

What is meant by fixed base index number?

Answer:

If the period of observation is kept fixed for all current years is named as fixed – base index number.

Question 14.

whatis meant by chain base index number?

Answer:

Chain base period is the relative changes in the level of phenomenon for any period are compared with that of the immediate preceding period.

Question 15.

Name the common average used in construction of index numbers.

Answer:

Arithmetic Mean

Question 16.

Theoretically which average is considered as the best average in the construction of index number?

Answer:

Geometric Mean

Question 17.

Why an index number based on AM would be higher than an index number based on GM?

Answer:

A.M gives greater weightage to bigger items, so index number which uses A.M is always higher than the G.M

Question 18.

Write down the formulae for Laspeyre’s, Paasche’s, Marshall Edgeworth’s, Dorbish-Bowley’s and Fisher’s price and quantity index numbers.

Answer:

Question 19.

Write down the expression for Kelly’s fixed weight price index number.

Answer:

Here q denotes the quantity for both base and current period.

Question 20.

Which system of weights is used in the construction of Laspeyre’s price index number?

Answer:

In Laspeyre’s price index number only Base year quantities are used as weights

Question 21.

Which system of weights is used in the construction of Paasche’s price index number?

Answer:

In Paasche’s price index number only Current year quantities are used as weights

Question 22.

Which system of weights is used in the construction of Marshall-Edge worthy’s and Fisher’s price index number?

Answer:

Both base and current year quantities are used

Question 23.

Which system of weights are used in the construction of Laspeyre’s & Paasche’s quantity index numbers?

Answer:

Base year price are used as weights in Laspeyre’s quantity index nos. Current year price are used as weights in Paasche’s quantity index nos.

Question 24.

Which system of weights are used in the construction of Marshall Edge Worth’s & fisher’s quantity index numbers?

Answer:

Both base year & current year prices are used as weights in Marshall-Edgeworth’s & Fisher’s quantity index numbers.

Question 25.

State the relation between Laspeyre’s, Paasche’s and Dorbish-Bowley’s index numbers.

Answer:

Question 26.

State the relation between Laspeyre’s, Paasche’s and Fisher’s indices.

Answer:

Fisher’s index number is Geometric Mean of Laspeyre’s, Paasche’s index numbers.

Question 27.

Name the index number which does not satisfy unit test.

Answer:

Simple aggregative Price Index number.

Question 28.

State the condition required to satisfy Time Reversal Test (TRT).

Answer:

TRT, P_{01} × P_{10} = 1

Question 29.

Name the index number which satisfies TRT.

Answer:

Fisher’s index number and Marshall Edgeworth index number.

Question 30.

State the condition required to satisfy Factor Reversal Test (FRT).

Answer:

Question 31.

Name the index number which satisfies FRT.

Answer:

Fisher’s index number.

Question 32.

Name the index number which satisfies both TRT and FRT.

Answer:

Fisher’s index number.

Question 33.

Does Marshall-Edgeworth’s index numbers satisfies TRT?

Answer:

Yes, Marshall-Edgeworth’s Index number satisfies TRT.

Question 34.

Does, Marshall-Edgeworth’s index numbers satisfies FRT?

Answer:

No, Marshall-Edgeworth’s index numbers does not satisfies FRT.

Question 35.

Name the index number which satisfies circular test

Answer:

Kelly’s fixed weights.

Question 36.

Which index number show upward bias?

Answer:

Laspeyre’s index number.

Question 37.

Why Paasche’s index number shows downward bias?

Answer:

Paasche’s index which uses the current year quantities as weights, it is an under-estimate because the greater variations of price will be paid lesser importance than needed. So it shows downward bias.

Question 38.

Why Fisher’s index number is free from bias?

Answer:

Fisher in is based on geometric mean which is the best average for averaging ratios so, it is free from bias.

Question 39.

Define consumer price index number (cost of living index number).

Answer:

Consumer price index is the index number of the cost met by a specified class of consumers in buying a ‘basket of goods and services’.

Question 40.

Which price of the commodities is used in the construction of cost of living index number?

Answer:

Retail price is used in the construction of CLI.

Question 41.

State the formula for computing CPI by family budget method.

Answer:

Calculation of CPI under family budget method:

Question 42.

State the formula for computing CPI by aggregative expenditure method.

Answer:

Consumer price index by aggregative expenditure method:

Section – B

### 2nd PUC Statistics Index Number Two Marks Questions and Answers

Question 1.

Define an index number.

Answer:

Index numbers are statistical tool that is designed to find the relative change with respect to various factors such as change in time, geographical location or other ‘characteristics such as income, profession, etc.

Question 2.

State two characteristics of index numbers.

Answer:

The two characteristics of index numbers are:

- Index numbers help in comparison of data
- Index numbers examine the effect relationship which cannot be measured directly.

Question 3.

State two uses of index numbers.

Answer:

The two uses of index numbers are:

- Comparative study of a data is made possible as the burden of the data is reduces.
- Purchasing power of money can be measured and used in times of deflation.

Question 4.

State two limitations of index numbers.

Answer:

The two limitations of index numbers are:

- Assignment of proper weights to various items are tough to ascertain as there is a difference of measurement from place to place.
- Each formulae gives different answer to one problem.

Question 5.

Price index for the current year with respect to base year is 140. If the price of a commodity in the base year is ₹ 60, then what would be the price in the current year?

Answer:

Question 6.

Quantity index number for current year is 250. If the number of units produced in the current year is 120 then find the number of units produced in the base year?

Answer:

Question 7.

Mention the steps involved in the construction of general price index number.

Answer:

Steps involved in the construction of an index number are

- Defining purpose of index number.
- Selecting the base period.
- Selecting the items.
- Obtaining the price quotations
- Choice of an average
- Selection suitable formula.
- Selection the weights.

Question 8.

What is meant by base period and current period?

Answer:

The Index number which shows the overall level of a group of related variables at a given time is called current period, Index number is compared at some other time is named as Base period

Question 9.

State any two considerations (norms) for the selection of base year.

Answer:

The two considerations (norms) for the selection of base year are:

- Base period should be economically stable.
- The base period should not be too distant from current period.

Question 10.

Briefly explain unit test.

Answer:

This test requires that the index numbers should be independent of the units in which price or quantities of various commodities are quoted.

This test is satisfied by all index numbers except simple aggregative price index number.

Question 11.

Explain TRT.

Answer:

In TRT, an index number (P_{01}) should be such that when base year and current year are interchanged (P_{10}) the resulting index number should be the reciprocal of the earlier. i.e., P_{01} × P_{10} = 1

Question 12.

Explain FRT.

Answer:

In FRT, the changes in the price multiplied by changes in the quantity should be equal to the total change in value. i.e., P_{01} × Q_{01} = V_{01}

Question 13.

Briefly explain circular test.

Answer:

The extension of time reversal test for more than two periods and is based on the shift ability of the base period is known as circular test.

Question 14.

Why Fisher’s index number is called ‘Ideal Index Number’?

Answer:

Fisher’s index number is called ‘ideal index number ‘ because of the following reasons:

- It is a geometric mean which is considered as the appropriate average for averaging ratios
- It takes into account of the base year quantities as well as the current year quantities
- It is free of bias.
- It satisfies both time reversal test and factor reversal tests

Question 15.

If Laspayre’s index Is 142.3 and paasche’s index is 144.1, find.

(a) Fisher’s index

(b) Dorbish-Bowley’s index

Answer:

Question 16.

If P^{p}_{01} = 270 and P^{DB}_{01} = 265.4 then find P^{L}_{01} = ?

Answer:

Question 17.

If P^{L}_{01} = 92 and P^{F}_{01} = 95 then P^{p}_{01}

Answer:

Question 18.

Given Σp_{0}q_{1} = 300 and Σp_{1}q_{1} = 375. construct a suitable price index number.

Answer:

Question 19.

Given Σp_{0}q_{1} = 172 and Σp_{0}q_{0} = 192. Compute suitable quantity index number.

Answer:

Question 20.

If Σp_{0}q_{1} = 1100 and Σp_{0}q_{1} = 1400, compute suitable index number.

Answer:

Question 21.

Write down the steps involved in the construction of consumer price index number?

Answer:

- Finding purpose and scope
- Making a survey in family budget and selection of units
- Preparing price quotations
- Calculating index numbers.

Question 22.

Write down any two uses of CPI.

Answer:

- It is used to fix salaries, allowances and bonus to the employees.
- They are used for formulation of economic policies

Question 23.

Construct the consumer price index Number for the following data

Answer:

Section – C

### 2nd PUC Statistics Index Number One Marks Questions and Answers

Question 1.

Write down the uses of index numbers.

Answer:

The uses of index numbers are:

- It facilitates comparative study by simplifying the data
- Study of trends and tendencies become easier.
- Index numbers help in ascertaining the current situation of the market by defining the purchasing power of money and also used for deflation.
- Cost of living of different groups of people can be measured by using index numbers.
- Formulation of various economic plans and policies are facilitated by index numbers.

Question 2.

Write down the limitations of index numbers.

Answer:

The limitations of index numbers are:

- Since index numbers are based on the sample data, they give their estimate as approximate only.
- There are chances of errors occurring at each stage of calculation of the construction of the index numbers.
- Quality of the product is not taken into consideration While construction of index .
- The results can be missed to get conclusion as desired just like other statistical devices.
- Collection of data will be difficult as customs, traditions and habits of people are vary from time to time and thus it is difficult to assign proper weights to the various items.
- Each formulae gives different answers and thus decision taking becomes complicated.

Question 3.

What are the steps involved in the construction of index number?

Answer:

The steps involved in the construction of index numbers are:

- Finding purpose and scope
- Making a survey in family budget and selection of units
- Preparing price quotations
- Calculating index numbers.

Question 4.

Show that Marshall-Edge worth’s index number satisfies TRT.

Answer:

According to TRT, P_{01} × P_{10} = 1

Thus Marshall-Edge worth’s index number satisfies TRT.

Question 5.

Show that Fisher’s index number satisfies TRT.

Answer:

According to

Here Thus Fisher’s index number satisfies TRT.

Question 6.

Show that Fisher’s index number satisfies FRT.

Answer:

Question 7.

Write down the uses of cost of living Index.

Answer:

The uses of cost of living Index are:

1. Purchasing power of money can be determined as well as for computing the real wages fixation of salary, dearness allowance (D.A) or grant of bonus to the employees are computed with the help of index numbers.

2. They are used by government for formulation of price policy, wage policy and general economic policies.

3. Comparative analysis between people of different classes can be made.

Cost of living index number is used widely in the wage negotiation and wage contracts.

Question 8.

Explain briefly the steps involved in the construction of cost of living index number.

Answer:

The steps involved in the construction of cost of living index number are:

1. Defining the purpose of the index number: The whole purpose of the process should be well known to the researcher in order to get desired result.

2. Conducting family budget enquiry and selecting the weights: The most important step is to do a survey on the expenses and income of the family and classify them in accordance with their expense. Items are classified according to food, clothing, fuel and lighting, house rent and miscellaneous. Here, the economic stability conduced on a random basis, during a period of economic stability. Thus the family budget enquiry gives us the average budget of that class.

3. Obtaining price Quotations: while constructing cost of living index number, collection of price of each commodity is to be found. Collection of retail price is a very difficult task and they vary from one place to another place and even at shop to shop and even at one shop from one consumer to another consumer. Therefore price quotations should be obtained from different localities and averaged. These averages are made use in the construction of index number

4. Computing the index numbers: There are two methods of calculating CPI. They are

a. Aggregative expenditure method

b. Family budget method

### 2nd PUC Statistics Index Number Exercise Problems

Question 1.

Calculate the price Index for the following data by using the aggregate method.

Answer:

P_{01} = 125.61

∴ 25.61% of price is increased in the current year When compare to base year.

Question 2.

Calculate the price index number using unweighed aggregative method for the year 2010 and 2011 on the basis of 2008 from the following data.

Answer:

Unweighted aggregative index for 2010 on the base of 2008

∴ 14.3 7% of price is increased in the current year

When compare to (base year) 2008.

Unweighted aggregative index for 2011 on the base of 2008

∴ 32.18% of price is increased in 2011 When compare to 2008.

Question 3.

From the following data calculate in weighted arithmetic mean index number and Geometric mean index number.

Answer:

unweighted arithmetic mean index number

∴ 9.36% of price is increased in 2012 when compare to 2010.

= Antilog(2.0368) = 108.8

∴ 8.8% of price is increased in 2012 when compare to 2010.

Question 4.

Compute Laspeyre’s, Paasche’s, MarshalJ Edge worth’s, DorbishBowley’s and Fisher’s price index numbers index numbers

Answer:

Question 5.

Calculate Laspeyre’s price index number for the following data and give your conclusion.

Answer:

Question 6.

Construct Marshall Edge worth’s, Dorbish-Bowley’s and Fishers Price index number for the following data.

Answer:

Question 7.

Compute suitable index number from the following data.

Answer:

Question 8.

Compute suitable index number from the following data

Answer:

Question 9.

Compute Kelly’s price Index number for the following data.

Answer:

Question 10.

Compute index number for 2009 and 2010 with base 2005. Hence compare the price levels in 2009 and 2010.

Answer:

Question 11.

Calculate the weighted A.M index number from the following

Answer:

Question 12.

Calculate the price Index by weighted average of price relative’s method using G.M.

Answer:

Question 13.

An enquiry into the budgets of middle class families in a family gave the following information

Compute Price index number by using

(i) Weighted AM of Price relatives,

(ii) Weighted GM of Price relatives.

Answer:

Weighted geometric mean index number

= antilog (1.9993) = 99.84

∴ 0.16% of price is decreased in 2001 when compare to 2000.

= 101.18

∴ 1.18% of price is increased in 2001 when compare to 2000.

Question 14.

Prices paid and quantities consumed of three commodities during two time periods are:

(a) Considering the quantity of period I as weight, what percentage change in prices has occurred between periods

(b) What is the percentage change in prices if the quantities of period II are used as the base?

(c) What is the percentage change in the quantities between the two periods where prices in periods I are the base.

(d) What percentage change in the value of consumption has occurred.

Answer:

(a) Base period quantity is q_{0}, if we consider only base year quantity the formula will be

Here we got 82.75, its less than 100, 100 – 82.76 = 17.24% decrease

(b) Period II quantity is q_{1}, if we consider only current year quantity the formula will be

Here we got 77.78, its less than 100, 100 – 77.78 = 22.22% decrease

(c) Quantity between two periods means q_{1}, q_{0} the formula will be

Here we got 93.10, its less than 100,100 – 93.1=6.9% decrease

(d) What is the percentage change in the value of consumption has occurred?

Here we got 72.41, its less than 100,100-72.41=27.59 decrease

Question 15.

Give Σp_{0}q_{0} =750 and Σp_{1}q_{0} = 900 construct suitable index

Answer:

Question 16.

Given Σp_{1}q_{1} = 500 and Σp_{0}q_{1} = 450, construct Suitable index

Answer:

Question 17.

If Laspeyre’s index number is 130.6 and Paasche’s index number is 125.4. Find Dorbish. Bowley & Fisher’s index number.

Answer:

Question 18.

If P^{p}_{01} = 190.6, P^{DB}_{01} = 200.4 then find P^{L}_{01} = ?

Answer:

P^{DB}_{01} = \(\frac { 1 }{ 2 }\) (P^{p}_{01} + P^{L}_{01})

(200.4) = \(\frac { 1 }{ 2 }\) (l90.6 + P^{L}_{01})

(200.4)2 = 190.6 + P^{L}_{01}

P^{L}_{01} = 400.8 – 190.6 ⇒ P^{L}_{01} = 210.2

Question 19.

If P^{L}_{01} = 96.8 and P^{F}_{01}=97.6 then find Paasche’s index number.

Answer:

Question 20.

Compute Laspeyre’s, Paasche’s, Marshall edge worth’s, Dorbish Bowleys and Fisher’s Quantity. Index numbers from the following data.

Answer:

Question 21.

Compute Fisher’s ideal quantity index number for the current year on the basis of the following information

Answer:

Question 22.

From the data given below, calculate Quantity Index number,s for the year 2010 by using

(i) Marshall Edge worth’s

(ii) Dorbish Bowley’s

(iii) Fisher’s Formulae

Answer:

Question 23.

Compute suitable quantity Index number from the following information.

Answer:

Question 24.

Compute an Index number by using the following data

Answer:

Question 25.

Given Σp_{0}q_{0} = 1400 Σp_{0}q_{1} = 1500. construct a suitable index

Answer:

Question 26.

Given Σq_{0}p_{1} = 625 Σq_{1}p_{1} = 600. construct a suitable index

Answer:

Question 27.

If Q^{L}_{01} = 146.2 and Q^{p}_{01} = 148.4 find Q^{F}_{01} and Q^{DB}_{01}

Answer:

Question 28.

If Q^{L}_{01} = 434.6 and Q^{DB}_{01} = 434.5 and Q^{P}_{01}

Answer:

Q^{DB}_{01} = \(\frac { 1 }{ 2 }\) (Q^{L}_{01} + Q^{P}_{01})

434.5 = \(\frac { 1 }{ 2 }\) (434.6 + Q^{P}_{01})

(434.5)2 = 434.6 + Q^{P}_{01}

⇒ 869 = 434.6 + Q^{P}_{01}

Q^{P}_{01} = 869 – 434.6

⇒ Q^{P}_{01} = 434.4

Question 29.

If Q^{p}_{01} = 92 and Q^{F}_{01} = 94 then find Laspeyre’s Quantity index

Answer:

Question 30.

Compute value index number for the current year, w.r.t base year on the basis of the following information.

Answer:

Question 31.

Given Σp_{0}q_{0} = 4200 and Σp_{1}q_{1} = 5000 compute suitable index number

Answer:

Question 32.

If total value in base year and current year are respectively 800 and 1000. Compute value index

Answer:

Question 33.

For the following data compute Fisher’s ideal index number and show that Fisher’s index number satisfies time reversal test and factor reversal test for the given data

Answer:

Question 34.

Verify whether Marshall-Edgeworths index number satisfies TRT using the following data

Answer:

Question 35.

verify whether Fisher’s Index Number satisfies TRT.

Answer:

Question 36.

Calculate CPI by aggregative expenditure method

Answer:

Question 37.

Compute cost of living index number by aggregative expenditure method

Answer:

Question 38.

Compute cost of living index number

Answer:

Question 39.

An enquiry into the budgets of the middle class families in certain cities in India gave the following information

What is the cost of living index number of 1996 as compared with that of 1995 using family budget method?

Answer:

Question 40.

Construct consumer price index number by family budget method

Answer:

Question 41.

Given Σp_{1}q_{0} = 350 and Σp_{0}q_{0} = 325. construct a suitable consumer price index

Answer:

Question 42.

Calculate cost of living index number fr om the following

Answer:

Question 43.

Calculate cost of living index number

Answer:

Question 44.

The group index and the corresponding weights for the working class in an industrial city for the years 2005 and 2010 with base 2000 are given below:

Answer:

Question 45.

A family budget enquiry revealed that the average expenditure of the families on food, clothing, house rent, fuel and misc are 30%, 10%, 20% 20% and 20% respectively of the respective group indices are 130, 170, 160, 200 and 180. Find the consumer price index number?

Answer:

Question 46.

The following are the price of commodities in 2005 and 2010. Calculate:

(a) Unweighted arithmetic mean index number

(b) Unweighted geometric mean index number

(c) Unweighted aggregative price index number

Answer:

(i) Unweighted AM index number

∴ 15.105% of the price increased in the current year when compared to base year

(ii) Unweighted GM index number

= Antilog 2.0602 = 114.86

∴ 14.86% of the price increased in the current year when compared to base year

(iii) Unweighted aggregative price index number

∴ 14.28% of the price increased in the current year when compared to base year

Question 47.

Calculate Laspeyre’s, Passche’s, Dorbish – Bowley’s, Marshall – Edgeworth’s and Fisher’s index numbers.

Answer:

∴ 2.91% of the price is increased in the current year when compared to base year

∴ 6.67% of the price is increased in the current year when compared to base year.

P^{DB}_{01} = \(\frac { 1 }{ 2 }\)[P^{2}_{01} + P^{p}_{01}] = \(\frac { 1 }{ 2 }\)[102.91 + 106.67] = 104.79

∴ 4.79% of the price is increased in the current year when compared to base year.

∴ 5.12% of the price is increased in the current year when compared to base year

∴ 4.89% of the price is increased in the current year when compared to base year

Question 48.

Compute Fisher’s ideal index number from the following data

Answer:

∴ 21.24% of the price is increased in the current year when compared to base year

Question 49.

Calculate the index number for 2010 with 2005 as base using weighted average of price relative method using arithmetic mean.

Answer:

Question 50.

Calculate weighted Geometric Mean index number for the following data.

Answer:

Question 51.

Calculate Laspeyere’sPasche’s and Marshall – Edgeworths quantity index number.

Answer:

Question 52.

On the basis of following information calculate Dorbish – Bowley’s and Fisher’s quantity index number.

Answer:

Question 53.

Calculate kelly’s fixed weight price index number from the following data.

Answer:

∴ 16.1% of the price is increased in the current year when compared to base year

Question 54.

Compute Fisher’s ideal price index number and also verify whether it satisfies Reversal Test and Factor Reversal Test.

Answer:

∴ 31.24% of the price is increased in the current year when compared to base year

∴ Fisher’s index number satisfies TRT

∴ Fisher’s index number satisfies FRT

Question 55.

Verify whether Marshall – Edgeworth’s index number satisfies Time Reversal Test.

Answer:

Question 56.

Calculate consumer price index number from the following data.

Answer:

∴ 95.07% of the price is increased in the current year when compared to base year.

Question 57.

Compute cost of living index number.

Answer:

∴ 100.19% of the price is increased in the current year when compared to base year.

Question 58.

Compute consumer price index number from the following data

Answer:

Question 59.

Calculate the cost of living index number for 2012 with base 2010.

Answer:

∴ 22.94% of the price is increased in the current year when compared to base year.

Question 60.

From the following data calculate consumer price index number for 2008 and 2009

Answer:

∴ CPI for 2009 has increased when compared to CPI for 2008.

Question 61.

A family budget enquiry revealed that the average expenditure of the families on food, clothing, house rent, fuel and miscellaneous are 30%, 10%, 20%, 15% and 25% respectively. If the respective group imdices are 160,170,150, 220 and 200.

Find the consumer price index number.

Answer: