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Page 1
NCERT
SOLUTIONS
CLASS - 11th
aglase .co
SOLUTIONS
CLASS - 11th
aglase .co
Page 2
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
Class : 11th
Subject : Statistics
Chapter : 8
Chapter Name : Index Numbers
Q1 An index number which accounts for the relative importance of the
items is known as
(i) weighted index
(ii) simple aggregative index
(iii) simple average of relatives
Answer. Option (i) is correct. Weighted index accounts for the relative importance of the
items.
Page : 118 , Block Name : Exercises
Q2 In most of the weighted index numbers the weight pertains to
(i) base year
(ii) current year
(iii) both base and current year
Answer. Option (i) is correct. In the weighted index, weight pertains to base year.
Page : 118 , Block Name : Exercises
Q3 The impact of change in the price of a commodity with little weight in
the index will be
(i) small
(ii) large
(iii) uncertain
Answer. Option (i) is correct. If the commodity has a low weightage, it will have lesser
impact due to price changes.
Page : 118 , Block Name : Exercises
Q4 A consumer price index measures changes in
(i) retail prices
(ii) wholesale prices
Page 1 of 14
Class : 11th
Subject : Statistics
Chapter : 8
Chapter Name : Index Numbers
Q1 An index number which accounts for the relative importance of the
items is known as
(i) weighted index
(ii) simple aggregative index
(iii) simple average of relatives
Answer. Option (i) is correct. Weighted index accounts for the relative importance of the
items.
Page : 118 , Block Name : Exercises
Q2 In most of the weighted index numbers the weight pertains to
(i) base year
(ii) current year
(iii) both base and current year
Answer. Option (i) is correct. In the weighted index, weight pertains to base year.
Page : 118 , Block Name : Exercises
Q3 The impact of change in the price of a commodity with little weight in
the index will be
(i) small
(ii) large
(iii) uncertain
Answer. Option (i) is correct. If the commodity has a low weightage, it will have lesser
impact due to price changes.
Page : 118 , Block Name : Exercises
Q4 A consumer price index measures changes in
(i) retail prices
(ii) wholesale prices
Page 1 of 14
Page 3
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
(iii) producers prices
Answer. Option (i) is correct. The consumers are affected by prices in retail. Hence, a
better analysis is possible by measuring the price index in retail.
Page : 118 , Block Name : Exercises
Q5 The item having the highest weight in consumer price index for
industrial workers is
(i) Food
(ii) Housing
(iii) Clothing
Answer. Option (i) is correct. Food is the most important component, hence it is the item
with the highest weight.
Page : 118 , Block Name : Exercises
Q6 In general, inflation is calculated by using
(i) wholesale price index
(ii) consumer price index
(iii) producers’ price index
Answer. Option (i) is correct. Wholesale price index indicates the inflation rate of the
economy as a whole.
Page : 119 , Block Name : Exercises
Q7 Why do we need an index number?
Answer. We need index numbers for the following reasons:
1. We can measure the change in pricing.
2. We can study the change in standard of living.
3. We can determine the rate of production.
4. Index numbers also help in the policy making.
Page : 119 , Block Name : Exercises
Q8 What are the desirable properties of the base period?
Page 2 of 14
(iii) producers prices
Answer. Option (i) is correct. The consumers are affected by prices in retail. Hence, a
better analysis is possible by measuring the price index in retail.
Page : 118 , Block Name : Exercises
Q5 The item having the highest weight in consumer price index for
industrial workers is
(i) Food
(ii) Housing
(iii) Clothing
Answer. Option (i) is correct. Food is the most important component, hence it is the item
with the highest weight.
Page : 118 , Block Name : Exercises
Q6 In general, inflation is calculated by using
(i) wholesale price index
(ii) consumer price index
(iii) producers’ price index
Answer. Option (i) is correct. Wholesale price index indicates the inflation rate of the
economy as a whole.
Page : 119 , Block Name : Exercises
Q7 Why do we need an index number?
Answer. We need index numbers for the following reasons:
1. We can measure the change in pricing.
2. We can study the change in standard of living.
3. We can determine the rate of production.
4. Index numbers also help in the policy making.
Page : 119 , Block Name : Exercises
Q8 What are the desirable properties of the base period?
Page 2 of 14
Page 4
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
Answer. The desirable properties of a base period are:
1. It should not be too recent or too old.
2. It should be neither too long nor too short.
3. The data for each year in the base period must be available.
4. The base period must be updated to adjust the changes over the time.
Page : 119 , Block Name : Exercises
Q9 Why is it essential to have different CPI for different categories of
consumers?
Answer. It is essential to have different CPI for different categories of consumers
because the consumption basket of different categories of consumers differs a lot.
Hence, all the consumers don’t consume in the same manner.
Page : 119 , Block Name : Exercises
Q10 What does a consumer price index for industrial workers measure?
Answer. The consumer price index for industrial workers measures the change in prices
of the commodities consumed by industrial workers. It gives an accurate idea of inflation
and its effect on the consumer.
Page : 119 , Block Name : Exercises
Q11 What is the difference between a price index and a quantity index?
Answer. The differences between price index and quantity index are:
Price Index Quantity Index
It measures general changes in prices It measures the average change in
between the current and the base years. commodities which are consumed.
It is measured by Simple Aggregative It is measured by weighted average of
method and Simple Average of Price price relative method and Weighted
Relative method. Aggregative Method
It takes into consideration the prices of It considers weights of commodities
both the base and current years. based on their quantities.
Page 3 of 14
Answer. The desirable properties of a base period are:
1. It should not be too recent or too old.
2. It should be neither too long nor too short.
3. The data for each year in the base period must be available.
4. The base period must be updated to adjust the changes over the time.
Page : 119 , Block Name : Exercises
Q9 Why is it essential to have different CPI for different categories of
consumers?
Answer. It is essential to have different CPI for different categories of consumers
because the consumption basket of different categories of consumers differs a lot.
Hence, all the consumers don’t consume in the same manner.
Page : 119 , Block Name : Exercises
Q10 What does a consumer price index for industrial workers measure?
Answer. The consumer price index for industrial workers measures the change in prices
of the commodities consumed by industrial workers. It gives an accurate idea of inflation
and its effect on the consumer.
Page : 119 , Block Name : Exercises
Q11 What is the difference between a price index and a quantity index?
Answer. The differences between price index and quantity index are:
Price Index Quantity Index
It measures general changes in prices It measures the average change in
between the current and the base years. commodities which are consumed.
It is measured by Simple Aggregative It is measured by weighted average of
method and Simple Average of Price price relative method and Weighted
Relative method. Aggregative Method
It takes into consideration the prices of It considers weights of commodities
both the base and current years. based on their quantities.
Page 3 of 14
Page 5
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
Page : 119 , Block Name : Exercises
Q12 Is the change in any price reflected in a price index number?
Answer. No, the price index number reflects only relative values, hence a change in
price keeps it unaffected.
Page : 119 , Block Name : Exercises
Q13 Can the CPI for urban non-manual employees represent the changes
in the cost of living of the President of India?
Answer. No, because the consumption basket of the President of India and the urban
non-manual employees is different.
Page : 119 , Block Name : Exercises
Q14 The monthly per capita expenditure incurred by workers for an industrial centre
during 1980 and 2005 on the following items are given below. The weights of these
items are 75,10, 5, 6 and 4 respectively. Prepare a weighted index number for cost of
living for 2005 with 1980 as the base.
Items Price in 1980 Price in 2005
Food 100 200
Clothing 20 25
Fuel & lighting 15 20
House rent 30 40
Misc 35 65
Answer. The cost of living index can be calculated as :
Commodity Price in Price in Weight Price relatives RW
1980 2005 ( (W) (R)
Page 4 of 14
Page : 119 , Block Name : Exercises
Q12 Is the change in any price reflected in a price index number?
Answer. No, the price index number reflects only relative values, hence a change in
price keeps it unaffected.
Page : 119 , Block Name : Exercises
Q13 Can the CPI for urban non-manual employees represent the changes
in the cost of living of the President of India?
Answer. No, because the consumption basket of the President of India and the urban
non-manual employees is different.
Page : 119 , Block Name : Exercises
Q14 The monthly per capita expenditure incurred by workers for an industrial centre
during 1980 and 2005 on the following items are given below. The weights of these
items are 75,10, 5, 6 and 4 respectively. Prepare a weighted index number for cost of
living for 2005 with 1980 as the base.
Items Price in 1980 Price in 2005
Food 100 200
Clothing 20 25
Fuel & lighting 15 20
House rent 30 40
Misc 35 65
Answer. The cost of living index can be calculated as :
Commodity Price in Price in Weight Price relatives RW
1980 2005 ( (W) (R)
Page 4 of 14
Page 6
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
( ) )
Food 100 200 75 15,000
=200
Clothing 20 25 10 1250
=125
Fuel and lighting 15 20 5 666.65
=133.33
House Rent 30 40 6 799.98
=133.33
Miscellaneous 35 65 4 742.84
=185.71
=100
Cost of Living (CPI) =
=
=
The CPI shows an increase of 84.59% to the base year.
Page : 119 , Block Name : Exercises
Q15 Read the following table carefully and give your comments.
INDEX OF INDUSTRIAL PRODUCTION BASE 1993–94
Page 5 of 14
( ) )
Food 100 200 75 15,000
=200
Clothing 20 25 10 1250
=125
Fuel and lighting 15 20 5 666.65
=133.33
House Rent 30 40 6 799.98
=133.33
Miscellaneous 35 65 4 742.84
=185.71
=100
Cost of Living (CPI) =
=
=
The CPI shows an increase of 84.59% to the base year.
Page : 119 , Block Name : Exercises
Q15 Read the following table carefully and give your comments.
INDEX OF INDUSTRIAL PRODUCTION BASE 1993–94
Page 5 of 14
Page 7
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
Industry Weight in % 1996-97 2003-04
General index 100 130.8 189.0
Mining and 10.73 118.2 146.9
quarrying
Manufacturing 79.58 133.6 196.6
Electricity 10.69 122.0 172.6
Answer. The following observations can be made from the table:
1. The manufacturing section has the highest weight.
2. The General index is higher in 2003-2004 than in 1996-1997.
3. The mining industry has shown the lowest growth.
Page : 119 , Block Name : Exercises
Q16 Try to list the important items of consumption in your family.
Answer. The important items of consumption in our family are:
1. Food
2. Clothes
3. Transport
4. Electricity
5. Education
Page : 119 , Block Name : Exercises
Q17 If the salary of a person in the base year is Rs 4,000 per annum and
the current year salary is Rs 6,000, by how much should his salary be
raised to maintain the same standard of living if the CPI is 400?
Answer. Current year salary = Rs 400
Then, base year salary = Rs 4000
Current year salary = Rs 6000
Let’s assume base year CPI as 100.
Page 6 of 14
Industry Weight in % 1996-97 2003-04
General index 100 130.8 189.0
Mining and 10.73 118.2 146.9
quarrying
Manufacturing 79.58 133.6 196.6
Electricity 10.69 122.0 172.6
Answer. The following observations can be made from the table:
1. The manufacturing section has the highest weight.
2. The General index is higher in 2003-2004 than in 1996-1997.
3. The mining industry has shown the lowest growth.
Page : 119 , Block Name : Exercises
Q16 Try to list the important items of consumption in your family.
Answer. The important items of consumption in our family are:
1. Food
2. Clothes
3. Transport
4. Electricity
5. Education
Page : 119 , Block Name : Exercises
Q17 If the salary of a person in the base year is Rs 4,000 per annum and
the current year salary is Rs 6,000, by how much should his salary be
raised to maintain the same standard of living if the CPI is 400?
Answer. Current year salary = Rs 400
Then, base year salary = Rs 4000
Current year salary = Rs 6000
Let’s assume base year CPI as 100.
Page 6 of 14
Page 8
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
Salary for initial standard of living =
= Rs 16000
Amount required to maintain the same standard of living = 16000- 6000
= Rs 10000
Page : 119 , Block Name : Exercises
Q18 The consumer price index for June, 2005 was 125. The food index was 120 and
that of other items 135. What is the percentage of the total weight given to food?
Answer. We know that CPI = 125
Using the formula, CPI = , we get:
125 =
X =
X = 66.67
Therefore, the weight given to food is 66.67%.
Page : 119 , Block Name : Exercises
Q19 An enquiry into the budgets of the middle class families in a certain
city gave the following information;
Expenses Food Fuel Clothing Rent Misc.
on items 35% 10% 20 % 15 % 20%
Price (in Rs) 1500 250 750 300 400
in 2004
Price (in Rs) 1400 200 500 200 250
in 1995
What is the cost of living index during the year 2004 as compared with
1995?
Page 7 of 14
Salary for initial standard of living =
= Rs 16000
Amount required to maintain the same standard of living = 16000- 6000
= Rs 10000
Page : 119 , Block Name : Exercises
Q18 The consumer price index for June, 2005 was 125. The food index was 120 and
that of other items 135. What is the percentage of the total weight given to food?
Answer. We know that CPI = 125
Using the formula, CPI = , we get:
125 =
X =
X = 66.67
Therefore, the weight given to food is 66.67%.
Page : 119 , Block Name : Exercises
Q19 An enquiry into the budgets of the middle class families in a certain
city gave the following information;
Expenses Food Fuel Clothing Rent Misc.
on items 35% 10% 20 % 15 % 20%
Price (in Rs) 1500 250 750 300 400
in 2004
Price (in Rs) 1400 200 500 200 250
in 1995
What is the cost of living index during the year 2004 as compared with
1995?
Page 7 of 14
Page 9
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
Answer. The Cost of Living Index can be calculated as:
Item Base year Current year Weight (W) Relative RW
price in price in prices (R)
1980 2005
Food 35 1400 1500 3749.90
Fuel 10 200 250 1250
Clothing 20 500 750 3000
Rent 15 200 300 2250
Misc 20 250 400 3200
Now, CPI =
=
= 134.49
Page : 120 , Block Name : Exercises
Q20 Record the daily expenditure, quantities bought and prices paid per unit of the daily
purchases of your family for two weeks. How has the price change affected your family?
Answer. The observations and quantities are organised in the table below:
Week 1
Page 8 of 14
Answer. The Cost of Living Index can be calculated as:
Item Base year Current year Weight (W) Relative RW
price in price in prices (R)
1980 2005
Food 35 1400 1500 3749.90
Fuel 10 200 250 1250
Clothing 20 500 750 3000
Rent 15 200 300 2250
Misc 20 250 400 3200
Now, CPI =
=
= 134.49
Page : 120 , Block Name : Exercises
Q20 Record the daily expenditure, quantities bought and prices paid per unit of the daily
purchases of your family for two weeks. How has the price change affected your family?
Answer. The observations and quantities are organised in the table below:
Week 1
Page 8 of 14
Page 10
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
Bread Milk
Days Price
Total Price Total
per Quantity Quantity
expense per litre expense
loaf
Monday 25 2 50 40 1 40
Tuesday 24 1 24 39 2 78
Wednesday 24 1.5 36 38 1.5 57
Thursday 23 2 46 40 1 40
Friday 24 1 24 39 2 78
Saturday 22 2.5 55 37 1 37
Sunday 24 2 48 39 1.5 58.5
283 330
Week 2
Bread Milk
Days
Price Total Price Total
Quantity Quantity
per loaf expense per litre expense
Monday 26 2 52 42 1 42
Tuesday 23 2 46 40 2 80
Wednesda
24 1.5 36 39 2 78
y
Thursday 25 2 50 39 1 39
Friday 26 1 26 40 2 80
Saturday 22 2.5 55 39 1 39
Sunday 23 2 46 39 1.5 58.5
358
307
Page 9 of 14
Bread Milk
Days Price
Total Price Total
per Quantity Quantity
expense per litre expense
loaf
Monday 25 2 50 40 1 40
Tuesday 24 1 24 39 2 78
Wednesday 24 1.5 36 38 1.5 57
Thursday 23 2 46 40 1 40
Friday 24 1 24 39 2 78
Saturday 22 2.5 55 37 1 37
Sunday 24 2 48 39 1.5 58.5
283 330
Week 2
Bread Milk
Days
Price Total Price Total
Quantity Quantity
per loaf expense per litre expense
Monday 26 2 52 42 1 42
Tuesday 23 2 46 40 2 80
Wednesda
24 1.5 36 39 2 78
y
Thursday 25 2 50 39 1 39
Friday 26 1 26 40 2 80
Saturday 22 2.5 55 39 1 39
Sunday 23 2 46 39 1.5 58.5
358
307
Page 9 of 14
Page 11
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
Since the total expense has increased, an increase in price will lead to an increase in
the expenses of the family.
Page : 120 , Block Name : Exercises
Q21 Given the following data-
Year CPI of Industrial CPI of agricultural WPI
Workers Workers (1993-94=100)
(1982=100) (1986-87)
1995-96 313 234 121.6
1996-97 342 256 127.2
1997-98 366 264 132.8
1998-99 414 293 140.7
1999-00 428 306 145.3
2000-01 444 306 155.7
2001-02 463 309 161.3
2002-03 482 319 166.8
2003-04 500 331 175.9
Source: Economic Survey, 2004–2005, Government of India
(i) Comment on the relative values of the index numbers.
(ii) Are they comparable?
Answer. Inflation using the CPI of Industrial Workers can be calculated as:
Year CPI of Industrial Workers Inflation rate (in %)
(1982 =100)
Page 10 of 14
Since the total expense has increased, an increase in price will lead to an increase in
the expenses of the family.
Page : 120 , Block Name : Exercises
Q21 Given the following data-
Year CPI of Industrial CPI of agricultural WPI
Workers Workers (1993-94=100)
(1982=100) (1986-87)
1995-96 313 234 121.6
1996-97 342 256 127.2
1997-98 366 264 132.8
1998-99 414 293 140.7
1999-00 428 306 145.3
2000-01 444 306 155.7
2001-02 463 309 161.3
2002-03 482 319 166.8
2003-04 500 331 175.9
Source: Economic Survey, 2004–2005, Government of India
(i) Comment on the relative values of the index numbers.
(ii) Are they comparable?
Answer. Inflation using the CPI of Industrial Workers can be calculated as:
Year CPI of Industrial Workers Inflation rate (in %)
(1982 =100)
Page 10 of 14
Page 12
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
1995-96 313
1996-97 342
1997-98 366
1998-99 414
1999-00 428
2000-01 444
2001-02 463
2002-03 482
3004-04 500
Inflation using CPI of agricultural labourers:
Year CPI of agricultural Inflation rate (in %)
labourers
(1986-87 =100)
1995-96 234
1996-97 256
1997-98 264
Page 11 of 14
1995-96 313
1996-97 342
1997-98 366
1998-99 414
1999-00 428
2000-01 444
2001-02 463
2002-03 482
3004-04 500
Inflation using CPI of agricultural labourers:
Year CPI of agricultural Inflation rate (in %)
labourers
(1986-87 =100)
1995-96 234
1996-97 256
1997-98 264
Page 11 of 14
Page 13
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
1998-99 293
1999-00 306
2000-01 306
2001-02 309
2002-03 319
2003-04 331
Inflation using WPI:
Year WPI (1993-94=100) Inflation rate (in %)
1995-96 121.6
1996-97 127.2
1997-98 132.8
1998-99 140.7
1999-00 145.3
2000-01 155.7
Page 12 of 14
1998-99 293
1999-00 306
2000-01 306
2001-02 309
2002-03 319
2003-04 331
Inflation using WPI:
Year WPI (1993-94=100) Inflation rate (in %)
1995-96 121.6
1996-97 127.2
1997-98 132.8
1998-99 140.7
1999-00 145.3
2000-01 155.7
Page 12 of 14
Page 14
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
2001-02 161.3
2002-03 166.8
2003-04 175.9
Therefore, the inflation rate is highest for Industrial Workers and Lowest for WPI.
(ii) No, they cannot be compared as the base years are different.
Page : 120 , Block Name : Exercises
Q22 The monthly expenditure (Rs.) of a family on some important items and the Goods and
Services Tax (GST) rates applicable to these items is as follows:
Item Monthly Expense GST Rate in %
Cereals 1500 0
Egg 250 0
Fish, Meat 250 0
Medicines 50 5
Biogas 50 5
Transport 100 5
Butter 50 12
Babool 10 12
Tomato Ketchup 40 12
Biscuits 75 18
Cakes, Pastries 25 18
Page 13 of 14
2001-02 161.3
2002-03 166.8
2003-04 175.9
Therefore, the inflation rate is highest for Industrial Workers and Lowest for WPI.
(ii) No, they cannot be compared as the base years are different.
Page : 120 , Block Name : Exercises
Q22 The monthly expenditure (Rs.) of a family on some important items and the Goods and
Services Tax (GST) rates applicable to these items is as follows:
Item Monthly Expense GST Rate in %
Cereals 1500 0
Egg 250 0
Fish, Meat 250 0
Medicines 50 5
Biogas 50 5
Transport 100 5
Butter 50 12
Babool 10 12
Tomato Ketchup 40 12
Biscuits 75 18
Cakes, Pastries 25 18
Page 13 of 14
Page 15
Book : Statistics for Economics Ncert Solutions | Chapter - 8 Statistics
Branded Garments 100 18
Vacuum Cleaner, Car 1000 28
Calculate the average tax rate as far as this family is concerned
Answer.
Category Expenditure Weight GST Rate (X) WX
(W)
Category 1 2000 0 0
Category 2 200 0.05 10
Category 3 100 0.12 12
Category 4 200 0.18 36
Category 5 1000 0.28 280
3500 338
Average Tax Rate = = 0.966 = 9.66%
Page : 120 , Block Name : Exercises
Page 14 of 14
Branded Garments 100 18
Vacuum Cleaner, Car 1000 28
Calculate the average tax rate as far as this family is concerned
Answer.
Category Expenditure Weight GST Rate (X) WX
(W)
Category 1 2000 0 0
Category 2 200 0.05 10
Category 3 100 0.12 12
Category 4 200 0.18 36
Category 5 1000 0.28 280
3500 338
Average Tax Rate = = 0.966 = 9.66%
Page : 120 , Block Name : Exercises
Page 14 of 14
Document Details
| Board / Org | NCERT |
| Exam | Class 11 |
| Type | Solution |
| Pages | 15 |
| Updated | 30 Apr 2026 |