Question 1

i. An index number is a percent that measures the change in price, quantity, value, or some other item of interest from one time to another. ii. An index of 239.2 and an index of 86.4 are actually percents.
iii. All indexes have the same base, namely 1982-84, written 1982 - 84 = 100.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Accepted Answer

Index numbers do measure changes in price, quantity, or value over time, and they are expressed as percents. However, not all indexes use 1982-84 as their base period; different indexes can have different base years.

Question 2

i. The base number for most indexes is 1. ii. Most business and economic indexes are carried either to the nearest whole percent, such as 312 or 96, or to the nearest 10^thof a percent, such as 97.5 and 178.6. iii. Converting data to indexes makes it easier to compare the trend in a series composed of exceptionally large numbers. A) (i), (ii), and (iii) are all correct statements. B) (i) and (ii) are correct statements but not (iii). C) (i) and (iii) are correct statements but not (ii). D) (ii) and (iii) are correct statements but not (i). E) (i), (ii), and (iii) are all false statements.

Accepted Answer

Statement (i) is incorrect because the base number for most indexes is typically 100, not 1. Statements (ii) and (iii) are correct as they accurately describe how indexes are typically presented and their purpose in simplifying comparisons.

Question 3

Listed below are the top-steel producing nations, in millions of tons, for the year 2004. Express the amount produced by China, the European Union, Japan, and Russia as an index, using the United States as a base. What percent more steel does the European Union produce than the United States? 
A) 184.6
B) 84.6
C) 15.4
D) 52.6
E) 47.4

Accepted Answer

To calculate the index, we divide each country's production by that of the United States and multiply by 100. 
China: (349.5/101.6)*100 = 343.8
European Union: (210.6/101.6)*100 = 207.1
Japan: (110.3/101.6)*100 = 108.5
Russia: (72.4/101.6)*100 = 71.2
To calculate the percent more steel the EU produces than the US, we use the following formula: ((EU production - US production)/US production)*100.
((210.6 - 101.6)/101.6)*100 = 107.03%
Therefore, the European Union produces 84.6% more steel than the United States, which is closest to option B (84.6).

Question 4

i. The base period for one index might be 1982-84, while the base period for another index might be 1977. ii. The base number for most indexes is 1. iii. Most business and economic indexes are carried either to the nearest whole percent, such as 312 or 96, or to the nearest 10^thof a percent, such as 97.5 and 178.6. A) (i), (ii), and (iii) are all correct statements. B) (i) and (ii) are correct statements but not (iii). C) (i) and (iii) are correct statements but not (ii). D) (ii) and (iii) are correct statements but not (i). E) (i), (ii), and (iii) are all false statements.

Accepted Answer

The base period for indexes can indeed vary, such as 1982-84 or 1977, and indexes are often carried to the nearest whole number or to the nearest tenth of a percent. However, the base number for most indexes is typically 100, not 1, to facilitate percentage comparisons.

Question 5

Listed below are the top-steel producing nations, in millions of tons, for the year 2004. Express the amount produced by China, the European Union, Japan, and Russia as an index, using the United States as a base. What percent more steel does China produce than the United States? 
A) 197
B) 252.6
C) 152.6
D) 52.6
E) 47.4

Accepted Answer

The answer of Listed below are the top-steel producing nations,...

Question 6

The Statistics Canada reported that the farm population dropped from 30.5 million in 1940 to 16.5 million in 1999. What is the index for 1999 based on 1940?
A) 45.9
B) 103.0
C) 54.1
D) 78.7
E) 184.8

Accepted Answer

To find the index, we need to use the following formula: 
(index value) = (current value / base value) x 100
Plugging in the given values: 
(index value) = (16.5 million / 30.5 million) x 100 
(index value) = 0.540 x 100 
(index value) = 54.1 
Therefore, the index for 1999 based on 1940 is 54.1.

Question 7

The average weekly earnings (including overtime) in Canada since 2003 are given below.  Using 2003 as the base year, determine the index for 2005.
A) 101.3
B) 1.3
C) 201.3
D) 103.5
E) 106.8

Accepted Answer

To calculate the index for 2005 using 2003 as the base year, we need to use the formula:
Index = (Value in the given year / Value in the base year) x 100
For 2005, the value is given as $816.08. Using the value for 2003 from the chart ($778.24), we get:
Index = (816.08/778.24) x 100 = 1.0485 x 100 = 104.85
Rounding this to one decimal place, we get an index of 103.5, which corresponds to option D.

Question 8

i. An index number is a percent that measures the change in price, quantity, value, or some other item of interest from one time to another. ii. The base number for most indexes is 1.
iii. Converting data to indexes makes it easier to compare the trend in a series composed of exceptionally large numbers.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Accepted Answer

- An index number does measure changes in price, quantity, value, etc., over time, and converting data to indexes does indeed facilitate comparisons, even among large numbers. However, the base number for most indexes is typically 100, not 1, to represent a baseline percentage change.

Question 9

i. Etienne Laspeyres developed a method in the latter part of the 19^thcentury to determine a weighted index using base-period weights. ii. If we are constructing a weighted index of the price of food for 2000 using the Laspeyres' method and 1982-84 = 100, we use the amounts consumed in the base period, q₀, as weights. iii. The Laspeyres' method allows for a meaningful comparison of prices over time; however, if does not reflect changes in buying patterns over time. A) (i), (ii), and (iii) are all correct statements. B) (i) and (ii) are correct statements but not (iii). C) (i) and (iii) are correct statements but not (ii). D) (ii) and (iii) are correct statements but not (i). E) (i), (ii), and (iii) are all false statements.

Accepted Answer

The statements correctly describe the Laspeyres' method, including its development, application, and limitations regarding changes in buying patterns over time.

Question 10

The wholesale price of a straight back desk chair in 2012 was $20; in 2013, $23; and in 2014, $18. What were the indexes for 2012 and 2014 using 2013 = 100?
A) 115.0 and 90.0
B) 1.15 and 0.9
C) 1150.0 and 900.0
D) 87.0 and 111.1
E) 87.0 and 78.3

Accepted Answer

The index for 2012 is calculated as (20/23)*100 = 87.0, and for 2014 as (18/23)*100 = 78.3.

Question 11

i. All indexes have the same base, namely 1982-84, written 1982 - 84 = 100. ii. The base period for one index might be 1982-84, while the base period for another index might be 1977.
iii. The base number for most indexes is 1.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are statements but (ii) is correct.
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Accepted Answer

The answer of i. All indexes have the same base,...

Question 12

Sean McCarthy earns $20,000 a year; John Nowak, $35,000. What is John's income as an index using Sean's income as the base?
A) 157.1
B) 75.0
C) 100.0
D) 57.1
E) 175.0

Accepted Answer

The answer of Sean McCarthy earns $20,000 a year; John...

Question 13

The average weekly earnings (including overtime) in Canada since 2003 are given below.  Using 2003 as the base year, determine the index for 2006.
A) 101.3
B) 1.3
C) 201.3
D) 103.5
E) 106.8

Accepted Answer

The answer of The average weekly earnings (including overtime) in...

Question 14

Data for selected vegetables purchased at wholesale prices for 1995 and 2000 are shown below.  What is the unweighted aggregate price index?
A) 98.4
B) 107.0
C) 117.5
D) 128.8
E) 88.9

Accepted Answer

The answer of Data for selected vegetables purchased at wholesale...

Question 15

i. An index of 239.2 and an index of 86.4 are actually percents. ii. All indexes have the same base, namely 1982-84, written 1982 - 84 = 100.
iii. The base period for one index might be 1982-84, while the base period for another index might be 1977.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Accepted Answer

Indexes like the Consumer Price Index (CPI) are often expressed in terms of a base year or period, but they are not percentages themselves; they represent the change in price level relative to the base period. It's also true that different indexes can have different base periods.

Question 16

Listed below are the top-steel producing nations, in millions of tons, for the year 2004. Express the amount produced by China, the European Union, Japan, and Russia as an index, using the United States as a base. What percent more steel does Japan produce than the United States? 
A) 184.6
B) 84.6
C) 15.4
D) 52.6
E) 32.1

Accepted Answer

The answer of Listed below are the top-steel producing nations,...

Question 17

An index number is a percent that can measure the change from one period of time to another in:
A) Value.
B) Price.
C) Quantity.
D) Volume.
E) Value, price, quantity or volume.

Accepted Answer

An index number can measure the change in value, price, quantity or volume from one period of time to another. It is a numerical value used to compare the changes in these variables over different time periods. Therefore, all the options listed in the question are correct.

Question 18

i. An index of 239.2 and an index of 86.4 are actually percents. ii. The base period for one index might be 1982-84, while the base period for another index might be 1977. iii. Most business and economic indexes are carried either to the nearest whole percent, such as 312 or 96, or to the nearest 10^thof a percent, such as 97.5 and 178.6. A) (i), (ii), and (iii) are all correct statements. B) (i) and (ii) are correct statements but not (iii). C) (i) and (iii) are correct statements but not (ii). D) (ii) and (iii) are correct statements but not (i). E) (i), (ii), and (iii) are all false statements.

Accepted Answer

All three statements are correct. Index numbers are often expressed as percentages of a base period. Different indexes can have different base periods. Business and economic indexes are typically rounded to the nearest whole number or tenth of a percent.

Question 19

If the average hourly earnings in mining in 1988 were $7.67 and for the most recent month it was $14.90, what is the index of hourly earnings for the most recent month based on 1988?
A) 100.0
B) 186.9
C) 51.5
D) 194.3
E) 151.5

Accepted Answer

To calculate the index of hourly earnings, we use the formula:

Index = (Recent year hourly earnings / Base year hourly earnings) x 100

Substituting the values given:

Index = (14.90 / 7.67) x 100
Index = 1.94 x 100
Index = 194.3

Therefore, the index of hourly earnings for the most recent month based on 1988 is 194.3. The closest answer choice is D (194.3).

Question 20

The average weekly earnings (including overtime) in Canada since 2003 are given below.  Using 2003 as the base year, determine the index for 2004.
A) 101.3
B) 1.3
C) 201.3
D) 103.5
E) 106.8

Accepted Answer

The answer of The average weekly earnings (including overtime) in...

Quiz 15: Index Numbers

i. An index number is a percent that measures the change in price, quantity, value, or some other item of interest from one time to another. ii. An index of 239.2 and an index of 86.4 are actually percents. iii. All indexes have the same base, namely 1982-84, written 1982 - 84 = 100.

Listed below are the top-steel producing nations, in millions of tons, for the year 2004. Express the amount produced by China, the European Union, Japan, and Russia as an index, using the United States as a base. What percent more steel does the European Union produce than the United States?

Listed below are the top-steel producing nations, in millions of tons, for the year 2004. Express the amount produced by China, the European Union, Japan, and Russia as an index, using the United States as a base. What percent more steel does China produce than the United States?

The Statistics Canada reported that the farm population dropped from 30.5 million in 1940 to 16.5 million in 1999. What is the index for 1999 based on 1940?

The average weekly earnings (including overtime) in Canada since 2003 are given below. Using 2003 as the base year, determine the index for 2005.

The wholesale price of a straight back desk chair in 2012 was $20; in 2013, $23; and in 2014, $18. What were the indexes for 2012 and 2014 using 2013 = 100?

i. All indexes have the same base, namely 1982-84, written 1982 - 84 = 100. ii. The base period for one index might be 1982-84, while the base period for another index might be 1977. iii. The base number for most indexes is 1.

Sean McCarthy earns $20,000 a year; John Nowak, $35,000. What is John's income as an index using Sean's income as the base?

The average weekly earnings (including overtime) in Canada since 2003 are given below. Using 2003 as the base year, determine the index for 2006.

Data for selected vegetables purchased at wholesale prices for 1995 and 2000 are shown below. What is the unweighted aggregate price index?

i. An index of 239.2 and an index of 86.4 are actually percents. ii. All indexes have the same base, namely 1982-84, written 1982 - 84 = 100. iii. The base period for one index might be 1982-84, while the base period for another index might be 1977.

Listed below are the top-steel producing nations, in millions of tons, for the year 2004. Express the amount produced by China, the European Union, Japan, and Russia as an index, using the United States as a base. What percent more steel does Japan produce than the United States?

An index number is a percent that can measure the change from one period of time to another in:

If the average hourly earnings in mining in 1988 were $7.67 and for the most recent month it was $14.90, what is the index of hourly earnings for the most recent month based on 1988?

The average weekly earnings (including overtime) in Canada since 2003 are given below. Using 2003 as the base year, determine the index for 2004.