CHAPTER 7 - Index Numbers.pdf

QMT412 Business Statistics

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INTRODUCTION

sanizah@tmsk.uitm.edu.my

We often hear of index numbers such as:   

CHAPTER 7 INDEX NUMBER

 

Kuala Lumpur Composite Index EMAS Index Quality Air Index Air Pollution Index Consumer Price Index

What is index number? • Index number is a statistical tool used to measure changes in average price, quantity, value, air condition and economic economic health of a country for a stated period of time. time .


By Sanizah Ahmad

3 sanizah@tmsk.uitm.edu.my

ILLUSTRATION API

Air Pollution Level

0 - 50

Good

51 - 100

Moderate

101 - 200

Unhealthy

201 - 300

Very Unhealthy

301+

Hazardous

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TYPES OF INDEX NUMBERS


1. Price Index – measures changes in prices of prices of goods and services over time. time. (i.e. The Consumer Price Index measures the changes in the price of consumer goods) Note:

When CPI , living expenses  and cost of living (normally, comparison is based on annual basis)

2. Quantity Index – measures changes in the quantity of of goods over time. time. 3. Quality Index


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FACTORS IN CONSTRUCTING INDEX NUMBER

Simple Index Numbers Price index and Quantity Index

• Number of items – a group of items or only one item. • Base year – the year used to compare its value with the values of the other years ▫ Index number for the base year is always 100. ▫ The base year should be a normal/stable year and not too far from the year that index is computed.

• Weight – value that shows the importance of an item in the index number ▫ the higher the weights, the more important the item is.

Unweighted Index

Weighted Index

1. Simple Relative Index

1. Weighted Aggregate Index

2. Simple Average of Relative Index

2. Laspeyres’ index

3. Simple Aggregate Index

3. Paasche’s index

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1. SIMPLE RELATIVE INDEX (SRI) • Ratio of the price of a single commodity in a given period to its price in the base period

UNWEIGHTED INDEX

• Price relative

• Quantity relative


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Solution Ex 1

EXAMPLE 1 Prices of petrol in 2004 and 2005 were RM1.30 and RM1.45 respectively. Taking 2004 as the base year, find the price relative index for 2005.

The price of petrol in year 2005 has increased by 11.54% compared to the base year 2004.

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EXAMPLE 2 The

table below gives the number of water filters sold by a company from 2008 to 2011. Year

2008

2009

2010

2011

Number of water filters

400

550

800

1600

Calculate : Quantity relatives (quantity index) of sales for 2011 taking 2008 as the base year.


Solution Ex 2

This means that in 2011, the number of water f ilter sold was 400 percent of the number sold in 2008, that is an increase of 300%.


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Example 3 • The table below shows the prices of three types of washing machines A, B and C in 2003 and 2005 and the price relatives in 2005, taking 2003 as the base year. Find the values of x, y and z. 2003=100

Price in 2003(RM)

Price in 2005 (RM)

Price Relative

A

800

1000

x

B

1200

y

140

C

z

600

120


2. Simple Average of Relative Index (SARI) • SARI compares the overall changes for a group of commodities or items under consideration • Simple Average of relative price index

• Simple Average of relative quantity index

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Example 4



• The table below shows a country’s prices of petrol, diesel and cooking gas for 2004, 2006 and 2008. Compute the simple average of price relative index for year 2008 with 2004 as base year.

Item Petrol

2004 1.20

2006 1.35

2008 1.50

Diesel

0.60

0.70

1.00

Cooking gas

1.00

1.20

1.30

Example 5 • Calculate the simple average of relative quantity index of three of foods A, B and C for 2005 taking 2003 as the base year. Type of Food

Quantity sold (kg) 2003

2005

A

600

650

B

1800

2200

C

1200

1400


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3. SIMPLE AGGREGATE INDEX (SAI) • This is an unweighted aggregate index. • Simple aggregate price index

WEIGHTED INDEX

• Simple aggregate quantity index

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1. WEIGHTED AGGREGATE INDEX

EXAMPLE 6

• When the importance of each item needs to be included, we will have to calculate weighte d index. • A weighted price index

• For the data given below, calculate the weighted aggregate price index for 2006 using 2004 as the base year

• A weighted quantity index

Type of food

Weight

Price 2004

Price 2006

A B

3

1.50

2.00

5

2.80

3.20

C

8

5.00

6.00

• Calculate weighted aggregate price index for 2006


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EXAMPLE 7

2. LASPEYRES’ INDEX

• For the data given below, calculate the weighted aggregate quantity index for 2006 using 2003 as the base year. Type of commodity


Weight

Quantity 2003

• Laspeyres’ price index : • Use the base year quantities as the weight

Quantity 2006

A

3

15

25

B

4

20

30

C

5

50

40

• Laspeyres’ quantity index : • Use the base year prices as the weight


3. PAASCHE’S INDEX • Pasche’s price index • Use the current year quantities as the weight


EXAMPLE 9

Shelly Industry produce electrical components that require four main raw materials. The following tables shows the price and quantity required for each material. Raw Material

• Pasche’s quantity index • Use the current year prices as the weight

Price per kg (RM)

Quantity (kg)

2004

2006

2004

A

4.00

5.00

4000

3500

B

6.00

7.00

2750

3000

C

5.00

4.00

2000

3000

D

8.00

9.00

1000

2000

Using 2004 as the base year, calculate a)Laspeyres’ price index for year 2006 b)Paasche’s price index for 2006



2006

CHAPTER 7 - Index Numbers.pdf

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