Understanding Index Numbers: Definition, Characteristics, Types, and Applications, Study notes of Statistics

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Index Numbers

Dr. ViVek Tyagi

STaTiSTicS DeparTmenT n.a.S. college, meeruT

Index Numbers

• What is Index Number?
• Definitions used for all Index Numbers
• Why Convert Data to indices?
• Types of Index Number
• Some Important Price indices

Definition

• “Index numbers are quantitative measures of growth of prices, production, inventory and other quantities of economic interest.”
• “Index number indicate the the level of certain phenomenon at a given time or place in comparison with the level of the same phenomenon at some other standard time or place

Characteristics Of Index Numbers

• Index numbers are specialised averages.
• Index numbers measure the change in the level of a phenomenon.
• Index numbers measure the effect of changes over a period of time.
• Index numbers are Economic Barometers.
• Index numbers are sign and guide posts of Business.
• Index number are the ratio of the current value to a base value.

• An index is a convenient way to express a change in a diverse group of items.
• Converting data to indices also makes it easier to assess the trend in a series composed of exceptionally large numbers.

Why Convert Data to Indices?

• Many times we have to combine several items and develop an index to compare the cost of this aggregation of items in two different time period  For example, we might be interested in an index for items that relate to the expense of operating and maintaining an automobile. The items in the index might include tires, oil changes, and gasoline prices  Or we might be interested in a college student index. This index might include the cost of books, tuition, hostel, meals, and entertainment.
• There are several ways we can combine the items to determine the index.

Price Index  Price Relative :- The price relative of an item is defined as: Where: p t = price in current period p o = price in base period  Price Relative Index provides a ratio that indicates the change in price of an item from one period to another. o t p p Price Relative 

Simple Price Index

• The simple price index finds the percentage change in the price of an item from one period to another.
• An index number is always referenced back to a base year which is always given a value of 100.
• Subsequent figures (the next years) are then scaled in relation to the base year, so an index gives the change since the base year.

Suppose we have the price of an item for each year over a four year period:

Year Price

Unweighted indices Simple Aggregate Price Index :- In most cases we are interested in the prices of a “basket of goods”, and not just one item. We therefore need an aggregate index.

1. Add up column of prices
2. Use Item Price Yr0 Price Yr1 Price Yr A 1.00 1.10 1. B 2.00 2.30 2. C 5.00 5.60 5. 8.00 9.00 9. 100 112.5 115  100   o t P P 100 8 9 

Interpretation

• A price index of 113 would indicate an increase of 13%

relative to the base year.

• A price index of 75 would indicate a decrease of 25%

relative to the base year.

Unweighted Indices (Average of Relative Prices)

• The Average of Relative Prices is the average of the individual simple price indices of all items.  It does not take into account the quantity of each item sold.  It is a vast improvement on the simple aggregate index.

Average of Relative Prices Where: k = number of items p t = price in current period p o = price in base period k p p k o t  (^)            100 sum of the simple price indexes Average of Relative Prices