Base Shifting, Splicing and Deflating - Index Numbers, Business Mathematics and Statistics

# Base Shifting, Splicing and Deflating - Index Numbers, Business Mathematics and Statistics - Business Mathematics and Statistics - B Com

Base shifting

Shifting of base period or reference period of the index is known as base shifting. This can be done using the following relation as,

Example The following are the index numbers of a commodity taking 1991 as the base.

Find the index numbers by changing the base to 1994.

Solution

Splicing The process of combining two or more index numbers covering different bases into a single series is called splicing.
Suppose we have two series A and B, and if series A is spliced with B, then

If series B is spliced with A, then

Example The following are two series A and B of the index numbers of a commodity taking 1991 and 1994 as the base years.

a. Splice the index series of A to B
b. Splice the index series of B to A

Solution
a.
Index series A spliced with index series B

b. Index series B spliced with index series A

Deflating
It is a technique used to make allowances for the effect of changing price values. It is used to measure the purchasing power of money.

It can also be found using the relation

Example The table below shows the income of a company and its price index taking the year 1991 as the base.

Calculate the deflated value for every year taking 1991 as the base.

Solution

The document Base Shifting, Splicing and Deflating - Index Numbers, Business Mathematics and Statistics | Business Mathematics and Statistics - B Com is a part of the B Com Course Business Mathematics and Statistics.
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## FAQs on Base Shifting, Splicing and Deflating - Index Numbers, Business Mathematics and Statistics - Business Mathematics and Statistics - B Com

 1. What is base shifting in index numbers?
Ans. Base shifting is a method used in index numbers to change the base period from which the index is calculated. In this method, the values of the index numbers are adjusted to reflect the change in the base period. This is done by multiplying the index numbers of the old base period by a conversion factor that takes into account the value of the new base period.
 2. What is splicing in index numbers?
Ans. Splicing is a technique used in index numbers to combine two or more index series into a single series. This is done by aligning the two series at a common point in time and then adjusting the values of one or both series to reflect the change in the other series. The aim of splicing is to create a smooth and continuous series that accurately reflects the underlying data.
 3. What is deflating in index numbers?
Ans. Deflating is a method used in index numbers to adjust for the effects of inflation or deflation on a series of values. This is done by dividing the nominal values by a price index to obtain real values that reflect changes in purchasing power. The aim of deflating is to create a series of values that is comparable over time, by removing the effects of changes in prices.
 4. What are some applications of index numbers in business mathematics and statistics?
Ans. Index numbers are commonly used in business mathematics and statistics to measure changes in various economic variables over time. Some of the applications of index numbers include tracking changes in stock prices, analyzing changes in consumer prices or wages, and measuring changes in the production of goods and services. Index numbers are also used to construct economic indicators, such as the consumer price index or the gross domestic product.
 5. How do you calculate a simple index number?
Ans. A simple index number can be calculated by dividing the value of a variable in a given period by its value in a base period, and multiplying the result by 100. The formula for a simple index number is: Index number = (Value in current period / Value in base period) x 100 For example, if the value of a variable is \$500 in the current period and \$400 in the base period, the simple index number would be: Index number = (500 / 400) x 100 = 125

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