To obtain a new series of index numbers, the old index numbers are multiplied with which of the following common factor? 

Key Points

• Index numbers are used to measure and track changes in various economic and statistical indicators over time. They provide a way to compare the relative changes in different periods and capture the overall trend.
• When a new series of index numbers is constructed, it is often desirable to establish a new base year for comparison. The base year serves as a reference point with a value of 100. By using a common base year, it becomes easier to analyze and compare changes across different time periods.
• To align the old index numbers with the new base year, a common factor is applied. This factor is calculated as the reciprocal of the index number of the new base year, multiplied by 100. Mathematically, it can be expressed as: \(\frac{100}{\text{Index number of new base year}}\).
• By multiplying the old index numbers by this factor, we rescale them so that they are relative to the new base year value of 100. This adjustment ensures that the old and new series are on the same scale and facilitates meaningful comparisons between them.
• This rescaling allows for consistent analysis and interpretation of the index numbers across different time periods, enabling us to measure the relative changes and trends accurately.
• By using the common factor, the relative proportions and relationships among the index numbers are maintained while adjusting them to the new base year. It helps ensure that the new series of index numbers accurately reflects the changes and trends in the underlying data relative to the chosen base year. 

Hence, the required common factor is \(\rm \frac{100}{Index\ number \ of \ new \ base \ year}\)