What is the formula for calculating a simple index number?

A simple index number is a statistical measure used to show the change in a variable, such as price or quantity, over time relative to a specific base period. The formula calculates this change by dividing the value in the current period by the value in the base period and then multiplying the result by 100. This converts the ratio into a percentage, making it easier to interpret, with the base period always having an index value of 100.

B. This formula is the inverse of the correct calculation and would incorrectly show a decrease when there is an increase, and vice versa.

C. This is an incorrect ratio (base/current) and omits the standard practice of multiplying by 100 to express the value as an index.

D. This provides the correct ratio but is not a complete index number, as it has not been multiplied by 100 for standardization.

1. Taylor, L. (n.d.). Lecture 10: Index Numbers. University of Cape Town, Department of Statistical Sciences. Retrieved from https://www.stats.uct.ac.za/stats/courses/sta1000/notes/Lec102013.pdf (See page 2, "Simple Price Index").

2. Illowsky, B., & Dean, S. (2018). Introductory Statistics. OpenStax, Rice University. Chapter 13, Appendix: Mathematical Phrases, Symbols, and Formulas. The general form of an index number is given as (current value / base period value) 100.