# How to Calculate Index Numbers

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Index numbers represent the amount of change compared to a base value. For example, the consumer price index measures the total price of commonly purchased items relative to a base year to determine the inflation rate. The base year is always set to 100, so subsequent values are quickly recognized as increasing (greater than 100) or decreasing (less than 100). This format also allows researchers to quickly extrapolate the percent change as the difference between the index number and 100. Differences between non-base years can be calculated using the index numbers without knowing the actual values.

Acquire the values for the base and subject variables. For example, if you wanted to measure business growth, you might use the first year's profits as the base value to compare with profits from subsequent years.

Divide each subject value by the base value. Continuing with the example, if you had profits of \$20,500 the first year and \$23,500 the second year, divide \$23,500 by \$20,500 to get 1.146.

Multiply the result by 100 to convert it to a percentage of the base value. In the example, 100 times 1.146 yields 114.6.

Interpret the results. In the example, the index itself shows the second year's profit was 114.6 percent of that of the base year. Subtracting 100 shows a 14.6 percent increase in profits from the base year to the subsequent year.

## Tips & Warnings

• To calculate the percent change between two non-base index numbers, subtract the second index from the first, divide the result by the first index and then multiply by 100. In the example, if the third-year index was 119.1, subtract 114.6 from 119.1 and divide by 114.6. Multiply the resulting 0.039 to find the 3.9 percent increase between years two and three without needing to reference the actual values.
• If you calculated index numbers for multiple years, you could also graph the results to see the growth over time.

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