Chapter 2: Measurement in Statistics - Index Numbers

Vocabulary and key concepts regarding index numbers, the Consumer Price Index (CPI), and inflation rates as presented in Chapter 2 of Statistical Reasoning for Everyday Life.

Index Number

A simple way to compare measurements made at different times or in different places by comparing them to a specific reference value.

Reference Value (or Base Value)

The value at one particular time or place chosen to be the standard for comparison; it is usually assigned an index of $100$.

Consumer Price Index (C P I)

A monthly reported index based on prices in a sample of more than $60,000$ goods, services, and housing costs used to track price changes over time.

Price Index Formula (Example: Gas Price)

The calculation where the current price is divided by the reference price and multiplied by $100$ to express the current price as a percentage of the reference value.

Annual Inflation Rate

The relative change in the CPI from one year to the next, calculated as: $$\frac{\text{CPI}x - \text{CPI}{x-1}}{\text{CPI}_{x-1}} \times 100\%$.

Relative Increase in CPI (2019 to 2020)

Calculated by subtracting the 2019 CPI ($255.7$) from the 2020 CPI ($258.8$) and dividing by the 2019 CPI, resulting in an inflation rate of about $$1.2\%$.

Mean Baseball Salary Increase (1987 to 2021)

A comparison showing that while the CPI rose by a factor of about $2.4$ (from $113.6$ to $271.0$), the mean salary rose by more than a factor of $10$ (from $\$412,000$ to $\$4,410,000$).

Producer Price Index (P P I)

A price index that measures the prices that producers (manufacturers) pay for the goods they purchase rather than the prices paid by consumers.

Consumer Confidence Index

An index based on a survey designed to measure consumer attitudes to help businesses gauge if people are likely to spend or save.

Table 2.1 Reference Point

The average gasoline price in $1985$ ($\$1.20$) which is used as the reference value with a price index of $100.0$.

Adjusting for Inflation using CPI

The process of comparing prices or costs across different years by multiplying the original cost by the ratio of the CPI values for the two years.