CPI Annual Average vs. December-to-December: Two Different Comparisons

Estimated reading time: 4 minutes

“Inflation for the year” needs a comparison label. A change between annual-average CPI levels isn’t the same calculation as a December-to-December change.

The original exercise below gives two monthly paths the same beginning and ending values. Their results still differ under one comparison. The point is to choose the question before choosing the percentage—not to select whichever number makes a headline look better.

Separate the two comparisons

Two invented paths with identical December endpoints

These are fictional index values, not published CPI observations. Call the baseline Year A and the following year Year B. Every month of Year A has an index of 100. Year B has two alternative paths: a jump in July or a jump in December. They are separate scenarios, not different geographic areas.

Assume one consistent, not-seasonally-adjusted monthly index on the same reference base. All 12 months in each year are available, with no revisions, missing values or other changes. The number 100 is an index level, not a dollar budget or a percentage.

Work out each result without changing the path

Year A’s total is 12 × 100 = 1,200, so its mean is 100. For the July-jump scenario, Year B’s total is (6 × 100) + (6 × 112) = 1,272. Dividing by 12 gives 106. The change from the baseline mean is (106 − 100) ÷ 100 × 100 = 6%.

For the December-jump scenario, the total is (11 × 100) + 112 = 1,212. Its mean is 101, producing (101 − 100) ÷ 100 × 100 = 1%.

Both scenarios nevertheless end at 112 after Year A ended at 100. Their endpoint calculation is identical: (112 − 100) ÷ 100 × 100 = 12%.

The July path has six months at 112; the December path has only one. The five extra elevated months add 5 × 12 = 60 index points to the sum of monthly levels. Spread across 12 months, that adds five points to the mean. This accounts for the difference between 106 and 101 without changing either December endpoint.

Test a tempting shortcut

In each invented Year B path, exactly one monthly change is 12% and the other 11 are zero. Averaging those 12 percentages gives 1% for either path.

That shortcut happens to match the December-jump result, but fails for the July-jump result of 6%. One coincidental match isn’t a valid method. The supplied monthly levels are the inputs to the annual-average comparison; the list of monthly percentage changes is a different set of numbers.

The exercise also can’t recover the full monthly path from the two December levels alone. Those endpoints fit both tables’ scenarios. Treating 12% as evidence of when the increase happened would invent information the endpoints don’t contain.

Carry a labeled result into your research

A precise classroom summary is: “In the July-jump scenario, the annual mean rises 6%, while the December endpoint rises 12% from the preceding December.” Both statements follow from the same invented records. Neither is a current U.S. inflation estimate.

Before using a real figure, save the exact series, geography, item group, seasonal treatment, reference base, observation period and release date. Identify which comparison your sentence needs. If observations or documentation are missing, follow the publisher’s notes; don’t fill gaps from this toy example.

A CPI comparison isn’t a calculation of your own budget. For that separate exercise, see budget buying power with a fixed basket. For a different time-window problem, read why an ACS five-year estimate is not the final year alone.

Primary guidance checked October 28, 2026 UTC; BLS factsheet last modified February 9, 2023. General financial-data education. All index values and calculated scenario results above are original hypothetical examples, not an official series or forecast.