Federal Reserve Economic Data

The FRED® Blog

Confidence intervals and sampling variation

Making apples-to-Big-Apple comparisons

In a recent FRED Blog post, we discussed how confidence intervals show the level of certainty about the accuracy of an estimate. In short: Wider confidence intervals signal more uncertainty.

Also, larger survey sample sizes increase the statistical accuracy of the data collected and allow data users to confidently compare apples to apples. Today’s post offers a bite-size example.

Our FRED graph above shows US Census estimates for median household income in three US counties:

  • Pitkin, CO (solid blue line), home to the town of Aspen.
  • New York, NY (dashed red line), the borough of Manhattan in New York City.
  • Teton, WY (solid green line), home to the town of Jackson in the Jackson Hole valley.

Between 1989 and 2023, estimated median household income was frequently very similar for all three locations listed above: the coastal urban center and the two mountainous rural areas. But the number of residents was vastly different.

Population size influences the number of households sampled to collect income data: The more populous the county, the more households are sampled. So the estimated data are relatively more precise in more populous counties (e.g., New York County) than in less populous counties (e.g., Pitkin and Teton counties).

FRED also has data that capture the confidence intervals reported along with the estimated income data. The relative confidence interval for New York, NY, data can be as much as five times smaller than those for the Pitkin, CO, and Teton, WY, data, as seen in the graph below. That means far less uncertainty about the accuracy of the reported figures.

So, clearly, it’s best to be cautious when you try to make fair apples-to-apples data comparisons, including data from the Big Apple itself.

How these graphs were created: Search FRED for and select “Estimate of Median Household Income for Pitkin County, CO.” Click on the “Edit Graph” button and select the “Add Line” tab to search for “Estimate of Median Household Income for New York County, NY.” Don’t forget to click on “Add data series.” Repeat the last two steps to add the third series: “Estimate of Median Household Income for Teton County, WY.” Lastly, use the “Format” tab to customize the line styles. For the second graph, follow the same general procedure, except that each line is now composed of three series: Search first for “90% Confidence Interval Upper Bound…,” then “90% Confidence Interval Lower Bound…,” and finally the above mentioned estimate. Then apply the formula (a-b)/c on each line.

Suggested by Diego Mendez-Carbajo.

Food affordability and estimated poverty

The US Census Bureau collects data and reports on the poverty level each year. Their statistical definition of poverty has to do with the affordability of food. As they describe, the Office of Management and Budget’s Directive 14 sets a money income threshold related to the after-tax spending by families on a food plan defined by the Department of Agriculture. At the time of this writing, the poverty income threshold for a family of four is $32,130.

The solid orange line in our FRED graph above shows the number of people, measured in millions, who lived in poverty between 1989 and 2023. In 2023, that number was estimated to be 40,763,043 persons. The dashed lines above and below the solid line show the boundaries (or range) of the 90% confidence interval associated with the poverty estimate.

Why does the Census provide a range for its poverty measure?

The Census Bureau estimates poverty rates using data from several different surveys. The regional sample size of the surveys impacts their reliability: In statistics, data obtained from small samples tend to be less reliable than data obtained from larger samples. The Census estimates take all this into account and include a 90% confidence interval for the reported figures.

What’s a 90% confidence interval?

In short, a confidence interval is the level of certainty about the accuracy of the estimate. The Census Bureau routinely employs a 90% confidence interval for its estimates. As they explain, a 90% confidence interval provides a level of certainty that, if you measure poverty using the same procedure multiple times, the estimated value will be within the range 90 out of 100 times.

How this graph was created: Search FRED for and select “90% Confidence Interval Upper Bound of Estimate of People of All Ages in Poverty for United States.” Click on the “Edit Graph” button and select the “Add Line” tab to search for “Estimate of People of All Ages in Poverty for United States.” Don’t forget to click on “Add data series.” Use the “Add Line” tab again to search for and add “90% Confidence Interval Lower Bound of Estimate of People of All Ages in Poverty for United States.” Lastly, use the “Format” tab to customize the line styles.

Suggested by Diego Mendez-Carbajo.

Real GDP growth by state: Third quarter 2025

On January 23, 2026, the Bureau of Economic Analysis released real GDP data for all US states for the third quarter of 2025. The FRED map above shows the percentage change growth rates from the previous quarter: Light yellow denotes slight growth (below 2%), light green denotes moderate growth (2% to 4%), and dark green denotes robust growth (above 4%).

Highlights

  • All 50 state economies plus Washington, DC, grew in the third quarter, with a national average of 4.4% growth annualized.
  • The median state grew at 4.5% annualized, slightly above the US average; 23 other states had slower growth than the US average.
  • Kansas had the fastest growth, at 6.5% annualized.
  • North Dakota had the slowest growth, at 0.4% annualized. But this comes after having the fastest growth during the second quarter.

The St. Louis Fed’s Eighth District includes Arkansas, Illinois, Indiana, Kentucky, Mississippi, Missouri, and Tennessee. All these states except Illinois grew faster than the national average. Growth in Arkansas was the fastest, at 5.8%, while growth in Illinois was only slightly below the US average, at a still-robust rate of 4.3%.

NOTE: These data are subject to future revision by the source. Our ALFRED database records vintages of the data, so users can view the data as they appeared at various points in history. The link takes you to real GDP for Missouri, as of January 23, 2026.

How this map was created: Search FRED for “Real Total Gross Domestic Product for Missouri” and click the first available series. Click the “View Map” button and then the blue “Edit Map” button. Modify the units to “Compounded Annual Rate of Change.” Use “Format” to switch the number of color groups to 3, with the data grouped by “User Defined Method”; then define the scales to be 2, 4, and 10. For values less than 2, choose light yellow to show slight growth; for values less than 4, choose light green to show moderate growth; for values less than 10, choose dark green to show robust growth.

Suggested by John Fuller and Charles Gascon.



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