Reviews
Part of Statistics Verification Guide: A Reading Framework
Counts, percentages, rates, indexes, and averages compared
Statistical measures compared across counts, proportions, percentages, rates, ratios, indexes, means, medians, change measures, and seasonal adjustment.
What to take away
- Counts answer how many recorded units, not how common an event is.
- Percentages and proportions require a named denominator.
- Rates add a population and often a time basis.
- Index values measure change relative to a base, not an ordinary quantity.
- Mean and median describe different features of a distribution.
Statistical language is compact, which makes substitution easy. A count becomes a rate. A percentage-point increase becomes a percent increase. An index level is described as a price. A mean becomes what a typical person experienced. Keep the unit in every note, formula, chart, and sentence.
Quick comparison
| Measure | Basic form | Good use | Frequent error |
|---|---|---|---|
| Count | Number of recorded units | Workload, events, people, transactions | Ignoring population size or duplicates |
| Proportion | Part divided by whole | Share of a defined group | Wrong or shifting denominator |
| Percentage | Proportion multiplied by 100 | Readable share | Confusing points with percent change |
| Rate | Events divided by population or exposure, often over time | Frequency across unequal groups | Omitting exposure or period |
| Ratio | One quantity divided by another | Relative size of distinct quantities | Calling every ratio a rate |
| Index | Relative measure against a base | Change in prices, production, or other composite | Reading 120 as a physical amount |
| Mean | Sum divided by count | Center when distribution permits | Distortion by extreme values |
| Median | Middle ordered value | Center for skewed distributions | Treating it as the average of all values |
Counts, proportions, and percentages
A count depends on a recording system. State whether it represents reports, incidents, charges, people, visits, devices, claims, or rows. Remove duplicates only when the definition calls for unique units.
A proportion's numerator belongs within its denominator. A percentage is the same relationship expressed per hundred. If 30 of 120 respondents choose an option, the result is 25 percent of those 120 respondents, subject to design and missing-response rules.
The CDC's archived epidemiology lesson on ratios, proportions, and rates distinguishes these forms and defines a rate as event frequency in a defined population over a specified period. The formulas arise in epidemiology, but the unit discipline applies across news data.
Rates and ratios
Rates allow comparison when group sizes or exposure differ. A traffic-death rate might use deaths per 100,000 residents or per distance traveled. Those denominators answer different questions.
Name the numerator, denominator, scale factor, geography, and period. Check whether age standardization, exposure weighting, or smoothing was used. Do not compare a crude rate with an adjusted one as if they were identical.
A ratio may compare quantities that do not form a part-to-whole relationship, such as students per teacher. Avoid calling it a percentage unless the denominator represents the whole containing the numerator.
Absolute, percent, and percentage-point change
If a share rises from 20 percent to 25 percent:
- absolute change is 5 percentage points
One Rise, Three Statements
- 20%starting share
- 25%ending share
- 5percentage points gained
- 25%relative percentage change
Each statement is mathematically correct and rhetorically different. Report the start and end values beside the change when readers could confuse them. For a move from a very small base, give counts as well as percentages.
Indexes
An index combines or rescales data relative to a base, often set to 100. A value of 120 does not mean $120 or 120 items. It means the defined index is 20 percent above its base level, subject to its construction and revisions.
Check the index population, basket or components, weights, formula, base period, seasonal status, and whether the published change uses rounded or unrounded levels. Do not compute a household's exact cost change from a broad index without matching the concept.
Mean, median, and distribution
The mean uses every value and can move sharply with extremes. The median identifies the middle after ordering values and is less sensitive to extreme tails. Neither alone describes variation, clusters, or inequality.
Show the distribution or additional quantiles when the shape matters. For income, response time, home prices, or claim size, a median may describe the middle case better than a mean. For total resource planning, the mean may still matter.
Adjusted and unadjusted series
Seasonal adjustment estimates and removes recurring within-year patterns so short-term movements are easier to see. It does not remove every irregular event or make a series final.
The Bureau of Economic Analysis explains why the adjustment is made with an example worth borrowing: jewelry spending always falls in January once the Christmas season ends. So ask not whether it fell, but whether it fell more or less than normal.
An adjusted January that reads as growth describes a smaller decline than usual. Label every series and compare like with like.
Choose language by measure
- "The agency recorded 400 reports" for a count.
- "Reports equaled 12 per 10,000 accounts" for a rate.
- "The share rose 3 percentage points, from 40 to 43 percent" for a proportion change.
- "The median wait was 18 minutes" for the middle observation.
- "The seasonally adjusted index rose 0.4 percent from May" for an adjusted index change.
Common questions
Is per capita always a rate?
It is a ratio to population and may be called a rate in common use. Include the period when events accumulate over time.
Can the mean and median both be correct?
Yes. They summarize different aspects of the same distribution.
Why can adjusted data change later?
New observations and revised seasonal factors can change recent estimates.
Should percentages total 100?
Only when categories are exhaustive, mutually exclusive, use one denominator, and rounding permits it.
