United States Department of Labor

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## Distribution Statistics

### Definition

BLS produces statistics in a variety of formats. Below are some key definitions to know when using BLS data.

Below are terms that convey the central tendency of the data.

Average, mean, or arithmetic mean. The sum of a set of numbers divided by the number of members in the set. Example: the average of 2, 4, 12 is 6. (2+4+12)/3=6.

Median or 50th percentile. The midpoint of a set of values. This is the point where half of the values are greater and half are less than the value. Example: among the following values (2, 4, 6, 12, 60), 6 is the median value. Two numbers (12 and 60) are greater than 6 and two numbers (2 and 4) are less than 6.

Geometric mean. A geometric mean is used to find the central tendency of numbers that are multiplied together (most often found in price measures). The geometric mean is the nth root of the product of a set of numbers, where n is the number members in the set.  Using the example from the arithmetic mean, the geometric mean of 2, 4, 12 is 4.58 ∛(2×4×12).

BLS also uses terms that convey the distribution of the data.

Percentile. Percentile refers to the proportion, or percent, of a distribution that is less than the nth percentile. For example, if the wages at the 20th percentile are $10.00, then 20 percent of the wages are less than$10.00.

Quartile. A quartile divides a distribution into four equal segments. The lowest quartile spans from the lowest value to the 25th percentile; the second quartile spans from the 25th percentile to the 50th percentile; the third quartile spans from the 50th percentile to the 75th percentile; and the highest quartile spans from the 75th percentile to the highest value.

Quintile. A quintile is similar to a quartile, except it divides a distribution into five equal segments. The lowest quintile spans from the lowest value to the 20th percentile; the second quintile spans from the 20th percentile to the 40th percentile; the third quintile spans from the 40th percentile to the 60th percentile; the fourth quintile spans from the 60th percentile to the 80th percentile; and the final quintile spans from the 80th percentile to the highest value.

Decile. A decile is similar to quintiles and quartiles, but divides a distribution of values into 10 equal segments.

### Why does BLS have so many measures?

Sometimes, a mean, or average doesn’t convey much information, particularly if there is a wide distribution of values. For example, wages for a particular occupation may vary quite a bit. Learning about the distribution of wages can give more information about what an entry-level wage may look like compared with a wage with more experience.