GlossaryStatistics and interpretation
Mean
The mean divides the sum of values by the observation count. Learn how extremes, missing values, and group weights affect a reported average.
The mean is the sum of included values divided by the number of observations. It is often called the arithmetic average. It summarizes the level of a set of values, but it does not describe every observation or necessarily match the experience of a typical person, call, or incident.
State what is averaged
A mean response interval should identify the beginning and ending milestones, eligible calls, time period, and unit. Averaging call-to-arrival durations is different from averaging dispatch-to-arrival durations, even when both results are expressed in minutes.
NIST defines the arithmetic mean as the sum divided by the observation count and distinguishes it from other measures of a distribution's center. The choice matters when the values have long tails or unusual extremes. NIST measures of location.
Example
Hypothetical example: Five eligible service intervals are 4, 5, 5, 6, and 20 minutes. Their sum is 40 minutes, so the mean is eight minutes. The median, or middle value, is five minutes.
The 20-minute observation raises the mean. Reporting the mean is not an arithmetic error, but saying that most intervals were eight minutes would misdescribe the records. Four of the five were shorter, and none was exactly eight.
Common confusion
“Average” can be used loosely for a mean, median, or other summary. A report should name the actual measure instead of leaving readers to infer it. A mean also does not show the range or how often very long intervals occurred.
Averaging group means without their observation counts can produce the wrong overall result. If one station has 10 calls averaging four minutes and another has 90 averaging eight, the combined mean is 7.6 minutes: (10 × 4 + 90 × 8) ÷ 100. The simple average of the station means, six minutes, answers a different question by giving each station equal weight.
Check eligibility and missing values
Specify how missing timestamps, canceled responses, and invalid intervals are handled. An unknown duration is not zero minutes. A mean calculated only for records with complete times describes that included set; it may not describe every response.
Keep extreme observations unless a documented reason supports correction or exclusion. Pairing the mean with a median, percentile, or distribution can show whether the single summary hides meaningful variation.