GlossaryStatistics and interpretation
Median
The median identifies the middle of ordered values. Learn the even-sample calculation, its difference from the mean, and limits on combining medians.
The median is the middle value after observations are ordered from smallest to largest. For an even number of numerical observations, the usual convention averages the two middle values. It describes the center by position, which makes it less sensitive than the mean to a few extremely high or low values.
A positional summary
A response-time median places the included intervals in order and identifies their middle. It does not add the durations and divide by the number of calls; that calculation produces the mean.
NIST's statistical handbook provides the odd- and even-observation formulas and distinguishes the median from other measures of center. A published median should still identify the observations, units, and eligibility rules behind it. NIST measures of location.
Example
Hypothetical example: Five eligible arrival intervals are 3, 4, 6, 8, and 29 minutes. The median is six minutes, the third value in order. The mean is ten minutes.
If a sixth interval of 10 minutes is included, the ordered values become 3, 4, 6, 8, 10, and 29. The median is seven minutes, the average of six and eight. It need not equal an interval observed for any one call.
Common confusion
A median of six minutes does not mean every call took six minutes, or that all calls met a six-minute objective. Ties and the calculation convention affect how many observations fall strictly below or above the median. Use a fuller distribution when the slower end of the service experience matters.
A median also differs from the midpoint of the smallest and largest values. In the five-value example, that midpoint is 16 minutes, not six. Looking only at the extremes does not locate the middle observation.
Combining and comparing medians
Do not average station medians and label the result the agency-wide median. The combined median generally requires the underlying observations or enough distribution information to calculate it. Groups with different call counts and distributions cannot be combined by treating their medians as ordinary totals.
Check that the same interval and eligible call types are used across periods. A median based on emergency responses cannot be compared directly with one including scheduled transports without explaining the difference. Missing durations should remain distinct from zero. The median is a useful summary of the included records, but it does not correct incomplete coverage or incompatible definitions.