Mean, median, variance, and percentiles.

Imagine each row is one window of 100 requests. In the steady window, every request takes 195 ms. In the second, 95 requests take 100 ms and five take 2,000 ms. Both means are 195 ms: the fast majority offsets the slow requests when all 100 values are added together.

The mean is the sum divided by the count, so both windows average to 195 ms. The median is the middle observation after sorting: it shows the typical request shifted from 195 ms to 100 ms. The table also shows why the mean alone cannot tell you whether the slow requests matter to users.

The range reports only the minimum and maximum. Variance uses every observation: subtract the mean from each value, square each difference, then average those squared differences. Squaring keeps fast and slow deviations from canceling and gives distant values more influence.

For the 100-request long-tail window above, population variance is 171,475 ms². Standard deviation is its square root, about 414 ms, which brings the spread back to latency units. The steady window has zero variance because every request takes the same time.

Variance is useful when comparing how dispersed two sets of measurements are, but squared units are hard to explain as a user-facing target. Standard deviation is still sensitive to extreme values and does not say what share of requests crossed a deadline. Use percentiles when the question is about a latency threshold.

For nearest rank, sort n observations, calculate the one-based position ceil(0.95 × n), and select that value. With 100 observations, p95 is item 95. In the long-tail example, items 1 through 95 are 100 ms, so p95 is 100 ms; p99 reaches the 2,000 ms requests. A p95 tells you where the 95% threshold falls. It does not summarize the remaining five percent.

Nearest rank is one convention. Some tools interpolate between observations, so compare systems using the same definition. Do not average two reported p95 values to get a combined p95; use the underlying observations or a mergeable distribution summary whose approximation limits are known.

Start with the same-mean example. The two windows both average 195 ms, but their p99 and variance tell a different story. Change one or two current measurements, then compare the median, p95, p99, and maximum. Try the small-sample example too: with only five readings, nearest-rank p95 selects the maximum, so one request controls the result.

Compare the same request population, units, time window, and percentile convention. Relative change is (current − baseline) / baseline × 100. A release policy can use a stated threshold to flag a change for investigation—for example, a p95 increase greater than 15%.

A flag is a decision rule, not proof that the release caused the change. Check traffic mix, sample size, errors, and other changes in the same window. Use the threshold to decide when a person should look closer, not as a substitute for understanding what users experienced.

Work through nearest-rank p95, a fuller latency summary, and a threshold comparison. Each ticket uses the same percentile rule in TypeScript and Go.