confidence interval
/ KON-fi-dens IN-ter-val /
When a weather app says tomorrow's high will be around 20 degrees, you instinctively read it as a band, not a promise: probably somewhere in the high teens to low twenties. A confidence interval makes that hedge precise. Instead of pretending your measured average is the exact truth, it states a range that the true value very likely lies inside.
A confidence interval is a range built around your sample mean, wide enough that, in the long run, a stated percentage of such intervals — usually 95 percent — would capture the true value. Its width comes from how scattered your measurements are and how many you took: a noisier method or fewer repeats gives a wider, more humble interval; tighter data and more repeats give a narrow one.
It matters because it turns a single number into an honest statement of how sure you are, which is what regulators, journals, and customers actually need. The most common misreading is to say there is a 95 percent chance the true value is in this particular interval; more carefully, it is the procedure that succeeds 95 percent of the time, and any one interval either contains the truth or does not.
Four measurements of lead in water average 11.2 micrograms per litre. The 95 percent confidence interval works out to 11.2 plus or minus 0.6, so the result is reported as 10.6 to 11.8 micrograms per litre.
A mean reported with the range the true value most likely falls in.
A 99 percent interval is wider than a 95 percent one for the same data: demanding more confidence forces you to cast a wider net. With few measurements the interval is built using the t-distribution rather than the Gaussian.