Confidence intervals — Data, 14–17 years
Describe an estimate together with the uncertainty caused by limited data. Data, 14–17 years.
What a confidence interval is
A confidence interval gives a range of plausible values for a population quantity, based on a sample. It says more than a single estimate because it shows how much the result could vary from sample to sample. A wider interval means more uncertainty, not necessarily a worse measurement.
Why estimates need a range
The problem is that we usually cannot ask every person or measure every object in a population. Samples give useful estimates, but another fair sample would not give exactly the same answer. Confidence intervals developed to communicate that sampling uncertainty instead of hiding it behind a neat single number.
A poll estimate
In a poll, 52% of 1,000 people support a proposal, with a reported margin of error of 3 percentage points. The estimate is 52%, and the interval is 49% to 55%, found by 52 − 3 and 52 + 3. It is more honest to report the range than to claim the whole population is exactly 52%.
The trap
A common mistake is to say that there is a 95% chance the fixed population value lies in this already-calculated interval. That wording feels natural, but the population value is fixed; the random part is the interval produced by the sampling method. In school reports, say the method gives intervals that capture the value about 95% of the time.
Where it appears
Confidence intervals appear in opinion polls, medical research, climate estimates and quality testing. A climate scientist may give a range for a warming estimate, while a pollster gives a range for support. The interval describes sampling uncertainty; it cannot repair biased data or a badly designed study.
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