Because we can't measure all the world's oak trees, statisticians come up with an estimated range of heights based on probability and all the data at their disposal. This range is called a confidence interval and it consists of two numbers: one that is probably smaller than the true value and one that is probably larger. The true value is probably somewhere between.
"A '95 percent confidence interval' means that 95 out of 100 times that the confidence interval is constructed this way, the interval will include the true value," says Drake. "If we measured samples of oak trees 100 times, the confidence interval based on the data collected in 95 of those experiments would include the population mean, or the average height of all oak trees. Thus, a confidence interval is a measure of the precision of an estimate. The estimate gets more and more precise as you collect more data. This is why the confidence intervals get smaller as more data becomes available."
So, a confidence interval helps show how good or bad the estimate is. When we flip a coin just four times, our estimate of 75 percent has a wide confidence interval because our sample size is very small. Our estimate with 40 coin flips would have a much narrower confidence interval.
The actual meaning of a confidence interval has to do with repeating an experiment over and over. In the case of the four coin flips, a 95 percent confidence interval means that if we repeated the coin flip experiment 100 times, in 95 of those, our probability of getting heads will fall within that confidence interval.