Point Estimation

A point estimate is a single value, calculated from sample data, used as the best guess for an unknown population parameter. The sample mean, $\bar{x}$, is the standard point estimate for the population mean, $\mu$.

If you take a random sample and calculate its mean, that sample mean is your point estimate for the population mean. The larger and more representative the sample, the more likely this estimate is to be close to the true population value.

You can also use sample data to estimate the population standard deviation. This uses a very similar calculation to the sample standard deviation, and in Core Maths you'll typically use your calculator's statistical functions to find this directly from raw or grouped sample data.

A point estimate gives a single ‘best guess’ value but no sense of how reliable or uncertain that guess is. This is why point estimates are often paired with a confidence interval, showing the plausible range around the point estimate.

(a) Sum = 980+1005+995+1010+990+1000+1015+985 = 7980. Point estimate = 7980÷8 = 997.5 hours.

(b) A sample of only 8 bulbs is quite small, so it may not be fully representative of the whole batch — a different sample of 8 bulbs could easily give a noticeably different mean, meaning this point estimate carries a fair amount of uncertainty (a larger sample would generally give a more reliable estimate).

1. 62.5÷5 = 12.5.
2. A point estimate is a single value, calculated from sample data, used as the best available estimate of an unknown population parameter (e.g. the sample mean used to estimate the population mean).
3. It is being used to estimate the population mean.
4. A confidence interval gives a sense of how reliable/uncertain the estimate is (a range of plausible values), whereas a point estimate alone gives no indication of how much the true value might differ from the estimate.
5. Because of sampling variability — each sample is a different, randomly selected subset of the population, so by chance the specific values included (and therefore the calculated mean) will differ slightly from sample to sample, even though both samples come from the same underlying population.