Yes. But statistics are never completely "accurate". You always make estimates.
A population is defined as an entire set of similiar items, we want to say something about the population; with our example the population is all people living in a certain country. There is a true mean (called µ) and a true standard deviation (called σ), 2/3 of all values fall between mean plus/minus one standard deviation. It's impossible to determine the true values µ/σ (here: due to practical reasons) and we can only estimate them.
Therefore we make samples (containing n values), that are randomly chosen and should reflect the population (e.g. they are representative for the population). For example: If you want to say something about the IQ of a nation, you don't go to one town and measure the IQ there, because the IQ taken there is only representative for the townsfolk and you also don't take only academics, etc., the mere act of data collection is extremely difficult. The empirical data can then be used to make estimates for the true values.
We use X̅ (mean of the sample) as an estimate for the true mean µ and s (standard deviation of the sample) as an estimate for the true standard deviation σ. Then there is the standard error of the mean (SEM); it tells you how much we know about the mean. It is defined as SEM = s/√n - in 2/3 of all cases the intervall X̅+/-SEM overlaps with the true mean µ; you can decrease the SEM and increase certainty with a bigger sample size (n), bigger sample sizes are always favorable. It is important to know that µ/σ are existing parameters with one defined value, while X̅/s are completely stochastical (e.g. depending on chance) and nothing more than estimates for these true values. In statistics you always work with estimates. In IQ research you most of the time get very clear results due to huge sample sizes.
Could really be the case.
