The whole and the part
A population is the complete set you care about: every customer, every voter, every loaf from the bakery this year. A sample is the part you actually measured. Statistics exists because populations are usually too big, too expensive or too destructive to measure whole (you cannot taste every loaf). The science is in choosing a sample that can speak for the population, and in pricing the uncertainty that sampling leaves behind.
A bakery sells about 1,200 loaves a week and wants the average weight. Weighing all 1,200 is the population route: exact, and a lot of lifting. Weighing 60 loaves chosen across days and batches is the sample route. If those 60 average 502 g with SD 9 g, the inferential statement is: the week's mean is estimated at 502 g, with a standard error of about 9 / √60 ≈ 1.2 g. The sample does not give the population value; it gives a tight neighbourhood for it.
Representative beats big
A sample's value comes from how it was chosen, not only how large it is. Random selection gives every population member a fair chance of inclusion, which is what makes the mathematics of standard errors valid. A huge convenience sample (weigh only Monday's loaves, survey only your followers) can be precisely wrong: tiny standard error around a biased answer. Classic polling failures are exactly this, large n and all.
Volunteer samples: reviews, call-in polls, opt-in surveys. People with strong feelings volunteer; everyone else is undercounted. The results describe the volunteers accurately and the population hardly at all.
The symbols keep the two apart
Population quantities get Greek letters (mean μ, standard deviation σ) and are usually unknown constants. Sample quantities get Latin letters (x̄, s) and are computed from data. The n − 1 in the sample variance exists precisely because a sample is not the population it estimates. The guide on parameters and statistics, linked below, keeps the full cast straight.
Frequently asked questions
What makes a sample representative?
A selection method that does not systematically favour part of the population: ideally random sampling from a complete list of members, with attention to who fails to respond. Size helps precision; method decides validity.
Is a sample of 1,000 always better than a sample of 100?
It is more precise if both are drawn the same way: standard error shrinks like 1 over root n, so 1,000 beats 100 by about a factor of 3.2 in precision. A biased 1,000 can still be worse than an honest 100.
Can a sample ever be the population?
Yes: a census. Also, sometimes the 'sample' in front of you is all you will ever care about (this month's defects), and then it is the population for your purposes and descriptive methods apply.