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Population vs. Sample

In Statistics, we take information from smaller groups (samples) to draw conclusions about larger groups (populations) that share a characteristic which we are interested in.

For example, we may be interested in understanding how a prescription drug affects a population of U.S. adults. We can take a sample (smaller group) of the population to examine it's effects. We can then make conclusions about the larger population, based on the results of the sample.


The practice of taking information from samples and drawing conclusions about populations is called inferential statistics.

We make a hypothesis or claim about a population, and then test that claim to see if it is likely (aka probable or statistically significant).

We assume that populations are "normally distributed," meaning that most of the values occur closer to a mean, with decreasingly fewer values occurring further away from it. This must be true to conduct meaningful statistical analysis.

The law of large numbers states that the larger the sample size, the closer the sample results will be to the true population mean.

We use parameters to describe populations, which are expressed using Greek symbols including 'μ' for population mean and 'σ' for population standard deviation.


The Central Limit Theorem states that as a sample size gets bigger, it's distribution becomes more approximately "normal."

The larger our sample, the closer our results will be to the true population.

Samples also must be randomly selected to avoid bias and ensure results that are as close as possible to that of the true population.

Various sampling methods are used to avoid bias.

We use descriptive statistics to describe samples, which are represented by Latin alphabet letter variables, including x̄ for sample mean, s or SE for sample standard deviation aka standard error, and n for sample size.


Next, let's take a break - and then learn more about populations, samples, and hypothesis testing.

Contact us for practice materials regarding standard deviation, the bell curve, the empirical rule, normal probability, and more.

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