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.

## Populations

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.

## Samples

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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