# 5.1 Introducing Statistics: Why Is My Sample Not Like Yours?

#exploringdata

#sampling

#experimentation

#anticipatingpatterns

#statisticalinference

written by

brianna bukowski josh argo harrison burnside

(editor)

## Sampling Distribution Defined

A sampling distribution is a distribution of all possible samples of a given size. In the previous units, every distribution consisted of one sample, such as a class of students grade in a class. With a sampling distribution, you take the average of all means (quantitative) or proportions (categorical) of each possible sample size (n) and use these averages as your data points. The normal model now also represents the distribution of all possible samples of a given sample size.

### Differences

To find the sampling distribution for differences in a sample proportion or mean, remember that variances always add to find the new variance. If one needs the standard deviation, you should take the square root of the variance. However, for means you can just subtract.

### Discrete vs. Continuous Random Variables

There are two major types of random variables in AP Statistics: Discrete and Continuous. Discrete Random Variables are variables that have a certain and definite set of values that the variable could be. Usually, these are whole numbers in real world situations (1, 2, 3, 4, 5…, 100, etc.). For Discrete Random Variables, to calculate the mean, you use the expected variable formula: For Discrete Random Variables, to calculate the standard deviation, you use a formula similar (in a way) to the expected value formula, but with a square root:. The other type of random variable, Continuous Random Variables, can take on any value at any point along an interval. Generally, Continuous Random Variables can be measured while Discrete Random Variables are counted. A histogram is used to display continuous data, while a bar graph displays discrete data!

## Parameters vs Statistics

In AP Statistics, you will be asked to compare Statistics from a Sample to the Parameters of a Population. Here is a chart to help you remember which symbols are from sample statistics and from population parameters:

 Measurement Population Parameter Sample Statistic Mean 𝝁 x̅ Standard Deviation σ s Proportions 𝝆 p̂