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Common Core: 7.SP.1

# Random & Probability Sampling

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Author: Sophia Tutorial
##### Description:

This lesson explains what random sampling is and why it's used.

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Tutorial

This tutorial is on random and probability sampling methods, focusing on:

1. Random Sample
2. Probability

## 1. RANDOM SAMPLE

The term “random” is used a lot in everyday speech, but what does it mean when it comes to statistics? Well, let’s figure out what it does not mean. It does not mean unusual or haphazard. Just because something isn't done with discernible order, doesn't necessarily mean random.

What a random sample does in fact mean in a mathematical sense is that it's unpredictable in the short term, but consistent in the long run. So if you want a random sample, you would need to select participants in such a way that every member of that population has an equal chance of being selected for the sample. You can do that. It’s called a probability sampling plan.

You can also “weight” certain people so that they might be more likely to be selected for the sample too.

• Random Sample
• A sample that has been selected in a manner where every member of the population has some predetermined chance of being selected for the sample.
• Probability Sampling Plan
• The way to collect a random sample that guarantees a certain likelihood for each member of the population to be selected.

IN CONTEXT

What does a random sample look like in context? Let’s say there are 15 billiard balls from a pool table, and you place them all on a hat, and you shake the hat, and voila, here's a sample of five.

Shake #1:

We took ball numbers 1, 5,7, 10, and 14.

Shake #2:

This is another sample of five and they’re not that different than the previous example and if you conducted the same hat trick over and over again, they would all have equal chance of being pulled.

Shake #3:

What happened here was we got balls 9, 11, 12, 13, and 14. All of which happened to be striped billiard balls. No solid. If you only had access to this information, you might be led to believe that all the balls in the hat were striped, which wouldn't be the case.

This may seem odd, but it can certainly happen even though you took this randomly-- you did a probability sampling plan. The reason being, this sample of five is just as likely as any other sample of five to be chosen.

• Random Selection
• The method of obtaining a random sample.

Might you get something that's unrepresentative? Yes. But the vast majority of time it will be representative.

The best method for selecting a sample that's representative is a random sample and a probability sampling plan. Now, this won't always get you a representative sample. But often, you will get one when you do random samples.

Good luck!

Source: This work is adapted from sophia author jonathan osters.

Terms to Know
Probability Sampling Plan

The way to collect a random sample that guarantees a certain likelihood for each member of the population to be selected

Random Sample

A sample that has been selected in a manner where every member of the population has some predetermined chance of being selected for the sample

Random Selection

The method of obtaining a random sample