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Relative Frequency Probability/Empirical Method

Relative Frequency Probability/Empirical Method

Author: Ryan Backman
Description:

Calculate relative frequency given a certain situation.

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Tutorial

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Hi. This tutorial covers relative frequency probability, sometimes also known as the empirical method for calculating probability. So there are three ways to make a probability statement, the first being theoretical probability, also known as the a priori method; experimental probability, also known as relative frequency probability, and sometimes referred to as the empirical method; and the third one is subjective probability.

So we're going to spend most of the time here talking about experimental probability. And at the end of the tutorial, we'll touch on subjective probability, but we're not going to spend a lot of time discussing that. OK, so let's start with a definition. So experimental probability or relative frequency probability-- these two terms can be used interchangeably-- is a method of calculating probability where the probability is the ratio of the number of trials where the desired event occurs to the number of total trials.

And this is usually going to be in the long run, so they're going to give you data that has occurred in the long run, and you're going to calculate a probability based on that. And again, this is also known as the empirical method of calculating probability.

So the probability of an event of E, P of E-- remember that this is probability notation, so this stands for the probability of event E-- can be found by-- the probability of E is approximately equal to the number of times E occurs divided by the number of trials. So we're going to be using existing data to be making probability statements. So let's take a look an example.

So consider a frequency distribution for a sample of patients in an orthopedic clinic. What they did is they collected the heights and put them into intervals. So we have 4' 6" to 5 feet, 5 feet to 5' 6", 5' 6" to 6 feet, 6 feet to 6' 6". We have the frequencies of patients that have come in.

Notice, there's a lot of patients here, so this is data that's been accumulating for some time. So the chance experiment is a receptionist notes the height of the next patient that enters the clinic. We're going to let event E be the event of observing a patient in the 5 foot 6 to 6 feet height interval. Then we want to know, what's the probability of E?

So basically what we're doing with relative frequency probability is we're using frequency data that's already been collected and using that to make a prediction about the probability of some event. So if we're calculating probability of E, the probability of E is going to approximately be equal to-- so let's actually use a squiggly equals sign here-- the total number of trials needs to go on the bottom.

So what we need to do to calculate the number of trials is go to the calculator and add up all of those frequencies-- so 512 plus 2,189 plus 1,710 plus 423. And if we add those all up, it is about 4,834. So that goes on the bottom of the fraction. So that's how many observations there were.

And then the number of times E occurs or has occurred-- so that value is this 1,710. OK, so that is my probability there. So now what I want to do is I want to divide those two numbers-- so 1,710 divided by 4,834. And to get that as a decimal value, I'm going around it to the nearest thousandth, so it would be approximately equal-- or excuse me-- 0.354.

So if we think about that in terms of percent, that means that there's about a 35% chance that the next person that walks through the door will have a height between 5 foot 6 and 6 feet. So again, that was a calculating probability of an event using relative frequency. And as promised, let's just talk a little bit about subjective probability.

Subjective probability is a probability statement that an individual makes based on a personal judgment to describe the likelihood of an event. So this isn't really using any sort of statistical reasoning. It's just based on somebody's judgment. So this subjective probability doesn't really belong in a statistics class, but you do see these statements quite a bit.

So example-- I have an 85% chance of passing my statistics exam. So maybe I'm using a little bit of reasoning to come up with that 85%, but it's not really-- it's really just based on my own judgment. You hear is subjective probabilities a lot, but just know that those aren't really based on sound statistical reasoning. So that has been the tutorial on relative frequency probability. Thanks for watching.

Terms to Know
Experimental Probability/Relative Frequency Probability/Empirical Method

A way of assigning probabilities that states that the probability of an event is equal to the number of times it has occurred in identical trials of a chance experiment, divided by the number of trials of the chance experiment.

Subjective Probability

Not a true probability model at all, this method assigns probabilities based on how likely an individual feels the event is.

Formulas to Know
Experimental Probability/Relative Frequency Probability/Empirical Method

P left parenthesis E right parenthesis space equals space fraction numerator n u m b e r space o f space t i m e s space E space o c c u r s over denominator n u m b e r space o f space t r i a l s end fraction