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# Frequency Tables

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Author: Sophia Tutorial
##### Description:

This lesson will explain frequency tables.

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Tutorial

This tutorial will introduce you to the basic principles of frequency tables. You will learn about:

1. Frequency and Frequency Tables
2. Relative Frequency

## 1. Frequency and Frequency Tables

Frequency tables are tables that show how often data occurs. Frequency is the number of times that particular value occurs in a data set.

Frequency

How often a data value, or range of values, occurs.

Frequency Table

A table showing the values of the data, and their respective frequencies.

Let's look at several examples to show how easy it is to summarize frequencies in a table.

Suppose I have the 15 billiard balls from a pool table. One of the variables about these billiard balls that I might be interested in is their color. The one ball is yellow, the two ball is blue, the six ball is green, the nine ball is also yellow.

I could take the values that the variable color takes and put them in a table.

Frequency is how often these values occur. Two of the balls are yellow, two are blue, two are orange, two are green, et cetera. The only one that only has one is black, the eight ball.

What about when we use quantitative data? Suppose an ice cream taste tester was asked to rate his satisfaction of 20 different ice creams.

Try to construct a frequency table for these scores.

What you should have come up with is this.

One ice cream received a score of one. None of them received a score of two. Two of them received a score of three, and so on. This is how often this score was received.

Often we don't want to look at the raw data, we'd rather just look directly at the frequency table. This is useful if the data set is very large, like one that has the heights of 333 sixth-grade students.

These heights are rounded to the nearest inch. This means there are 55 59-inch, 4' 11", students. There are 51 5-foot students, 60 inches.

## 2. Relative Frequency

Oftentimes it's preferable not necessarily to just look at frequency, but to ask what percent of the students a particular value represents. We can create a value called relative frequency, created by dividing each value by the total.

Relative Frequency

The percent of the data points that take a particular value. This is obtained by dividing the frequency of each value by the total number of data points.

We can use relative frequency, or percents, to get a better picture of the portion that  11 students are of the whole population.  It's about 3%.

We can fill out the entire table as relative frequencies as opposed to just regular frequencies.

Data sets can be shown in frequency tables whether they're qualitative or quantitative. Frequency tables are particularly useful with large data sets, where you don't want to see all of the raw data and would rather to see it categorized. You can also use relative frequency to see what percent of the sample goes in each bucket of our frequency table. Frequency is the raw count, relative frequency is the percent, and both of those values can go into a frequency table.

Thank you and good luck.

Source: THIS WORK IS ADAPTED FROM SOPHIA AUTHOR JONATHAN OSTERS

Terms to Know
Frequency

How often a data value, or range of values, occurs.

Frequency Table

A table showing the values of the data, and their respective frequencies.

Relative Frequency

The percent of the data points that take a particular value. This is obtained by dividing the frequency of each value by the total number of data points.