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Frequency Tables

Author: Sophia

what's covered
This tutorial will introduce you to the basic principles of frequency tables. Our discussion breaks down as follows:

Table of Contents

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.

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

EXAMPLE

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

File:4154-billiards.png

Now, I could take the values that each variable color represents and put them in a table.

Color Frequency
Yellow 2
Blue 2
Red 2
Purple 2
Orange 2
Green 2
Maroon 2
Black 1

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

What about when we use quantitative data?

EXAMPLE

Suppose an ice cream taste tester was asked to rate his satisfaction of 20 different ice creams on a 1-10 scale. His satisfaction scores are listed below.

6, 6, 4, 8, 9, 7, 8, 5, 8, 9, 3, 4, 4, 3, 4, 1, 9, 8, 7, 10

Try to construct a frequency table for these scores. Hopefully, you came up with something that looks like this:

Score Frequency
1 1
2 0
3 2
4 4
5 1
6 2
7 2
8 4
9 3
10 1

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. The frequency represents how often a particular score was received.

Now, in some cases, you may not want to look at the raw data, but instead, look directly at the frequency table. This is useful if the data set is very large.

EXAMPLE

Consider the following frequency table that has the heights of 333 sixth-grade students.

Height Frequency
55 11
56 21
57 33
58 37
59 55
60 51
61 44
62 32
63 30
64 12
65 7

These heights are rounded to the nearest inch. This means 11 students are 55 inches tall (height of 4' 7"), 21 students who are 56 inches tall, and so forth.

terms to know
Frequency Table
A table showing the values of the data, and their respective frequencies.
Frequency
How often a data value, or range of values, occurs.

2. Relative Frequency

Often it's preferable to not just look at frequency, but rather 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.

We can use relative frequency, or percents, to get a better picture of the portion that 11 students are of the whole population.

Height Frequency Relative Freq
55 11 11/333 = 3%
56 21 21/333 = 6%
57 33 33/333 = 10%
58 37 37/333 = 11%
59 55 55/333 = 17%
60 51 51/333 = 15%
61 44 44/333 = 13%
62 32 32/333 = 10%
63 30 30/333 = 9%
64 12 12/333 = 4%
65 7 7/333 = 2%

As we can see, the 11 students who have a height of 55 inches make up about 3% of the population. We can fill out the entire table to find the relative frequencies as opposed to "regular" frequencies.

term to know
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.

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

Good luck!

Source: THIS TUTORIAL WAS AUTHORED BY JONATHAN OSTERS FOR SOPHIA LEARNING. PLEASE SEE OUR TERMS OF USE.

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.