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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.Color | Frequency |
---|---|
Yellow | 2 |
Blue | 2 |
Red | 2 |
Purple | 2 |
Orange | 2 |
Green | 2 |
Maroon | 2 |
Black | 1 |
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.Score | Frequency |
---|---|
1 | 1 |
2 | 0 |
3 | 2 |
4 | 4 |
5 | 1 |
6 | 2 |
7 | 2 |
8 | 4 |
9 | 3 |
10 | 1 |
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.
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.
Source: THIS TUTORIAL WAS AUTHORED BY JONATHAN OSTERS FOR SOPHIA LEARNING. PLEASE SEE OUR TERMS OF USE.