The frequency of something is how many times something happened. A frequency table is used to show the number of times that different things occurred.
For example, imagine we wanted to record the different number of soccer goals scored by the members of a soccer team over the course of a season. We can organize the information in the table below.
This table might seem a little confusing at first, but let's take a closer look.
The column on the left shows the different number of soccer goals scored. Imagine you went around to each person on the soccer team and asked them how many goals they scored, and put a tally mark next to their answer. For example, if someone scored 3 goals, you would put a tally mark in the row next to the "3" in the "Number of Soccer Goals Scored" column.
The frequency is the number of tally marks for each number of goals scored.
From this frequency table, we can see that 3 people scored 0 goals, 4 people scored 1 goal, 8 people scored 2 goals, and so on.
Now imagine you asked everyone in your class to write the number of pets they have down on a piece of paper. Once you receive the results, you lay the pieces of paper out on your desk, as shown below.
We can make a frequency table to organize your results. Imagine you sorted the cards on your desk so all the same numbers were together, as shown below.
On our frequency table, we can make a column labeled "Number of Pets," as the numbers on the cards represent the number of pets. We can tally how many of each card there are. The number of each card is the frequency.
The tally column is not essential to a frequency table, but it can be helpful to understand that the frequency is the same as the number of tallies.
By creating a frequency table, we can easily see the number of times that different results occurred. The frequency table above shows us that the most common number of pets is 2, since 7 people have 2 pets. The least common number of pets is 4, as only 1 person has 4 pets.
Now that we have seen a few examples of frequency tables, let's discuss the topic of probability.
Probability is a measure of how likely something is to occur. For example, we can say that the probability of rolling a 1 on a 6-sided dice is one in six or .
We can generalize, that probability is found by dividing the chances of a desired outcome by the chances of all other outcomes.
With the example involving dice, there are 6 possible outcomes. You can either roll a 1, 2, 3, 4, 5 or 6. Since we were interested in the chances of rolling a 1, we know that the probability will be one in six.
Recall the frequency table from earlier involving the number of pets the students of a class have.
If we were to select a student at random, what is the probability that the student has 0 pets at home?
To solve this problem, we need to find the number of students who have 0 pets and divide that amount by the total number of students that were surveyed.
Since 4 students have zero pets and a total of 18 students were surveyed, we can say that the probability of randomly choosing a student with zero pets is 4 in 18 or .
This fraction can be simplified by dividing the numerator and denominator each by 2.
This means that the probability of randomly selecting a student with zero pets is .
What about the probability of randomly selecting a student with 4 pets?
Since there is only 1 student who has 4 pets, and a total of 18 students were surveyed, the chances of selecting the student with 4 pets is .