2.9: Frequency Tables to Organize and Display Data

Difficulty Level: At Grade Created by: CK-12
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Practice Frequency Tables to Organize and Display Data

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Have you ever tried to keep track of numbers that seem to be changing? Well, when things happen in different frequencies or occur at different intervals, this can be tricky to record. Tania and Alex have been growing a garden.

As summer passes, the vegetables in Tania and Alex’s vegetable garden have been growing nicely. In fact, they have so many vegetables that they don’t know how they are going to have enough time to work on everything that needs to be done. Because having a garden is more work than they imagined, Tania and Alex have asked some of their friends to help them in the garden. Alex read an article in the newspaper about CSA’s, community supported agriculture. This is when people work on a farm and get some of the vegetables in exchange for their efforts. Tania and Alex have decided to do the same thing. They have offered their friends vegetables in exchange for their work. Now instead of two people working in the garden, they have seven. To be sure that everything gets done, they decide to keep track of how many people they have working in the garden each day. For two weeks, Alex and Tania keep track of how many people are working in the garden on each day. Here are their results.

2, 4, 5, 6, 1, 2, 3, 4, 5, 6, 6, 7, 1, 2

To get everything done in the garden, Tania and Alex know that at least three people need to be working on each day. When they look at the information they can see that this is not always the case. Tania wants to organize the information so that she can share it with the group. To do this, she will need a frequency table.

Use this Concept to learn all about frequency tables and how to create them.

Guidance

What is data?

Data is information, usually numbers, connected with real life situations. If we were going to count how many people came to an amusement park in one day, the number of people that we counted would be the data. What does it mean when we organize data? Organizing data means organizing numbers taken from real world information. For instance, if we use the example above, we would be taking the counts of the number of people who visited the amusement park and writing them in a way that is easy to read.

There are lots of different ways to organize data so that it is easy to read. One way of organizing data is to use a frequency table. A frequency table is a table that shows how often something occurs. First, we count or keep track of information, then we take that information and put it into a table with different columns.

John counted the number of people who were in the shoe store at the same time, in one day. Here are his results:

1, 1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8

We call this data organized data because it is in numerical order and isn’t all mixed up. When we have information or data like this, we can examine or analyze the data for patterns. You can see here that the range of people who were in the store was between 1 and 8. No more than eight people were in the shoe store at the same time on this particular day.

We can put this information into a frequency table. A frequency table is a chart that shows how often something occurs. For this problem, we will look at the frequency of people entering the store. To do this, we want to look at how many times one person was in the store, how many times two people were in the store, how many times three people were in the store, etc. Here is our table. Notice that it has two columns. Column 1 is named “Number of People Who Were In the Store” and Column 2 is named “Frequency”.

Number of people who were in the store Frequency
1 2
2 1
3 1
4 2
5 2
6 2
7 2
8 1

Whenever we want to see how often something occurs, we can do this by building a frequency table.

Now let's practice.

Example A

Here is information about the number of dogs counted in the dog park over five days.

4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8

Solution:

Number of dogs Frequency
4 3
5 6
6 4
7 2
8 2

Example B

Here is the number of children who entered the park throughout the day.

1, 1, 2, 3, 3, 3, 4, 5, 5, 7, 7, 8

Remember to include 6 in your chart even though there weren’t six children who entered the park. You would enter a 0 for the frequency of 6 children.

Solution:

Number of Children Frequency
1 2
2 1
3 1
4 1
5 2
6 0
7 2
8 1

Example C

Here are the number of people who bought ice cream in one hour.

5, 5, 5, 6, 7, 7, 7, 7, 9

Solution:

Number of people Frequency
5 3
6 1
7 4
8 0
9 1

Remember Tania and Alex and the garden? Well, now it is time to help Tania to create a frequency table and a display that shows the data she collected about the number of workers in the garden each day.

Let’s look at the problem once more.

As summer passes, the vegetables in Tania and Alex’s vegetable garden have been growing nicely. In fact, they have so many vegetables that they don’t know how they are going to have enough time to work on everything that needs to be done. Because having a garden is more work than they imagined, Tania and Alex have asked some of their friends to help them in the garden. Alex read an article in the newspaper about CSA’s, community supported agriculture. This is when people work on a farm and get some of the vegetables in exchange for their efforts. Tania and Alex have decided to do the same thing. They have offered their friends vegetables in exchange for their work. Now instead of two people working in the garden, they have seven. To be sure that everything gets done, they decide to keep track of how many people they have working in the garden each day. For two weeks, Alex and Tania keep track of how many people are working in the garden on each day. Here are their results.

2, 4, 5, 6, 1, 2, 3, 4, 5, 6, 6, 7, 1, 2

To get everything done in the garden, Tania and Alex know that at least three people need to be working on each day. When they look at the information they can see that this is not always the case. Tania wants to organize the information so that she can share it with the group. First, we go through and underline all of the important information. This has already been done for you. Next, you can see that we have unorganized data. Let’s organize the data that Tania and Alex collected so that it is easier to work with.

2, 4, 5, 6, 1, 2, 3, 4, 5, 6, 6, 7, 1, 2

1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 6, 6, 7

Here is the data reorganized numerically. We can see that the range of numbers is from 1 to 7. Next, we need to create a frequency table that shows this data.

# of People Working Frequency
1 2
2 3
3 1
4 2
5 1
6 3
7 1

Vocabulary

Here are the vocabulary words in this Concept.

Frequency
how often something occurs
Data
information about something or someone-usually in number form
Analyze
to look at data and draw conclusions based on patterns or numbers
Frequency table
a table or chart that shows how often something occurs

Guided Practice

Here is a list of the number of students who did not complete their homework in one month.

1, 1, 3, 3, 4, 3, 3, 5, 6, 1, 1, 1, 2, 2, 3

Create a frequency table of the data.

Number of Students Frequency
1 5
2 2
3 5
4 1
5 1
6 1

Video Review

http://www.hstutorials.net/math/preAlg/php/php_12/php_12_01_x13.htm – Solving a problem using frequency tables and line plots.

Practice

Directions: The following frequency table shows data regarding the number of people who attended different movies in one week. Use the following frequency table to answer each question.

# of People at the movies per week Frequency
20 4
50 3
85 3
90 5
120 2

1. If we were to create a list of this data, is the following list correct or incorrect?

20, 20, 20, 20, 50, 50, 50, 90, 90, 90, 85, 85, 85, 120, 120

2. Why?

3. Would you consider the list in number 1 to be organized or unorganized data?

4. Explain the difference.

5. How many showings had 90 people or more in attendance?

6. How many showings had less than 50 people in attendance?

7. How many showings had less than 70 people in attendance?

8. True or false. This data also tells you which showings had the most people in attendance.

9. True or false. There were two showings that had 78 people in attendance.

10. True or false. There were three showings that were the most popular.

11. True or false. There was one showing that was the most popular.

12. Does a frequency table show you how data changes over time?

13. Does a frequency table show you how often something happens?

14. Does a frequency table show you how many people don't attend an event?

15. Can you reorganize the data list from number 1 so that it is organized?

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Color Highlighted Text Notes

Vocabulary Language: English

TermDefinition
Analyze To analyze is to look at data and draw conclusions based on patterns or numbers.
bar chart A bar chart is a graphic display of categorical variables that uses bars to represent the frequency of the count in each category.
conditional probability The probability of a particular dependent event  given the outcome of the event on which it occurs.
Data Data is information that has been collected to represent real life situations, usually in number form.
Dependent Events In probability situations, dependent events are events where one outcome impacts the probability of the other.
Frequency In statistics, the frequency of an event is the number of times that event occurred.
Frequency table A frequency table is a table that summarizes a data set by stating the number of times each value occurs within the data set.
Independent Events Two events are independent if the occurrence of one event does not impact the probability of the other event.
two way tables Contingency tables are sometimes called two-way tables because they are organized with the outputs of one variable across the top, and another down the side.

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