# 2.9: Frequency Tables to Organize and Display Data

**At Grade**Created by: CK-12

**Practice**Frequency Tables to Organize and Display Data

Mrs. Jones wants to keep track of how many candy bars her students bring in to eat for Halloween treats. She decides to jot down a list of data of the number of candy bars each student brings in. The problem is, the list is unorganized and she cannot make any conclusions based on her data to see which students brought in a lot of candy versus students who only brought a few pieces.

Here is Mrs. Jones's data:

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

Mrs. Jones needs to organize the data and display it somehow so it is easy to analyze.

In this concept, you will learn how to organize data for creating a frequency table.

### Frequency Tables

**Data** is information, usually numbers, connected with real life situations. If you were going to count how many people came to an amusement park in one day, the number of people counted would be the data. Organizing data means organizing numbers taken from real world information. For instance, using the example above, you would take the counts of the number of people who visited the amusement park and would write them in a way that is easy to read.

There are many 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, you count or keep track of information, then you 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

This data is called **organized data** because it is in numerical order and isn’t all mixed up. Organized data allows you to 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.

This information can be put into a frequency table. This problem will look at the frequency of people entering the store. It will display 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 the completed table. Notice that it has two columns. Column 1 is titled “Number of People Who Were In the Store” and Column 2 is titled “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 |

### Examples

#### Example 1

Earlier, you were given a problem about Mrs. Jones and her class.

She wants to display the data she has collected on the frequency of students who brought in a certain number of candy bars for Halloween treats. Here is her data:

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

First, Mrs. Jones organizes the data.

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

Next, Mrs. Jones creates a frequency table and fills in her data.

Number of Candy Bars | Frequency |
---|---|

1 |
2 |

2 |
3 |

3 |
1 |

4 |
2 |

5 |
1 |

6 |
3 |

7 |
1 |

Then, Mrs. Jones double checks her work to make sure her data list and frequency table match up.

Now Mrs. Jones can analyze her data. For example, there were 2 students who brought in 1 candy bar for a treat whereas there were 3 students who brought in 6 candy bars!

#### Example 2

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

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

First, organize the data by putting the data in numerical order.

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

Next create a frequency table and input the data.

Number of students who did not complete homework |
Frequency |
---|---|

1 | 5 |

2 | 2 |

3 | 5 |

4 | 1 |

5 | 1 |

6 | 1 |

Then, check your work by making sure the frequency of each data matches the list of data you started with. This frequency table shows the following conclusions when you analyze the data:

5 different times throughout the month there was 1 student with incomplete homework.

2 different times throughout the month there were 2 students with incomplete homework.

5 different times throughout the month there were 3 students with incomplete homework.

1 time throughout the month there were 4 students with incomplete homework.

1 time throughout the month there were 5 students with missing homework.

1 time throughout the month there were 6 students with missing homework.

#### Example 3

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

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

First, organize the data.

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

Next, create the frequency table and fill in the data.

Number of dogs |
Frequency |
---|---|

4 | 3 |

5 | 6 |

6 | 4 |

7 | 2 |

8 | 2 |

Then, check that your data list and your frequency match up. There are 17 pieces of data in both the list and in the frequency column of the table. The data matches.

#### Example 4

Here is a list of the number of children who came to the park together throughout the day.

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

First, organize the data.

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 at one time. You would enter a 0 for the frequency of 6 children.

Next, create the frequency table and fill in the data.

Number of children |
Frequency |
---|---|

1 (came alone) | 2 |

2 | 1 |

3 | 1 |

4 | 1 |

5 | 2 |

6 | 0 |

7 | 2 |

8 | 1 |

Then, check your work to make sure your data list matches the frequency table data. There are 12 pieces of data in the list as well as in the table. The answer checks out.

#### Example 5

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

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

First, organize the data.

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

Next, create the frequency table and fill in the data.

Number of people |
Frequency |
---|---|

5 | 3 |

6 | 1 |

7 | 4 |

8 | 0 |

9 | 1 |

Then, make sure the data list matches the data in the table. The data checks out.

### Review

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 |

- 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

- Why?
- Would you consider the list in number 1 to be organized or unorganized data?
- Explain the difference.
- How many showings had 90 people or more in attendance?
- How many showings had less than 50 people in attendance?
- How many showings had less than 70 people in attendance?
- True or false. This data also tells you which showings had the most people in attendance.
- True or false. There were two showings that had 78 people in attendance.
- True or false. There were three showings that were the most popular.
- True or false. There was one showing that was the most popular.
- Does a frequency table show you how data changes over time?
- Does a frequency table show you how often something happens?
- Does a frequency table show you how many people don't attend an event?
- Can you reorganize the data list from number 1 so that it is organized?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 2.9.

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.### Image Attributions

In this concept, you will learn how to organize data for creating a frequency table.

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