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# Line Plots from Frequency Tables

## Represent data according to number of instances.

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Line Plots from Frequency Tables

Remember Tania and Alex and the garden in the Frequency Tables to Organize and Display Data Concept? Tania had her hands full trying to figure out how many workers were in the garden on which days. Tania has a frequency table, but how can she make a visual display of the data?

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

Using this frequency table, how can Tania make a line plot?

### Guidance

A line plot is another display method we can use to organize data.

Like a frequency table, it shows how many times each number appears in the data set. Instead of putting the information into a table, however, we graph it on a number line. Line plots are especially useful when the data falls over a large range. Take a look at the data and the line plot below.

This data represents the number of students in each class at a local community college.

30, 31, 31, 31, 33, 33, 33, 33, 37, 37, 38, 40, 40, 41, 41, 41

The first thing that we might do is to organize this data into a frequency table. That will let us know how often each number appears.

# of students Frequency
30 1
31 3
32 0
33 4
34 0
35 0
36 0
37 2
38 1
39 0
40 2
41 3

Now if we look at this data, we can make a couple of conclusions.

1. The range of students in each class is from 30 to 41.
2. There aren’t any classes with 32, 34, 35, 36 or 39 students in them.

Now that we have a frequency table, we can build a line plot to show this same data.

Building the line plot involves counting the number of students and then plotting the information on a number line. We use X\begin{align*}X\end{align*}’s to represent the number of classes that has each number of students in it. Let’s look at the line plot.

Notice that even if we didn’t have a class with 32 students in it that we had to include that number on the number line. This is very important. Each value in the range of numbers needs to be represented, even if that value is 0.

Now let's use this information to answer a few questions.

#### Example A

How many classes have 31 students in them?

Solution: 3

#### Example B

How many classes have 38 students in them?

Solution: 1

#### Example C

How many classes have 33 students in them?

Solution: 4

Now Tania can take the frequency table and make a line plot for the farm.

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

Now, let’s draw a line plot to show the data in another way.

Now that we have the visual representations of the data, it is time to draw some conclusions.

Remember that Tania and Alex know that there needs to be at least three people working on any given day. By analyzing the data, you can see that there are five days when there are only one or two people working. With the new data, Tania and Alex call a meeting of all of the workers. When they display the data, it is clear why everything isn’t getting done. Together, they are able to figure out which days need more people, and they solve the problem.

### Vocabulary

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
Line plot
Data that shows frequency by graphing data over a number line
Organized data
Data that is listed in numerical order

### Guided Practice

Here is one for you to try on your own.

Jeff counted the number of ducks he saw swimming in the pond each morning on his way to school. Here are his results:

6, 8, 12, 14, 5, 6, 7, 8, 12, 11, 12, 5, 6, 6, 8, 11, 8, 7, 6, 13

Jeff’s data is unorganized. It is not written in numerical order. When we have unorganized data, the first thing that we need to do is to organize it in numerical order.

6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 11, 11, 12, 12, 12, 13, 14

Next, we can make a frequency table. There are two columns in the frequency table. The first is the number of ducks and the second is how many times each number of ducks was on the pond. The second column is the frequency of each number of ducks.

Number of Ducks Frequency
6 5
7 2
8 4
9 0
10 0
11 2
12 3
13 1
14 1

Now that we have a frequency table, the next step is to make a line plot. Then we will have two ways of examining the same data. Here is a line plot that shows the duck information.

Here are some things that we can observe by looking at both methods of displaying data:

• In both, the range of numbers is shown. There were between 6 and 14 ducks seen, so each number from 6 to 14 is represented.
• There weren’t any days where 9 or 10 ducks were counted, yet both are represented because they fall in the range of ducks counted.
• Both methods help us to visually understand data and its meaning.

### 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: Here is a line plot that shows how many seals came into the harbor in La Jolla California during an entire month. Use it to answer the following questions.

1. How many times did thirty seals appear on the beach?

2. Which two categories have the same frequency?

3. How many times were 50 or more seals counted on the beach?

4. True or False. This line plot shows us the number of seals that came on each day of the month.

5. True or False. There weren’t any days that less than 30 seals appeared on the beach.

6. How many times were 60 seals on the beach?

7. How many times were 70 seals on the beach?

8. What is the smallest number of seals that was counted on the beach?

9. What is the greatest number of seals that were counted on the beach?

10. Does the frequency table show any number of seals that weren't counted at all?

Directions: Organize each list of data. Then create a frequency table to show the results. There are two answers for each question.

11. 8, 8, 2, 2, 2, 2, 2, 5, 6, 3, 3, 4

12. 20, 18, 18, 19, 19, 19, 17, 17, 17, 17, 17

13. 100, 99, 98, 92, 92, 92, 92, 92, 92, 98, 98

14. 75, 75, 75, 70, 70, 70, 70, 71, 72, 72, 72, 74, 74, 74

15. 1, 1, 1, 1, 2, 2, 2, 3, 3, 5, 5, 5, 5, 5, 5, 5

### Vocabulary Language: English

Analyze

Analyze

To analyze is to look at data and draw conclusions based on patterns or numbers.
Data

Data

Data is information that has been collected to represent real life situations, usually in number form.
Frequency

Frequency

In statistics, the frequency of an event is the number of times that event occurred.
Frequency table

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.
Line plot

Line plot

A line plot is a graph that shows the frequency of data over a number line.
Organized data

Organized data

Organized data is data that is listed in numerical order.