Lesson 3Representing Data Graphically

Learning Goal

Let’s represent data with dot plots and bar graphs.

Learning Targets

I can describe the information presented in tables, dot plots, and bar graphs.
I can use tables, dot plots, and bar graphs to represent distributions of data.

Lesson Terms

distribution
frequency

Warm Up: Curious About Caps

Clare collects bottle caps and keeps them in plastic containers.

A photo of two clear, plastic containers containing plastic bottle caps of various sizes and colors. The colors of the plastic bottle caps are red, orange, yellow, green, blue, and white.

Write one statistical question that someone could ask Clare about her collection. Be prepared to explain your reasoning.

Activity 1: Estimating Caps

Write down the statistical question your class is trying to answer.
Look at the dot plot that shows the data from your class. Write down one thing you notice and one thing you wonder about the dot plot.
Use the dot plot to answer the statistical question. Be prepared to explain your reasoning.

Activity 2: Been There, Done That!

Priya wants to know if basketball players on a men’s team and a women’s team have had prior experience in international competitions. She gathered data on the number of times the players were on a team before 2016.

men’s team

women’s team

Problem 1

Did Priya collect categorical or numerical data?

Problem 2

Organize the information on the two basketball teams into these tables.

Men’s Basketball Team Players

number of prior competitions	frequency (number)
$0$
$1$
$2$
$3$
$4$

Women’s Basketball Team Players

number of prior competitions	frequency (number)
$0$
$1$
$2$
$3$
$4$

Problem 3

Make a dot plot for each table.

Men’s Basketball Team Players

A number line from 0 to 4 labeled "number of prior competitions"

Women’s Basketball Team Players

Problem 4

Study your dot plots. What do they tell you about the competition participation of:

the players on the men’s basketball team?
the players on the women’s basketball team?

Problem 5

Explain why a dot plot is an appropriate representation for Priya’s data.

Activity 3: Favorite Summer Sports

Kiran wants to know which three summer sports are most popular in his class. He surveyed his classmates on their favorite summer sport. Here are their responses.

swimming
gymnastics
track and field
volleyball
swimming
swimming
diving
track and field
gymnastics
basketball

basketball
volleyball
track and field
track and field
volleyball
gymnastics
diving
gymnastics
volleyball
rowing

track and field
track and field
soccer
swimming
gymnastics
track and field
swimming
rowing
diving
soccer

Problem 1

Did Kiran collect categorical or numerical data?

Problem 2

Organize the responses in a table to help him find which summer sports are most popular in his class.

sport	frequency

Problem 3

Represent the information in the table as a bar graph.

A blank coordinate grid. The vertical axis has the numbers 0 through 10 indicated. The horizontal axis has 21 grid lines with no labels.

Problem 4

How can you use the bar graph to find how many classmates Kiran surveyed?
Which three summer sports are most popular in Kiran’s class?
Use your bar graph to describe at least one observation about Kiran’s classmates’ preferred summer sports.

Problem 5

Could a dot plot be used to represent Kiran’s data? Explain your reasoning.

Are you ready for more?

Pie charts are another way to represent data used to show the relationship of parts to a whole by comparing the section sizes of a circle visually. A pie chart is divided into sections according to the percentage of frequencies in each category of the distribution.

A local veterinarian counted the number of pets that were treated each day for a month. The following table represents the frequency of each type of pet for the month.

Type of Pet	Frequency
Dogs	600
Cats	120
Other types of Pets (Snakes, Rabbits, Birds, etc.)	30

Problem 1

Did the veterinarian collect categorical or numerical data?

Problem 2

Organize the responses in a pie chart using the following directions.

There are 360 degrees in a circle. The frequency of each type of pet should be converted to a proportional part of a circle. Use the formula
$Degrees = \frac{frequency (f)}{Sum of frequencies (n)} \cdot 360 °$
to find the number of degrees each type of pet represents on the pie chart.
Use a circular object to create a circle (paper plate, pie plate, jar lid, etc.) or a compass. Then, use a protractor to create sections based on the degrees found in part a.
Determine the percentage associated with each section by using the following formula and label each section with the percentage and type of pet.
$Percentage = \frac{frequency (f)}{Sum of frequencies (n)} \cdot 100$

Problem 3

Explain how the pie chart differs from the bar graph used in the previous activity.

Lesson Summary

When we analyze data, we are often interested in the distribution, which is information that shows all the data values and how often they occur.

In a previous lesson, we saw data about 10 dogs. We can see the distribution of the dog weights in a table such as this one.

weight in kilograms	frequency
$6$	$1$
$7$	$3$
$10$	$2$
$32$	$1$
$35$	$2$
$36$	$1$

The term frequency refers to the number of times a data value occurs. In this case, we see that there are three dogs that weigh 7 kilograms, so “3” is the frequency for the value “7 kilograms.”

Recall that dot plots are often used to to represent numerical data. Like a frequency table, a dot plot also shows the distribution of a data set. This dot plot, which you saw in an earlier lesson, shows the distribution of dog weights.

A dot plot for "dog weights in kilograms". The numbers 5 through 40, in increments of 5, are indicated. The data are as follows: 6 kilograms, 1 dot. 7 kilograms, 3 dots. 10 kilograms, 2 dots. 32 kilograms, 1 dot. 35 kilograms, 2 dots. 36 kilograms, 1 dot.

A dot plot uses a horizontal number line. We show the frequency of a value by the number of dots drawn above that value. Here, the two dots above the number 35 tell us that there are two dogs weighing 35 kilograms.

The distribution of categorical data can also be shown in a table. This table shows the distribution of dog breeds.

breed	frequency
pug	$9$
beagle	$9$
German shepherd	$12$

We often represent the distribution of categorical data using a bar graph.

A bar graph. The categories “pugs”, “beagles”, and “German shepherds” are labeled on the horizontal axis. The numbers 0 through 4 are indicated on the vertical axis. The data represented by the bars are as follows: pugs, 3. beagles, 3. German shepherds, 4.

A bar graph also uses a horizontal line. Above it we draw a rectangle (or “bar”) to represent each category in the data set. The height of a bar tells us the frequency of the category. There are 12 German shepherds in the data set, so the bar for this category is 12 units tall. Below the line we write the labels for the categories.

In a dot plot, a data value is placed according to its position on the number line. A weight of 10 kilograms must be shown as a dot above 10 on the number line.

In a bar graph, however, the categories can be listed in any order. The bar that shows the frequency of pugs can be placed anywhere along the horizontal line.