Unit 8, Lesson 1

Representing Data

Accelerated 6

1.1

Warm-up

Here is a dot plot for a data set.

A dot plot, labeled 0 to 4 by ones with tick marks every quarter. Beginning with 0 and counting by point 2 5, the number of dots above each increment is 1, 1, 2, 3, 2, 0, 4, 3, 1, 2, 2.

Determine if each of these would be an appropriate label to represent the data in the dot plot? Be prepared to explain your reasoning.
1. Number of children per class.
2. Distance between home and school, in miles.
3. Favorite subject in school.
4. Weight of elephants, in pounds.
5. Points received on a homework assignment.
Think of another label that can be used with the dot plot.
1. Write it below the scale of the dot plot. Be sure to include the unit of measurement.
2. In your scenario, what does one dot represent?
3. In your scenario, what would a data point of 0 mean? What would a data point of mean?

1.2

Activity

Ten sixth-grade students at a school were each asked five survey questions. Their answers to each question are shown here.

Data Set A

Data Set B

Data Set C

Data Set D

Data Set E

Here are the five survey questions. Match each question to a data set that could represent the students’ answers. Explain your reasoning.
- Question 1: Flip a coin 10 times. How many heads did you get?
- Question 2: How many books did you read in the last year?
- Question 3: What grade are you in?
- Question 4: How many dogs and cats do you have?
- Question 5: How many inches are in 1 foot?
How are survey Questions 3 and 5 different from the other questions?

1.3

Activity

Priya wants to know if basketball players on 2 teams have had prior experience in international competitions. She gathers data on the number of times the players were on a team before 2016.

Team 1

Team 2

Did Priya collect categorical or numerical data?
Organize the information on the two basketball teams into these tables.

Team 1

number of prior
competitions frequency
(number)

0

1

2

3

4

Team 2

number of prior
competitions frequency
(number)

0

1

2

3

4
Make a dot plot for each table.

Team 1

Team 2
Study your dot plots. What do they tell you about the competition participation of:
1. The players on team 1?
2. The players on team 2?
Explain why a dot plot is an appropriate representation for Priya’s data.

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

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

Student Lesson Summary

We often collect data to answer questions about something. The data we collect may show variability, which means the data values are not all the same.

Some data sets have more variability than others. Here are two sets of figures.

Figure A is a box containing 5 large circles, 1 medium circle, 3 small circles, 2 large squares, 1 medium square, 1 small square. — A

Figure B is a box containing 3 different sized triangles, 3 different sized rectangles, 4 different sized circles, and 3 different sized squares. — B

Set A has more figures with the same shape, color, or size. Set B shows more figures with different shapes, colors, or sizes, so Set B has greater variability than Set A.

When a question can be answered only by using data, and we expect that data to have variability, we call it a statistical question. Here are some examples.

Who is the most popular musical artist at your school?
When do students in your class typically eat dinner?
Which classroom in your school has the most books?
How much do the dogs at a pet adoption center weigh?

The table contains data about 10 dogs.

The weights of the dogs are an example of numerical data, which are data that are numbers, quantities, or measurements. The weights of the dogs are measurements in kilograms.
The dog breeds are an example of categorical data, which are data containing values that can be sorted into categories. In this case, there are three categories for dog breeds: pug, beagle, and German shepherd.

dog name	weight (kg)	breed
Duke	36	German shepherd
Coco	6	pug
Pierre	7	pug
Ginger	35	German shepherd
Lucky	10	beagle
Daisy	10	beagle
Buster	35	German shepherd
Pepper	7	pug
Rocky	7	beagle
Lady	32	German shepherd

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. 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 3 dogs that weigh 7 kilograms, so 3 is the frequency for the value “7 kilograms.”

Like a frequency table, a dot plot also shows the distribution of a data set. This dot plot shows the distribution of dog weights.

A dot plot for "dog weights in kilograms".

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 that weigh 35 kilograms.

A set of categorical data has values that are words instead of numbers.

For example, Han asks 5 friends to each name their favorite color. Their answers are “blue,” “blue,” “green,” “blue,” and “orange.”

The distribution of a data set tells how many times each value occurs.

In the data set blue, blue, green, blue, orange, the distribution is 3 blues, 1 green, and 1 orange.
This dot plot shows the distribution for the data set 6, 10, 7, 35, 7, 36, 32, 10, 7, 35 kilograms.

A dot plot is a way to represent data with dots. Each dot above a number shows one time the value occurs in the set.

<p>a dot plot representing plant heights</p>

The frequency of a data value is how many times it occurs in the data set.

For example, there are 20 dogs in a park. The table shows the frequency of each color.

dog color	frequency
white	4
brown	7
black	3
multi-color	6

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Representing Data

Warm-up

Activity

Activity

Student Lesson Summary