Unit 8, Lesson 3
Representing Data Graphically
Grade 6
3.1
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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
3
0
0
0
0
1
0
0
0
0
0
0
Team 2
2
3
3
1
0
2
0
1
1
0
3
1
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:
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
Organize the responses in a table to help him find which summer sports are most popular in his class
| sport | frequency |
|---|---|
Represent the information in the table as a bar graph.
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 3 dogs that weigh 7 kilograms, so 3 is the frequency for the value “7 kilograms.”
Recall that dot plots are often used to represent numerical data. 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". 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 that weigh 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 12 are indicated on the vertical axis. The data represented by the bars are as follows: pugs, 9. beagles, 9. German shepherds, 12.
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 rearranged along the horizontal line.
The distribution of a data set tells how many times each value occurs.
This dot plot shows the distribution for the data set 6, 10, 7, 35, 7, 36, 32, 10, 7, 35 kilograms.
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 |