Minds On
Reviewing types of data: discrete and continuous
When we inquire with diverse questions, we receive diverse kinds of data. Each type of data can be graphed in various ways, or even combined on the same graph.
Data can be divided into two main types. Press ‘Continuous’ and ‘Discrete’ to explore definitions.
Student Tips
Continuous or discrete?
Unsure whether the data you’re examining is continuous or discrete? Ask yourself whether something being measured (continuous data) or counted (discrete data).
Brainstorm
Examine the graphs
Examine the following two graphs below. Answer the following questions about each graph:
- What do you notice about how the information is presented?
- Is the data continuous or discrete? How do you know?
Throughout this learning activity, you can record your ideas digitally, orally, or in print.
Action
Representing data
Data is important for understanding the world around us. For example, data helps various levels of government make decisions. It’s important to represent data in a way that will help people understand the story it tells.
Activity 1: Different ways to represent the same data
In the following table and graphs, the same data is represented. Investigate these representations.
Press ‘Population’ for a helpful definition.
Data table
This data table depicts the fishing of selected species in Canada, 2015.
| Total Fish Harvest, Selected Species, Canada, 2015 | |
|---|---|
| Species | Number harvested |
|
Bass |
20,370,825 |
|
Perch |
23,536,400 |
|
Pike |
25,114,724 |
|
Trout |
38,537,379 |
|
Walleye |
50,507,141 |
|
Other |
36,248,834 |
Bar graph
Check out how the data from the data table is used to make the following bar graph:
Circle graph
Explore how the same data is used to make the following circle graph:
Brainstorm
Time to compare!
Compare the data table, the bar graph, and the circle graph.
Complete Comparison: Data Representations in your notebook or use the following fillable and printable document. If you prefer, use another method to record your ideas.
| Compare the data table, bar graph, and circle graph to answer the following questions. |
|---|
|
What is the same in each of these data representations? |
|
Do these graphs represent discrete or continuous data? Hint: Ask yourself whether something is being measured (continuous data) or counted (discrete data). |
|
Which representation would help you answer the following question: Which two species of fish make up nearly half of the total fish harvested in Canada? |
|
How do percentages help us to analyze the distribution of data? |
Press the ‘Activity’ button to access Comparison: Data Representations.
Activity 2: Converting data into percentages
Press ‘Frequency table’ for a helpful definition.
Brainstorm
Examine the frequency table
The frequency table below gives information about the number of Ontarians in various age groups.
- Describe any relationships that you notice in the data.
- How could we adjust the information in the table to further examine the relationships in the data?
| Ontario Census Profile, 2016 | |
|---|---|
| Age group | Number (frequency) |
|
0-14 |
2,207,970 |
|
15-29 |
2,580,410 |
|
30-44 |
2,579,116 |
|
45-59 |
2,983,190 |
|
60-74 |
2,112,535 |
|
75-89 |
872,665 |
|
90+ |
112,609 |
|
Total |
13,448,495 |
Source: Modified from Statistics Canada,
https://www12.statcan.gc.ca/census-recensement/2016/dp-pd/prof/
details/Page.cfm?Lang=E&Geo1=PR&Code1=35&Geo2=&Code2=
&Data=Count&SearchText=Ontario&Sear
Student Tips
Use percentages to compare!
Did you find it difficult to compare the populations in the various age groups?
When you’re examining categories of a large population, it is easier to compare them by using percentages or relative amounts instead of exact quantities.
Press ‘Percent’ to review the definition.
Percent is a ratio expressed using the percent symbol: %. Percent means “out of a hundred.”
- For example, 30% means “30 out of 100.”
A percent can be represented by a fraction with a denominator of 100.
- For example, 30% = 30/100.
Calculating percent
To convert large sets of data to percentages, we need to calculate the total sum of the data.
To find the percent, divide each individual category by the total sum of data and then multiply by 100.
Press the age ranges below to see sample calculations.
Remember that when we write numbers with thousandths using decimals, we use a decimal point and places to the right of the decimal point. The thousandth place is three places to the right of the decimal point.
For 0-14, there are 2,207,970 people.
2,207,970 ÷ 13,448,495 (total number of people) = 0.164
We round to the nearest hundredth to find our percentage.
Therefore, the percent is 16%.
Test Your Skills!
Practise calculating percent
Complete Table: Ontario Census Profile, 2016 in your notebook or use the following fillable and printable document. Using a calculator or virtual tool, carry out the following steps:
- Convert the frequencies to the decimal thousandth.
- Convert the decimal thousandth to the percentage.
|
Age Group |
Number (Frequency) |
Relative Frequency (as decimal thousandths) |
Percentage |
|---|---|---|---|
|
0-14 |
2,207,970 |
0.164 |
16% |
|
15-29 |
2,580,410 |
||
|
30-44 |
2,579,116 |
||
|
45-59 |
2,983,190 |
||
|
60-74 |
2,112,535 |
||
|
75-89 |
872,665 |
||
|
90+ |
112,609 |
0.008 |
1% |
|
Total |
13,448,495 |
1.0 |
100% |
Press the ‘Activity’ button to access Table: Ontario Census Profile, 2016.
Consolidation
Reflect and extend
Explore the following completed version of the Ontario Census Profile table from the Action section. Consider how you would describe any relationships in the data now.
- How can using percentages help people understand the data?
- What could you do with this data to represent it in another way?
- Justify your selection.
|
Ontario Census Profile, 2016 |
|||
|
Age Group |
Number (Frequency) |
Relative Frequency (as decimal thousandths) |
Percentage |
|
0-14 |
2,207,970 |
0.164 |
16.42% |
|
15-29 |
2,580,410 |
0.191 |
19% |
|
30-44 |
2,579,116 |
0.191 |
19% |
|
45-59 |
2,983,190 |
0.221 |
22% |
|
60-74 |
2,112,535 |
0.157 |
16% |
|
75-89 |
872,665 |
0.064 |
6% |
|
90+ |
112,609 |
0.008 |
0.8% |
|
Total |
13,448,495 |
1.0 |
100% |
Source: Modified from Statistics Canada, https://www12.statcan.gc.ca/census-recensement/2016/dp-pd/prof/details/Page.cfm?Lang=E&Geo1=PR&Code1=35&Geo2=&Code2=&Data=Count&SearchText=Ontario&Sear
Reflection
As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.
I feel…
Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.
When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.
Press ‘Discover More’ to extend your skills.
Discover MoreUsing a virtual tool, paper, or concrete materials, identify a set of data that includes larger numbers and organize them in a table.
- Convert the numbers into percentages.
- List three (3) facts or conclusions that you can draw from your data.
- List some ways that percentages help us analyze the distribution of data.
Connect with a TVO Mathify tutor
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