Summarizing Categorical Data using Tables

Summarizing Categorical Data using Tables

Watch this video lesson to find out why data tables are an excellent way to summarize your categorical data. Learn what you need to do to your data before constructing a table and the two ways you can show your data.

Categorical Data

Categorical data is data that can be categorized or grouped. You see examples of categorical data all the time whenever you fill out applications for anything. When it asks you for your gender and occupation, it is asking for categorical data.

Once you answer those questions, whoever reads the application can place you into a group based on your gender or occupation. You can be grouped into the student group, or the groups can incorporate both sets of data, and you can be grouped into the female student group if you're a girl or the male student group if you're a boy.

While the answers to a piece of categorical data may not be numerical in nature, once a survey is done, the various groups can be counted to see how many are in each group. It is this information that we will focus on.

Prepping Your Data

Let's see how we go about summarizing our categorical data with a little scenario. Imagine that we have just surveyed a random group of people about their favorite junk food. Each person we survey chooses his or her favorite junk food from a list of five choices. Our choices are: potato chips, pizza, hamburgers, hot dogs, and fries. After our survey is done, we have a stack of papers of everyone's choices.

To prep our data so we can summarize it, we now need to count how many are in each group. We go through our stack of responses, and we separate them into various groups based on their answers. We then count the number of papers in each group. We found that 15 people chose potato chips, 23 people chose pizza, 18 people chose hamburgers, 8 people chose hot dogs, and 10 people chose fries.

We can take our group counts and input them directly into a table. Our table will have two columns: one for the type of junk food and the other for the result. Our top row will be our title row with 'Junk Food' and 'Result' as our titles for each respective column.

Junk Food Result

Potato chips 15

Pizza 23

Hamburgers 18

Hot dogs 8

Fries 10

We can reorder our data table so that the most popular is listed first and the least popular is listed last.

Junk Food Result

Pizza 23

Hamburgers 18

Potato chips 15

Fries 10

Hot dogs 8

This is one way we can use a data table to summarize our information. We can clearly see which junk food is the most popular out of our survey group and which is the least favorite. This does give us good information, but if we wanted to generalize our information to the general public, we would need to report our results in percentage form.

In order to change our data to percentages, we need to know the total number of people we surveyed. We can find out our total by adding up the number of responses: 23 + 18 + 15 + 10 + 8 = 74. To find out the percentage of each group, we take the number of each group and divide by our total.

We then convert this decimal to a percentage by multiplying by 100. So, for pizza, our percentage is 23 / 74 * 100 = 31%. For hamburgers, it is 24%. Potato chips has 20%, fries has 14%, and hot dogs has 11%.

We'll leave our data table the same, but just switch out our numbers for the percentages. To check that we've converted properly, the total percentage must equal 100%. Let's check: 31% + 24% + 20% + 14% + 11% = 100%. Our percentages are correct.

If our total is one percent off, we'll need to go back and check which one we can round up by 1%. Choose the one that is closest to being rounded up. For example, if two of our choices were 31.3% and 31.4%, we would choose to round the 31.4% to 32% to account for the 1% difference.

Junk Food Result

Pizza 31%

Hamburgers 24%

Potato chips 20%

Fries 14%

Hot dogs 11%

These percentages allow us to generalize our information. We can say that 31% of people will choose pizza over the other four choices, and we can say that only 11% of the people find hot dogs to be a favorite.

Lesson Summary

We've learned that categorical data is data that can be grouped. We can summarize our information using a data table in two ways. We can use the counts from each group, or we can convert our count into percentages. While we don't necessarily have to order from greatest to least, we can do so to make our data table more readable.

Learning Outcomes

After finishing this lesson, you should have the ability to:

• Prepare categorical data
• Create a data table
• Change data into percents
• Explain two ways to summarize categorical data