Quantitative data

Here you will learn about quantitative data, including what it is and how to use it in the statistical process.

Students first learn to work with quantitative data in the statistical process in 6 th grade.

What is quantitative data?

Quantitative data is numerical information that is countable or measurable.

There are two types of quantitative data: discrete and continuous.

• Discrete data – data that is represented by a specific set of numbers (typically whole numbers).
  For example,
  – Number of followers on social media
  – Number of people in a store
  – Number of survey questions on a customer satisfaction survey

• Continuous data – data that has infinitely possible values.
  For example,
  – Height or weight of people (which can be measured in meters, centimeters, millimeters, and so on…)
  – Daily temperature in a city (which can be measured in degrees to the nearest whole, tenth, hundredth, thousandth, and so on…)
  – Time needed to complete a specific task (which can be measured in hours, minutes, seconds, milliseconds, and so on…)

The statistical process gathers, analyzes and draws conclusions based on quantitative data.

The first part of the statistical process is creating a statistical research question. A statistical question should always allow for variability.

For example,

Many researchers also create hypotheses to go with the question, but this is not required.

The next part of the process is deciding on data collection methods (research methods) and then collecting it. Quantitative data collection may be collected with experiments, polls, interviews, focus groups, surveys, or questionnaires.

The method chosen depends on many things, some of which include…

• How much time is allowed for data collection.
• How much money can be spent on data collection.
• Whether data will be collected on the entire population or a sample.

For example,

On average, how many pets do the students at my school have?

One way this data can be collected is by emailing a survey to every student in the school – which would be a quick and free way to collect data on the entire population.

Once you have collected all observations (the final number of respondents or data points), it is time to begin the statistical analysis.

The analysis process begins with deciding which graphs or methods you will use to analyze the data. Analyzing quantitative data includes using box plots, histograms, dot plots and more.

Quantitative data analysis methods include calculating the mean, median, mode, range and other points that describe the center and variability of the data set.

Finally, quantitative data analysis is used to draw conclusions and answer the original question asked based on the collected data.

The answer to a statistical question should always take into account all parts of the process and anticipate ways in which the data may be a flawed representation.

What is quantitative data?

Common Core State Standards

How does this apply to 6 th grade math?

• Grade 6 – Statistics and Probability (6.SP.B.5a and 6.SP.B.5b)
  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

• Grade 6 – Statistics and Probability (6.SP.B.5a and 6.SP.B.5b)
  Summarize numerical data sets in relation to their context, such as by:
  • Reporting the number of observations.
  • Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

How to write a quantitative statistical question

In order to write a quantitative statistical question:

1. Think of a question that would be answered with a quantity.
2. Write the question to allow for variability.

Quantitative data examples

Example 1: writing a quantitative statistical question

Create a quantitative statistical question.

1. Think of a question that would be answered with a quantity.

How many siblings do you have?

This could be answered with 1, \, 2, \, 3, \, 4, etc. This is discrete, quantitative data.

2Write the question to allow for variability.

Since each person has a specific number of siblings, asking just one person will not provide a variety. Instead, you need to choose a group of people to be the population for the question.

For example,

On average, how many siblings do the kids in my neighborhood have?

Now the question will have a variety of answers, because the data population is all the kids in the neighborhood.

Example 2: writing a quantitative statistical question

Create a quantitative statistical question.

Example 3: writing a quantitative statistical question

Create a quantitative statistical question.

How to use the statistical process with quantitative data

In order to use the statistical process with quantitative data:

1. Ask a question that allows for variability and numerical data.
2. Decide on data collection methods and perform data collection.
3. Analyze the numerical data.
4. Draw conclusions to connect the data collected to the original question.

Example 4: going through the statistical process

Scenario: A school cafeteria has a rating scale, where students can rate the main dish on a scale from 1-5.

Describe how this could be used in the statistical process.

Example 5: going through the statistical process

Scenario: Julie is doing a research project. She wants to know how fast 6 th graders at her school can run a mile.

Describe how she can use the statistical process.

Example 6: going through the statistical process

Scenario: A coach records how many free throws each player makes during each game.

Describe how the coach can use the statistical process.

Teaching tips for quantitative data

• Give opportunities for students to write a question and collect data for their own quantitative research project. Going through the entire statistical process helps students remember and understand the methodology.

• Use real world examples of quantitative data in the classroom. These can be things like graphs or percentages from newspaper articles or data collected in the school setting (such as classroom surveys, fundraiser data or school garden measurements).

Easy mistakes to make

• Confusing a regular question with a statistical question
  A statistical question must account for variability. Even if a question has a number as an answer, if the answers can’t vary, it is not a statistical question.
  For example,
  How long does it take you to get home from school?
  This is NOT statistical if only one person is asked.
  On average, how long does it take 7 th graders to get home from school?
  This is statistical because it allows for variability.

• Making mistakes when analyzing data
  Analyzing data can be a complex and tedious process – even with data analysis tools. Always double check your work in any calculations and graphs.

• Making too broad of conclusions
  The conclusion should always reflect the question AND the data collected and nothing more.
  For example,
  On average, how long does it take 7 th graders to get home from school?
  The data from this question can only be applied to conclusions about 7 th graders and only 7 th graders at the school(s) that were included in the data collection. Including other grade levels or schools in the conclusions is extrapolation and NOT a valid conclusion.

• Confusing continuous and discrete data
  Both of these types of data are numerical, but they are not the same.
  Examples of discrete data are shoe sizes – there are a certain set of values.
  Examples of continuous data are the temperatures inside a refrigerator – degrees can be measured to any decimal point, so there is no specific set of values.

Related types of data lessons

• Types of data
• Qualitative data
• Discrete data
• Primary data
• Secondary data

The next lessons are

• How to find the average in math
• Representing data
• Frequency table
• Frequency graph

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