Variables
The next step in a statistical investigation is to decide what you’re measuring and how you’re going to collect the data. Data are often shown as a long list of information about a group of individuals, animals, or objects. What you choose to measure is called the variable. Some examples can include favorite color, height, cost, age, heart rate, state, and more.
variable
A characteristic that can be measured and has different values.
Qualitative and Quantitative Data
Data are the actual values of the variable. They may be numbers or they may be words. As such, data can be categorized as qualitative or quantitative data.
qualitative/categorical data
Qualitative data are the result of categorizing or describing attributes of a population.
Hair color, blood type, ethnic group, the car a person drives, and the street a person lives on are examples of qualitative data.
Qualitative data are generally described by words or letters. For instance, hair color might be black, dark brown, light brown, blonde, gray, or red. Blood type might be AB+, O-, or B+.
Qualitative data are also often called categorical data.
quantitative data (discrete and continuous)
Quantitative data are the result of counting or measuring attributes of a population. Amount of money, pulse rate, weight, number of people living in your town, and number of students who take statistics courses are examples of quantitative data.
Quantitative data are always numbers.
Quantitative discrete data are the result of counting. If you count the number of phone calls you receive for each day of the week, you might get values such as [latex]0, 1, 2, \mathrm{or} \ 3[/latex].
Quantitative continuous data refers to a type of numerical data that can take on an infinite number of values within a given range. Continuous data are often the results of measurements like lengths, weights, or times like a list of the lengths in minutes for all the phone calls that you make in a week.
We want to know the average amount of money first year college students spend at ABC College on school supplies that do not include books. We randomly survey [latex]100[/latex] first year students at the college. Three of those students spent [latex]$152.75[/latex], [latex]$211.10[/latex], and [latex]$225.50[/latex], respectively.
- While quantitative variables always have numerical data, not all numerical data is quantitative. Qualitative data can be numerical if the numbers don’t help us compare the values. For example, zip code has a numerical response, but we don’t compare zip codes numerically (think about how there is no such thing as an average zip code, and having a higher/lower zip code doesn’t really communicate information about where you live). Zip code is a categorical variable, not a quantitative one.
- Discrete data can include fractions or decimals. The key is to recognize whether any fraction or decimal would be accepted. Shoe size is a great example of quantitative discrete data that includes decimals since your shoe size can be 9, 9.5, 10, 10.5, but could not be any decimal between 9 and 9.5.
