7. Data Analysis I
7.3 Collecting Data
Learning Objectives
By the end of this section it is expected that you will be able to:
- State whether data is quantitative or qualitative
- Describe the random sampling methods: simple random sampling, systematic sampling, cluster sampling and convenience sampling
- Discuss potential problems that might arise when sampling from a population
Populations and Samples
In statistics, we generally want to study a population. You can think of a population as a collection of persons, things, or objects under study. It is often not feasible or possible to study the entire population. Instead we can select a sample. The idea of sampling is to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population.
Because it takes a lot of time and money to examine an entire population, sampling is a very practical technique. If you wished to compute the overall grade point average at your school, it would make sense to select a sample of students who attend the school. The data collected from the sample would be the students’ grade point averages. In elections, opinion poll samples of 1,000–2,000 people are taken. The opinion poll is supposed to represent the views of the people in the entire country.
Types of Data
Most data can be categorized as qualitative or quantitative.
Qualitative data are the result of categorizing or describing attributes of a population using our senses such as sight or touch. Hair color, blood type, ethnic group, the car model that 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+.
Quantitative data are always numbers. 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 are examples of quantitative data. Researchers often prefer to use quantitative data over qualitative data because it lends itself more easily to mathematical analysis. For example, it does not make sense to find an average hair color or median blood type.
EXAMPLE 1
Consider a high school math class and a sample of five student’s backpacks. Determine whether the data is quantitative or qualitative.
1. One data set is the number of books students carry in their backpacks.Two students carry three books, one student carries four books, one student carries two books, and one student carries one book.
2. For the sample of five backpacks you weigh the backpacks and contents. The weights (in kilograms) of their backpacks are 3.2, 5, 4.8, 5.1, 2.3.
3. For the sample of five students you record the colour of the backpacks. The books are red, blue or black.
Sol