Statistics: Random Samples & Comparing Data Sets

Categorical data sorts objects based on a qualitative attribute that can be described using distinct categories, like color, tree type, or drink sizes.

A frequency is the number of times something happens. In data, a frequency is the number of individuals or objects that fit in a particular category or that produce measurements within a bin interval.

I use data collection to answer questions. Particularly if the answer could be different for different individuals or objects. I can collect data to get information about a population.

Continuous data is quantitative, and it is measured using a tool that allows for a continuous set of possible measurements, like length, mass, or volume.

Data can be difficult to visualize and compare when it is written in a table. By making graphs, I can communicate a lot of intuitive information about the data easily and quickly.

A population is the group of individuals I am interested in. Populations can be people, pets, animals, plants, objects, etc. Populations need to be well defined, for example, if I am interested in studying middle school students in Arizona, I need to be specific. Just saying “people” implies everyone in the world, “people from Arizona” implies all Arizonans, while “people who are students in an Arizona middle school” adequately describes the population.

A sample is a subset of the population that a researcher selects to study. A sample should be representative of the population of interest, so if I am interested in “people who are students in a Michigan middle school,” I wouldn’t sample middle school students from outside Michigan, or sample elementary or high school students. Samples are important because they give information about the population without having to measure every member of the population. Sampling saves time and money.

A sampling method is the procedure I use to select a sample. There are many sampling methods, but the most important thing is to choose a sample that is likely to be representative of the population. Random sampling and a large enough sample size are the best ways to ensure a representative sample.

If a sample is different from the population, it is biased. Biased sampling means I can’t interpret the data properly or make conclusions about the population based on the results of the sample. I take samples so I can infer things about the population, but if the sampling method I choose doesn’t give a representative sample, then I can’t make inferences from that. Convenience sampling and low sample size can introduce bias to a sample.

A statistical question is one where the answer is uncertain, or where the answer may vary between individuals. For example, “how tall are Oklahoma middle school students?” is a statistical question because the height of a student changes from student to student. I can answer this question by taking a random sample of Oklahoma middle school students and measuring their heights. I can then use a histogram or line graph to summarize and display that data.