Descriptive statistics deals with methods of organizing, summarizing, and presenting data in a convenient and informative way.
Descriptive statistics are there to describe a sample. That’s pretty straightforward. You simply take a group that you’re interested in, record data about the group members, and then use summary statistics and graphs to present the group properties. With descriptive statistics, there is no uncertainty because you are describing only the people or items that you actually measure. You’re not trying to infer properties about a larger population.
Inferential statistics deals with methods of making estimates, predictions, or decisions about a population based on sample data.
Inferential statistics takes data from a sample and makes inferences about the larger population from which the sample was drawn. “Making inferences” means predicting, or estimating unknown population values, so there will always be some level of uncertainty associated with inferential statistics.
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You take a random sample of 100 students at your university and find that their average GPA is 3.1. If you use this information to help you estimate the average GPA for all students at your university, then you are doing what branch of statistics?
The Commissioner of Health in California State wanted to study malpractice litigation in Los Angeles last year. She randomly selected 32,000 medical records from the population of 3.5 million patients in Los Angeles last year. From this sample, she calculated the proportion of litigations, the average amount of money involved per litigation, and the proportion of litigations resulting in a conviction.
These calculations are all examples of doing statistics.