Descriptive Versus Inferential Statistics for AP Statistics
Statistics has two primary functions: to describe data and to make inferences from data. Descriptive statistics is often referred to as exploratory data analysis (EDA). The components of EDA are analytical and graphical. When we have collected some one-variable data, we can examine these data in a variety of ways: look at measures of center for the distribution (such as the mean and median); look at measures of spread (variance, standard deviation, range, interquartile range); graph the data to identify features such as shape and whether or not there are clusters or gaps (using dotplots, boxplots, histograms, and stemplots).
With two-variable data, we look for relationships between variables and ask questions like: "Are these variables related to each other and, if so, what is the nature of that relationship?" Here we consider such analytical ideas as correlation and regression, and graphical techniques such as scatterplots.
Inferential statistics involves using data from samples to make inferences about the population from which the sample was drawn. If we are interested in the average height of students at a local community college, we could select a random sample of the students and measure their heights. Then we could use the average height of the students in our sample to estimate the true average height of the population from which the sample was drawn. In the real world we often are interested in some characteristic of a population (e.g., what percentage of the voting public favors the outlawing of handguns?), but it is often too difficult or too expensive to do a census of the entire population. The common technique is to select a random sample from the population and, based on an analysis of the data, make inferences about the population from which the sample was drawn.
Parameters versus Statistics
Values that describe a sample are called statistics, and values that describe a population are called parameters. In inferential statistics, we use statistics to estimate parameters. For example, if we draw a sample of 35 students from a large university and compute their mean GPA (that is, the grade point average, usually on a 4-point scale, for each student), we have a statistic. If we could compute the mean GPA for all students in the university, we would have a parameter.
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