Statistics is a general field of numeric quantities and what they represent. For example, a statistic may be inferential or descriptive. Inferential statistics are special kinds of statistics that use sampling distributions to make inferences from a sample to a population of interest (hopefully that the sample represents). The inferences are more or less valid based on how well one meets the assumptions of a statistical method/model and how robust a statistical method is with respect to violations of an assumption.
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Why are measures of variability essential to inferential statistics?
There are two types of statistics. One is called descriptive statistics and the other is inferential statistics. Descriptive statistics is when you use numbers. Inferential statistics is when you draw conclusions or make predictions.
Descriptive statistics are meant to describe the situation such as the average or the range. Inferential statistics is used to differentiate between a couple of groups.
Descriptive and inferential
Inferential statistics, is used to make claims about the populations that give rise to the data we collect. This requires that we go beyond the data available to us. Consequently, the claims we make about populations are always subject to error; hence the term "inferential statistics" and not deductive statistics.