Mean, variance, t-statistic, z-score, chi-squared statistic, F-statistic, Mann-Whitney U, Wilcoxon W, Pearson's correlation and so on.
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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.
Inferential statistics is basically just a method of making a sort of prediction, generalization or like an estimate of something. So an example of it would be like saying "About 80% of the people living in the US have the last name of Smith, as is deduced by the information given."
Descriptive and inferential