Let’s start off by talking about descriptive statistics. Descriptive statistics describe data collected. Measures of central tendency, such as mean and median, and measures of dispersion such as standard deviation and range, are used to summarize and interpret some of the properties of a data set (e.g., sample, or subgroup) are known as descriptive statistics. Descriptive statistics can actually be verified from the data provided.
Example: Of the citations for speeding issued in July by Officer Hunt, 23% were given to drivers of red cars. This can be verified by looking at Officer Hunt’s July citation record.
Note that descriptive statistics do not infer the properties of a population. You need inferential statistics to do that.
By way of contrast, a mathematical method that employs probability theory for inferring the properties of a population parameter from which the sample is taken is known as inferential statistics. Inferential statistics is a set of methods used to make generalizations, estimations, or predictions.
Example: Of all the drivers pulled over and issued a citation for speeding in Florida, 23% of the drivers drove red cars. The state of Florida is the population and it is virtually impossible to keep track of the whole population. Instead, we take samples. Is from the samples that we infer parameters of a population. Notice that if it is a sample, it is called a statistic. If it is a population, it is called a parameter.
Use: You would use a descriptive statistic if you have all of the available data on hand – the whole population. It would not be economical, or even feasible, if you were to try to gather the whole population data. Instead, we use a sample to infer the characteristics of a population. This is popular in presidential election polls. Did they ask you before the election how you are going to vote? Probably not. They probably went out and asked 12 or 13 people how they were likely to vote and from that sample they made inferences about the whole population. In some recent elections the results of the earlier polling turned out to be fairly accurate on election day.
