Final answer:
The question deals with descriptive and inferential statistics used to analyze the social media data of a local band. Descriptive statistics summarize data, while inferential statistics allow making predictions and testing hypotheses on the larger population from the sample data. a) Descriptive statistics
Step-by-step explanation:
If a local band is interested in increasing its social media presence and uses raw data to calculate a sample mean x, they are engaging in the realm of statistics, specifically using descriptive statistics and possibly inferential statistics. Descriptive statistics involve summarizing and describing the features of a data set, which in this case could be the average number of likes, shares, or follows on the band's social media posts. The sample mean x is a form of descriptive statistics. On the other hand, inferential statistics apply when the band might want to draw conclusions or make predictions about their entire fan base based on the sample data. For instance, they could hypothesize that releasing certain types of content will result in increased engagement or compare the effect of different promotional strategies. A specific type of inferential statistics is hypothesis testing, which the band could use to test assumptions about their social media strategy effects. For example, they might use a t-test to compare the mean engagement before and after implementing a new strategy. Understanding the empirical rule is also important. In the context of a normally distributed set of data, it implies that sample means will fall within two standard deviations of the population mean approximately 95% of the time, which aids in gauging the representativeness of the sample mean.