Through summary statistics, we have gained insights on the overall patterns in our data. Let us take a moment to discuss each one individually.

You are already familiar with calculating means from our previous chapter. Here, we looked specifically at the mean soldier engagement and battle durations for past head to head conflicts. Again we see that the Wei forces tend to outnumber the Shu in battle. The average head to head battle has lasted 78 days.

A standard deviation helps to depict the amount of variability present in a collection of data. The sd(data) function can be used to calculate the standard deviation of a given dataset. In our soldier engagement data, the Wei army had a higher standard deviation than the Shu army. This indicates that the Wei forces tended to enter battle with a more variable number of soldiers than the Shu forces. Since the Wei army usually outnumbered the Shu in past battles, it is expected that its standard deviation would be larger.

The range of a dataset is composed of its minimum and maximum values. By using the range(data) function in R, we can list the minimum and maximum values of our data in a single command. Similar to the standard deviations, the Wei have a wider range of soldiers engaged than the Shu. This is a predictable outcome considering the Wei forces' larger numbers. The duration of past head to head conflicts ranged from 30 to a 120 days.

You also employed one of the most useful and versatile functions available to the R language. The summary(object) function generates descriptive statistics and other relevant calculations for an object automatically. In our case, the object was a dataset and our descriptive statistics included means, sums, medians, quartiles, minimums, and maximums. The wonderful thing about R's summary function is that it can be used on nearly any object. Depending on the type of object, the summary function will yield output that is relevant to that object. Therefore, it is not only a fast way to get an overall picture of your data, but it can be used in numerous situations. You should use summary(object) often, especially when you are beginning to analyze a dataset or want to inspect a newly created object.

You probably noticed that some of our summary statistic calculations yielded unsurprising and predictable results. This is not, however, reason to discount their value or an argument for abandoning them. In fact, using summary statistics to confirm that our data are normal is an essential early step in the data analysis process. In contrast, any value that stands out as peculiar in our summary statistics warrants further inspection. When this occurs, we may have discovered erroneous or outlying data points, or possibly counterintuitive or unforeseen trends and patterns.

For instance, the median duration of head to head battles (91 days) is noticeably higher than the mean duration (78 days). This may indicate that most battles tend to last on the longer side of our 30 to 120 day duration range and that our mean is being skewed downward by a small number of brief battles. By looking back at our head to head subset, we can confirm or deny this observation.

Now that you are familiar with deriving summary statistics, calculate the means, standard deviations, and ranges for each of the remaining battle methods surround, ambush, and fire. Also generate a summary of each subset. Follow a similar console structure and naming convention that we used with our head to head combat data. For example, you should create the following variables using your ambush data: