Are you prepared for the next chapter in our statistical journey with R? In this lesson, we're focusing on quantiles and the Interquartile Range (IQR). Quantiles divide our data into equal parts, and the IQR signifies the range within which half of our data lies. Understanding these tools is vital for describing the distribution of data and detecting outliers. By leveraging R’s built-in functions along with the dplyr package, we'll embark on the journey of calculating these measures.

Quantiles segment data into equal intervals. Take, for instance, when student scores are divided into quartiles (four equal parts). These are commonly denoted as Q1 (the first 25%, or the 25th percentile, the point below which 25% of the data falls), Q2 (or the median, marking the middle point or 50th percentile), and Q3 (representing the 75th percentile, or the point below which 75% of the data falls).

The Interquartile Range (IQR) simply illustrates the zone within which half of our data lies. Because it is resistant to outliers, it becomes essential when analysing data. For instance, an IQR analysis in a salary distribution would eliminate extreme values, thereby providing a truthful depiction of the range within which most salaries fall.

In R, we use the quantile() function to calculate quantiles. In a sorted data array, quantiles are derived at specific points. Q1 is the point below which 25% of the data falls, while Q3 is the point below which 75% of the data falls. Q2, or the median, is the mid-point of the data.

These critical values assist in identifying the spread or skewness in our dataset. Let's consider a dataset of student scores: