What is the first step students should take to find the interquartile range in a data set?

Finding the interquartile range (IQR) requires an understanding of the distribution of the data set, specifically focusing on the quartiles that divide the data into four equal parts. The first step in this process involves organizing the data set in ascending order.

By writing out the data from least to most, students can easily identify the first quartile (Q1) and the third quartile (Q3), which are essential for calculating the IQR. Once the data is sorted, determining these quartiles becomes straightforward, as they correspond to specific positions in the ordered data set. The IQR is then calculated by subtracting Q1 from Q3, indicating the range in which the middle 50% of the data lies.

The other choices do not facilitate finding the IQR directly. Calculating the mean or identifying the mode fails to provide the necessary framework for understanding quartiles, while graphing data on a number line, though visually helpful, does not establish the quartile positions needed for the IQR calculation. Sorting the data is a crucial and foundational first step that leads logically into these necessary subsequent calculations.