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Data analysis is the process of systematically applying statistical and logical techniques to describe, summarize, and evaluate data. When we are working with a set of numbers, like \(11, 13, 14, 15, 17\), we want to make sense of these numbers by finding out what they can tell us. This process helps us identify patterns or insights we might not immediately see.

In the context of this exercise, we're focusing on understanding the spread of data points. By conducting data analysis, we can figure out how spread out or closely packed these numbers are. This is crucial in statistics as it helps us understand variability in data sets, which is often a key piece of information when making real-world decisions.

The concepts of maximum and minimum values are essential when analyzing data sets. For any group of numbers, the **maximum value** is the largest number, and the **minimum value** is the smallest number.

• For the data set \(11, 13, 14, 15, 17\), the minimum value is \(11\).
• The maximum value is \(17\).

Knowing the maximum and minimum values is the first step in calculating the range. These values help us understand the boundaries within which our data points vary. Recognizing these numbers is crucial not only for calculating range but also for other statistical measures, helping us describe the overall structure of the data set effectively.

Calculating the range is a simple yet powerful statistical method for understanding the spread or the variability of a data set. The **range** is determined by subtracting the minimum value from the maximum value.
In our example, the calculations are as follows:

• Maximum Value: \(17\)
• Minimum Value: \(11\)
• Range = \(17 - 11 = 6\)

This tells us that the data set spans a width of \(6\) units. While calculating range is straightforward, it provides insight into the distribution. The range can help identify outliers and the level of consistency in the data. A larger range might indicate more variability among the numbers, whereas a smaller range suggests the numbers are more tightly clustered.