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In statistics, a data set is a collection of numbers or values that relate to a particular subject. These values can represent anything, like test scores, measurements, or observations. When you encounter a data set, it will often look like a list of numbers. For example, let's consider the data set from the exercise: \(3, 12, 15, 7, 9\). Each individual number in this set is called a data point. Data sets are fundamental in statistics because they provide the actual figures that we analyze. By examining these numbers, we can find patterns, make predictions, or summarize information concisely. It is like having a treasure chest of information where each number tells a part of the story. Understanding a data set's structure helps guide any analysis you perform, such as finding the range, which is a summary statistic used to describe a data set.

Among the first tasks you perform with a data set is finding the highest and lowest values. These two values help in calculating the range, an important measure of data variability. Let's imagine you have the data set \(3, 12, 15, 7, 9\).- **Highest Value**: This is the largest number in the data set. Look through the numbers and find the maximum value. In our example, the highest value is \(15\).- **Lowest Value**: This is the smallest number in the data set. Again, scan through the list to spot this minimum value. Here, the lowest value is \(3\).Pinpointing these values is crucial as they determine the spread of the whole data set. It provides boundaries that the data values fall between.

Once you have identified the highest and lowest values, calculating the range is straightforward. The range is defined as the difference between the highest and lowest values in a data set. It tells you how spread out the values are. To find the range, simply subtract the lowest value from the highest value:- Use the formula: Range = Highest Value - Lowest Value- For our data set \(3, 12, 15, 7, 9\), it becomes: \[ Range = 15 - 3 = 12 \]The range for this data set is \(12\). Understanding the range helps give a quick sense of the variability in your data. It indicates the span from the smallest to largest number, showing how much the data values differ from one another.