Final answer:
Non-overlapping intervals in histograms help represent data sets, where values on the left boundary of an interval are generally counted, except on the right boundary. The setup may vary, affecting the histogram's look but not the accuracy of data representation. These intervals help calculate statistical measures, including the median, mean, and interquartile range (IQR).
Step-by-step explanation:
When creating histograms to represent data sets, non-overlapping intervals, or class intervals, are used to group numerical data. These intervals each have a specific width and represent a range of data values. The method of counting data values that fall on interval boundaries can vary, but typically a value is included in an interval if it falls on the left boundary but not if it falls on the right boundary, with an exception for the first interval where data on both boundaries might be counted. This approach facilitates the calculation of various statistical measures such as the median, mean, and mode, as well as measures of spread like the interquartile range (IQR).
It is important to note that slight differences in how histograms are constructed can lead to different visual representations of the same data without affecting the accuracy of the data's description. Understanding the setup of histograms and the associated terminology is critical in the fields of data analysis and statistics.