Final answer:
The main reason the median is cumbersome to find with larger unorganized data sets is that all data must be ordered from least to most. For an odd number of values, the median is the middle value; for an even number, it is the average of the two middle numbers. Sorting the data is the most time-consuming part of finding the median.
Step-by-step explanation:
The identification of the median becomes increasingly cumbersome with larger sets of unorganized data primarily because data must be ordered from least to most before the median can be correctly identified. This is essential in defining the median, which is a number that separates ordered data into halves. With larger data sets, this sorting process becomes more time-consuming and intricate.
When the total number of data values is odd, determining the median involves locating the exact middle value in the ordered sequence. For instance, if there are 97 data values, the median is the 49th value after arranging the data from least to greatest. However, when the data set has an even number of observations, such as 14, the median is calculated by taking the average of the two middle values, which are the 7th and 8th values once the data is sorted.
The concept of the median is essential, especially when the data set contains outliers or extreme values, as the median provides a more accurate measure of the central tendency than the mean in such cases. It is also important to note that the median may or may not be a whole number, depending on whether the number of observations is odd or even.