Final answer:
The missing value in the dataset when the median is known to be 31.5 is 40.
Step-by-step explanation:
To find the missing value in a set of ordered data values when the median is known, you would first need to ensure the data values are in numerical order. Since this data set contains an even number of values (6), the median will be the average of the third and fourth values once they are organized.
Provided that the median is 31.5 and that the dataset, when ordered, should look like 5, 12, missing value, 23, 41, 48, we can determine the missing value by setting up the equation (23 + missing value) / 2 = 31.5. Solving for the missing value gives us (23 + missing value) = 63, and subsequently the missing value = 63 - 23, which equals 40.