Final answer:
The median of the data set 56, 78, and 92 is 78, as it is the middle number in the set. For an even number of observations, the median is calculated as the average of the two middle numbers.
Step-by-step explanation:
To find the median of a data set, the numbers must be arranged in ascending order. The median is the value that divides the data set into two equal halves. When there is an odd number of observations, the median is simply the middle number. However, if there is an even number of observations, the median is the average of the two middle numbers.
In the given data set of 56, 78, and 92, which contains only three numbers, the middle number is 78, thus the median is 78. No calculation of average is needed because there is an odd number of observations.
For the additional provided information: In a data set with 14 observations, the median is calculated by taking the average of the 7th and 8th numbers. If those numbers were 6.8 and 7.2, their average would be (6.8 + 7.2) / 2 = 7. In another data set with the values listed, the median is located between the 20th and 21st values, which are both 24, so the median is also 24 in this case.