What are mean, median, and mode
Mean, median, and mode are the three most common measures of central tendency in statistics, each summarizing a set of numbers in a different way. The mean is the sum of all values divided by how many values there are. The median is the value that sits exactly in the middle when the numbers are sorted. The mode is the value that repeats most often in the set.
Why use the median instead of the mean
The mean is sensitive to extreme values (outliers): a single number much larger or smaller than the rest can skew the result significantly. The median doesn't have that problem, since it only depends on the central position of the sorted data. That's why statistics like average income are often better represented by the median, which isn't pulled upward by a few very high values.
When a set has no mode, or more than one
If every value in a set appears exactly the same number of times, usually just once each, no value stands out as more frequent than the others, and the set is considered to have no mode. When two or more values tie for the highest frequency, the set is bimodal or multimodal, and all of those values count as the mode.
Practical example
In a class, test scores were 6, 7, 7, 8, and 10. The mean is 7.6, the median is 7 (the middle value of the sorted list), and the mode is 7 (the score that repeats most). In this case the median and mode happen to match, but that isn't always true.