I have looked at several math sites, covering a wide range of math abilities, but of the big three -- mean, median, and mode -- mode does not have a synonym.
In contrast, mean has synonyms ("average" or "arithmetic mean").
Median has a synonym ("middle value").
Here are the sites I examined:
Several of the sites have revealed a shortcoming with the synonyms. Consider the data set:
1 2 4 7
What is the "most common" value? While there is no single value, there are four "most common" values: 1, 2, 4 and 7. What is the mode? There is none, by definition.
Consider the data set:
1 2 2 3 4 6 7 7
What is the "most popular" value? There is no superlative, although 2 and 7 are perhaps more popular. The above data set is bimodal, and its modes are 2 and 7.
(By the way, think of sampling a population for basal levels of a sex hormone, like testosterone. If the sample included both men and women, the mean would not be very meaningful. However, the modes would be more meaningful, as the data would probably be bimodal, and you would get one mode for men and another for women.)
Although the OP has pleaded for an "easier to understand" synonym, I don't think there is a synonym for mode in the statistical sense.
I would recommend taking the time to define mode to the OPs (mostly) adult learners. Consider how the common words "nose," "legs," and "bouquet" take on a new, specialized meaning when sampling wines. Or how common words "liquid," "frozen," and "underwater" can take on new, specialized meanings when describing financial assets. In turn, "mode" can take on a new, specialized meaning with math. They wouldn't even have to learn a new vocabulary word; they could just re-purpose an existing one. With ice cream on top.