A bilaterally symmetrical distribution (the "left" and "right" sides of the center are mirror images of each other) that is triangular in shape (not mentioned in your book but actually a needed property) will have the same value for the mean, median, and mode. In real life, we should not expect to see perfect bilateral symmetry so in a distribution that is "approximately" bilaterally symmetric and triangular, the mean, median, and mode will be "close" to each other. From a statistical standpoint, triangular andbilaterally symmetric distributions are the easiest to work with. On the other hand, in the "real world," there are many instances when a distribution is less-than-ideal. For example, if we were to look at the weekly income for full-time employees in the USA, we would probably see a positive skewed distribution since there are very few individuals with incomes that are incredibly greater than the mean, median, and mode, while most full-time individuals would have incomes that are much closer to the "average" income (median of a little more than $900in the second quarter of 2019, according to theBureau of Labor Statistics Data(full url:https://www.bls.gov/opub/ted/2019/median-weekly-earnings-for-second-quarter-2019-increased-by-3-point-7-percent-over-the-year.htm).

For an original post, think of a numeric variable you have some familiarity with, describe the variable, and either state or make a reasonable guess at whether the distribution is likely to be bilaterally symmetric and triangular, positively skewed, negatively skewed, or something else (bimodal or multi-modal).

The full-time income example in the first paragraph is an example. There are very few people with very-high incomes in the millions of dollars andthe minimum income is zero with the vast majority of incomes being less than $2,000 per week so the distribution is positively skewed.