They are never used there is no point in learning about them. We have to because it is required in school. So learn it but you will never use it.
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On a standard box-and-whisker plot, the averages used are medians. Arithmetic means are used in some box-and-whisker plots, but most use medians.
Baseball stat recorders use it
stem and leaf plots are used in math
they aren't used in real life, not unless you need them in a situation were you would need to use them.
natural numbers are used in real life for counting, adding, subtracting and even for calculting money purposes