Question 467·Medium·Math

The mode is the age that occurs most often. The largest frequency is $6$, beside age $18$, so the mode is $18$ years. Don't report $6$: it counts students, not years.

The median is the middle of the ages in order. With $20$ students, the middle positions are $10$ and $11$. The six $18$s fill positions $1$ through $6$, and the five $19$s fill positions $7$ through $11$. Both middle ages are $19$, so the median is $19$ years. Count students, not table rows.

The mean is the total of the ages divided by the number of students. Enter the ages in Desmos table column $x_1$ and their matching frequencies in $y_1$. Then type $\frac{\operatorname{total}(x_1y_1)}{\operatorname{total}(y_1)}$. Desmos displays $20$ years. Multiplying the columns counts each age once per student, rather than once per row.

The mode is $18$, the median is $19$, and the mean is $20$. Since $18<19<20$, the order is mode $<$ median $<$ mean for these students' ages. Choice D.