Eight lists of seven numbers a sheet, and for each one the student writes the median - the value sitting in the middle once the list is put in order. The list is printed in the order it was drawn and never sorted first, so sorting is half the work and the half most often skipped. Reading a number off the middle of an unsorted list is the single most common way to get one of these wrong.
Every list here holds an odd number of values, which is what keeps the answer a single number the student can point to. An even-length list has two middle values and needs the mean of the pair - a different question, and an arithmetic one. The values are drawn independently from 1 to 20, so a number can appear more than once; that changes nothing, because a sorted list of seven has a fourth entry whatever repeats inside it.
Put the numbers in order from smallest to largest and take the middle one. For 12, 3, 8, 1, 5 the sorted list is 1, 3, 5, 8, 12, so the median is 5.
Because every list on these sheets has an odd number of values. Sorting seven numbers leaves a genuine middle entry - the fourth - so the answer is always a value already printed on the page. Even-length lists are not used here, since those ask for the mean of the two middle values instead.
No, and it does happen: the values are drawn independently from 1 to 20, and repeats are left in rather than redrawn. A sorted list of seven has a fourth entry whether anything repeats or not, and if the repeated value is the one in the middle then that value is the median.
The median is found by sorting and the mean by adding and dividing, so they part company when a list holds one unusually large value: it drags the mean upwards and leaves the median where it was. Mean Worksheets and Mode Worksheets each drill one of the others, Range Worksheets covers the spread, and the Mean, Median, Mode and Range page mixes all four on one sheet.