Question

Which data set could be represented by the box plot shown below? (Sorry for the grey line on the top of it. I accidentally drew that.)

Answer 1

C

Explanation:

1. It cannot be D as the smallest number on the box plot is 16 and D says 15 so we can rule that out.
2. If we want to work out the median, we add use this equation:
   `(n+1)/(2)` (This is just adding one to the amount of numbers and dividing that number by two. This tells you the place of the median. The box plot says the midpoint is 22 so we work out the numbers with 22 as their median.
3. If we try A, the amount of numbers is 12, so we add 1 to make 13 and divide by 2 to get 6.5 (Bare in mind this is the same for all 4 sets of numbers). If we want to work out the 6.5th place, we just get the 6th and the 7th place, add them together and divide by 2. (23 +23)/2 = 23 so that A cannot be correct.
4. The median is also 23 for B meaning that is also incorrect.
5. In C however, the median is in fact 22 indicating that C is indeed the correct answer