Maths problem: how to do, thanks?

P(at least 45) = 9/16 => 18/32

so, 18 values have a score of 45 or more

15 values are past the ink blot, hence the 3 blotted out are included in this group.

If the score is at least 45, the first value must be 45

Hence, 45, 46 and 47...if different

so, the 16th value is 46 and the 17th value is 47

The median of 32 numbers is mid-way between the 16th and 17th values...i.e. 46.5

Disagree with the teacher as this is the value. Even if you said the median was 46 or 47 to keep whole numbers that would only be a difference of 1 between least and greatest values.

:)>

A stem-and-leaf plot is a combination of a histogram and a simple list of numbers. This one represents the numbers 15, 24, 26, 27, 28, 30, ... 
Note that the numbers are in order, so the missing numbers can only be between 43 and 47 (inclusive).

(a)  Locate on the plot the highest 9/16 of the numbers. How many of the blotted-out numbers are included? This further restricts the possible values of the unknown numbers: in the lower 7/16 they must be no larger than 44, while in the higher 9/16 they must be no smaller than 45.
Combined with the restriction to not repeat numbers, you have enough information to identify all the missing numbers.

(b) This appears to be separate from (a), so forget that solution. go back to only the restrictions that the numbers are between 43 and 47 and that they are all different.
Locate the median in the plot (either one number or two). What are the smallest and largest values that could be placed there?