The mean is the value right at the middle of the data set when it is organized from the smallest to the biggest. The first step we need to do is organize the data set in that manner. We have:
There are a total of 5 values. The one right at the middle is 53, so this is the mean of the data set. We now need to discard one value in such a way that the mean is 52. When we discard one value we will have an even number of points in the data set so we will need to calculate the average of the two points in the middle, we want the average to be 52. If the two numbers are x and y, then the mean would be:
![\begin{gathered} \operatorname{mean}=(x+y)/(2)=52 \\ (x+y)/(2)=52 \\ x+y=104 \end{gathered}]()
We need to find two numbers that when added are equal to 104. We can get that result if we add 51 and 53, therefore they should be at the middle of the data set. To do that we need to discard 57. The new data set is:
The number to be discarded is 57.