If the mean of the new set is , then the sum of the diameters of the cylinders divided by the
number of cylinders must equal . Set up the equation: = = ,
where x is the unknown cylinder. Multiply both sides by 6 to simplify: 5 = + + + 1 +
+ x. Combine like terms (use your calculator, but be careful with parentheses!): 5 = +
x. Subtract from both sides and you get .
- 1 ≤ y ≤ 1.25
A set with an even number of elements will have as its median the average of the middle
two terms. In the current set, and 1 have an average of , so the new cylinder must be
equal to or greater than 1, so the median will be the average of and 1. The range of the set
of five cylinders is the greatest minus the least: – = . Because the new cylinder must
be inches to greater than , the cylinder must be between 1 and inches in diameter.
