What is the least value and the greatest value of each show after voting off the contestants?
Show A: The range does not change. Show B: The range changes to 12 years. Explanation: See solution.
Practice makes perfect
Consider the given ages of the contestants for Show A and Show B.
Show A: & 19, 20, 20, 21, 22, 25,
&27, 27, 29, 29, 30, 31 [0.5em]
Show B: & 19,20,21,22,22,24,
&25,25,27,27, 32, 48
Additionally, we have that the range for Show A is 31- 19=12 years and for Show B is 48- 19=29 years. We are asked how each range is affected after the 25-year-old and the 48-year-old is voted off from Show A and Show B, respectively. Let's analyze each situation one at a time.
Show A
The range of a data set is the difference of the greatest value and the least value. For Show A, the least value is 19 and the greatest value is 31. Therefore, voting off the 25-year-old will not affect the range, since it is neither the least value nor the greatest value from the show. The range will still be 12 years.
Show B
In this case, the least value is 19 and the greatest value is 48. Removing the 48-year-old will change the range, since the greatest value of the show will be now 32. Therefore, the range would be 32- 19=13 years.
