Question

yasmin has a set of 8 numbers, with a median of 27 and a range of 3. which statement must be true based on the given information? a if the greatest number is 28, then the least number is 24. b the least number is greater than 20. c the greatest number is less than 32. d at least one number is 27.

Explanation:

Step1: Recall range formula

Range = Largest number - Smallest number. Given range = 3, so Largest number - Smallest number = 3.

Step2: Analyze option A

If largest number is 28, then smallest number = 28 - 3=25, not 24, so A is false.

Step3: Analyze option B

Since range = 3 and median is 27, the smallest number can be 24, 25 or 26 (if the set has an odd - number of elements and is ordered). The smallest number is not greater than 20, so B is false.

Step4: Analyze option C

Since range = 3 and median is 27, the largest number can be 27 + 3=30, 29 or 28. The largest number is not less than 27, so C is false.

Step5: Analyze option D

Since range = 3 and median is 27, assume the set has an odd - number of elements. If the set is ordered, the middle number (median) is 27. The smallest number can be 24, 25 or 26 and the largest number can be 28, 29 or 30. It is possible that at least one number is 27.

Answer:

D