2022 · Q65
The data of different natural numbers 4, 7, 10, 14, 2x + 3, 2x + 5, 22, 23, 30, 50 are in ascending order. How many possible values are there for the median of the data for various values of x?
Elementary MathematicsStatistics
- AOnly one value
- BOnly two values
- COnly three values
- DFive values
Explanation
The median is (2x+3+2x+5)/2 = 2x+4. Distinctness and ascending order require 14 < 2x+3 < 2x+5 < 22 with 2x+3, 2x+5 natural, so x ∈ {6, 6.5, 7, 7.5, 8}, giving the five medians 16, 17, 18, 19, 20. The keyed option is D.