If a variable takes discrete values x + 4, x − 7/2, x − 5/2, x − 3, x − 2, x +…
2019
If a variable takes discrete values x + 4, x − 7/2, x − 5/2, x − 3, x − 2, x + 1/2, x − 1/2, x + 5, (x > 0) then the median is:
- A.
x − 1/2
- B.
x − 2
- C.
x − 5/4
- D.
x + 5/4
Attempted by 62 students.
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Correct answer: C
Key idea: since each expression is x plus a constant, their order depends only on the constants.
List the constants from the given values: +4, −7/2, −5/2, −3, −2, +1/2, −1/2, +5.
Sort the constants in ascending order: −7/2, −3, −5/2, −2, −1/2, 1/2, 4, 5. The corresponding expressions in order are: x − 7/2, x − 3, x − 5/2, x − 2, x − 1/2, x + 1/2, x + 4, x + 5.
There are 8 values (an even number), so the median is the average of the 4th and 5th ordered values.
The 4th value is x − 2 and the 5th is x − 1/2. Compute their average: [(x − 2) + (x − 1/2)]/2 = (2x − 2.5)/2 = x − 5/4.
Answer: x − 5/4.