If the standard deviation of the set of numbers 3, 6, x, 7, 5 is 2, find the least possible value of x.
A
2
B
3
C
4
D
6
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Numbers: 3, 6, x, 7, 5
Mean = \(\frac{(21 + x)}{5}\)
Standard deviation = 2, so the sum of squared deviations = 20.
Solving:
2x² - 21x + 27 = 0
x = 9 or x = 1.5 ≈ 2
The **least possible value of x is 1.5
Source: Myschool Past Questions Archive (Record #10417)