Answer:
y = 8
Explanation:
First, we know that the equation for standard deviation is
σ = √((1/N)∑(xₐ-μ)²), with σ being the standard deviation, N being the count of numbers, xₐ being individual values, and μ being the mean. Working backwards, we have
0 = √((1/N)∑(xₐ-μ)²)
Squaring both sides, we get
0 = (1/N)∑(xₐ-μ)²
Since 1/N cannot be 0, we know that
0 = ∑(xₐ-μ)²
Since (xₐ-μ)² can only be ≥0, this means that each value of xₐ-μ must be equal to 0, so
0 = xₐ-μ for each a
xₐ = μ
This leads to the conclusion that each value is equal to the mean, so the mean must be 8.
The mean is equal to the sum / amount of numbers. There are 6 numbers, and the sum is (40+y). The mean is
8 = (40+y)/6
multiply both sides by 6
6*8 = 40+y
48 = 40 + y
This means that
y = 8