What is the value of y, if the standard deviation of 8, 8, 8, 8, y, 8 is 0?​

y = 8

Step-by-step 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