What is the standard deviation of a population if the sum of the squared deviations is 81 and there are 9 people in the population?
A) The square root of 3
B) 1
C) 3
D) 9

Question

Quizplus · Accepted Answer

The formula for calculating the standard deviation of a population is:

SD = √(Σ(x-μ)²/N)

Where:
Σ = sum of
x = individual values in the population
μ = population mean
N = population size

We can use the given information to solve for the standard deviation:

Σ(x-μ)² = 81
N = 9

We don't know the population mean, but we do know that the sum of the squared deviations is the variance times the population size:

Σ(x-μ)² = σ²N

So we can rewrite the first equation as:

σ²N = 81
σ² = 81/9
σ = √9
σ = 3

Therefore, the standard deviation of the population is 3. Answer choice C is correct.

What Is the Standard Deviation of a Population If the Sum