The standard deviation of the given sample is √2. So, option A is correct.
The standard deviation of the sample is calculated by using the formula,
σ² = ∑(x - μ)²/N
Where,
σ - standard deviation
x - sample
μ - mean of the sample
N - the size of the sample
The given sample is {19, 20, 21, 22, 23}
where N = 5
Finding the mean:
mean μ = (19 + 20 + 21 + 22 + 23)/5 = 105/5 = 21
So,
∑(x - μ)² = (19 - 21)² + (20 - 21)² + (21 - 21)² + (22 - 21)² + (23 - 21)²
= (-2)² + (-1)² + 0 + (1)² + (2)²
= 4 + 1 + 0 + 1 + 4
= 10
Finding the standard deviation:
we have μ = 21, N = 5, and ∑(x - μ)² = 10
Then,
σ² = ∑(x - μ)²/N
= 10/5
= 2
⇒ σ = √2
Thus, the value of the standard deviation of the given sample is √2.
Learn more about the standard deviation here:
https://brainly.com/question/9814755
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