The **standard** **deviation** of the given sample is **√2**. So, option A is correct.

<h3>How to calculate the standard deviation of the sample?</h3>

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

<h3>Calculation:</h3>

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:

brainly.com/question/9814755

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