Given the sample data set: $2$, what is the standard deviation of this sample?

• A. $0$
• B. $2$
• C. $1$
• D.

Answer: (A)

Verified step by step guidance

1. Identify the sample data set, which in this case contains only one value: 2.
2. Calculate the sample mean \( \bar{x} \) using the formula: \[ \bar{x} = \frac{1}{n} \sum_{i=1}^n x_i \] where \( n \) is the number of data points and \( x_i \) are the data values.
3. Since there is only one data point, the mean \( \bar{x} \) will be equal to that value itself.
4. Calculate the sample variance using the formula: \[ S^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2 \] Note that for a sample, we divide by \( n-1 \) (degrees of freedom).
5. Finally, find the sample standard deviation by taking the square root of the variance: \[ S = \sqrt{S^2} \] Since there is only one data point, the variance and standard deviation will be zero.