Question

describe the process of calculating a standard deviation. give a simple example of its calculation (such as calculating the standard deviation of the numbers 2, 3, 4, 4, and 6). what is the standard deviation if all of the sample values are the same? the standard deviation of the numbers 2, 3, 4, 4, and 6 is approximately 1.483. (round to three decimal places as needed.) if all of the sample values are the same, then the standard deviation is

Explanation:

Step1: Calculate the mean

The mean $\mu = \frac{2+3+4+4+6}{5} = \frac{19}{5} = 3.8$

Step2: Compute squared differences from mean

$(2-3.8)^2=3.24$, $(3-3.8)^2=0.64$, $(4-3.8)^2=0.04$, $(4-3.8)^2=0.04$, $(6-3.8)^2=4.84$

Step3: Find variance (average of squared differences)

Variance $\sigma^2 = \frac{3.24+0.64+0.04+0.04+4.84}{5} = \frac{8.8}{5} = 1.76$

Step4: Take square root for standard deviation

Standard deviation $\sigma = \sqrt{1.76} \approx 1.327$ (Note: If using sample standard deviation with $n-1$, it's $\sqrt{8.8/4}=1.483$ as in the hint)

Step5: Standard deviation for identical values

If all values are the same, each squared difference from the mean is 0, so variance and standard deviation are 0.

Answer:

The standard deviation of 2,3,4,4,6 is approximately 1.483 (sample) or 1.327 (population). If all sample values are the same, the standard deviation is 0.
For the blanks: 1.483; 0