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? divide this sum by the total number of data values minus 1. the standard deviation is the square root of this quotient. the standard deviation of the numbers 2, 3, 4, 4, and 6 is approximately. (round to three decimal places as needed.)

Explanation:

Step1: Calculate the mean

$\bar{x} = \frac{2+3+4+4+6}{5} = \frac{19}{5} = 3.8$

Step2: Find squared deviations

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

Step3: Sum the squared deviations

$3.24 + 0.64 + 0.04 + 0.04 + 4.84 = 8.8$

Step4: Divide by $n-1$

$\frac{8.8}{5-1} = 2.2$

Step5: Take square root

$\sqrt{2.2} \approx 1.483$

Step6: Same values case

If all values are same, deviations are 0, so standard deviation is 0.

Answer:

1.483; 0