In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set.8, 6, 4, 16, 12(a)Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to four decimal places.)(b)Add 5 to each data value to get the new data set 13, 11, 9, 21, 17. Compute s. (Enter your answer to four decimal places.)(c)Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?Adding the same constant c to each data value results in the standard deviation remaining the same.Adding the same constant c to each data value results in the standard deviation increasing by c units.    Adding the same constant c to each data value results in the standard deviation decreasing by c units.There is no distinct pattern when the same constant is added to each data value in a set.

(a) To compute the standard deviation (s) of the original data set (8, 6, 4, 16, 12), we first need to find the mean (average) of the data set.

Mean = (8 + 6 + 4 + 16 + 12) / 5 = 9.2

Next, we subtract the mean from each data point and square the result:

(8 - 9.2)^2 = 1.44 (6 - 9.2)^2 = 10.24 (4 - 9.2)^2 = 27.04 (16 - 9.2)^2 = 46.24 (12 - 9.2)^2 = 7.84

We then find the mean of these squared differences:

(1.44 + 10.24 + 27.04 + 46.24 + 7.84) / 5 = 18.56

Finally, we take the square root of this mean to find the standard deviation:

s = sqrt(18.56) = 4.3081 (rounded to four decimal places)

(b) Now, we add 5 to each data point in the original data set to get the new data set (13, 11, 9, 21, 17) and repeat the process:

Mean = (13 + 11 + 9 + 21 + 17) / 5 = 14.2

Squared differences:

(13 - 14.2)^2 = 1.44 (11 - 14.2)^2 = 10.24 (9 - 14.2)^2 = 27.04 (21 - 14.2)^2 = 46.24 (17 - 14.2)^2 = 7.84

Mean of squared differences = (1.44 + 10.24 + 27.04 + 46.24 + 7.84) / 5 = 18.56

s = sqrt(18.56) = 4.3081 (rounded to four decimal places)

(c) Comparing the results of parts (a) and (b), we can see that the standard deviation remains the same even after adding the same constant to each data value. Therefore, adding the same constant c to each data value results in the standard deviation remaining the same.