In this problem, we explore the effect on the standard deviation of adding the s

Question

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 dataset. 15, 17, 7, 8, 5 use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to one decimal place.) Add 4 to each data value to get the new data set 19, 21, 1l, 12, 9. Compute s (Enter your answer to one decimal place.) 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.

Explanation / Answer

(a) 5.3

(b) 5.3

(c) Adding the same constant "c" to each value results in the standard deviation remaining the same.

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