Question

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 17, 6, 13, 6, 7. (a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to one decimal place.) s = (b) Multiply each data value by 2 to obtain the new data set 34, 12, 26, 12, 14. Compute s. (Round your answer to one decimal place.) s = (c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c? Multiplying each data value by the same constant c results in the standard deviation increasing by c units. Multiplying each data value by the same constant c results in the standard deviation being |c| times as large. Multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. Multiplying each data value by the same constant c results in the standard deviation remaining the same. (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 2.6 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? Yes No Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) s = km

Answer 1