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

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 14, 13, 7, 5, 14. (a) Use the defining formula, the computation formula, or a calculator to compute s. S= (b) Multiply each data value by 4 to obtain the new data set 56, 52, 28, 20, 56. Compute s. 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 being |c| times smaller. Multiplying each data value by the same constant c results in the standard deviation remaining the same. 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. (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s =2 miles. Your friend wants to know the standard deviation in meters. 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

Explanation / Answer

Since,the first 4 questions are correctly answered, I have directly solved the last one.

Here, 1 mile=1.6km

Therefore, 2 mile

=1.6*2

=3.20km

Please give a THUMBS UP!!!

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