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In this problem, we explore th

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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 15, 5, 6, 14, 16.

(a) Use the defining formula, the computation formula, or a calculator to compute s. (Round your answer to four decimal places.)
s =  

(b) Multiply each data value by 7 to obtain the new data set 105, 35, 42, 98, 112. Compute s. (Round your answer to four decimal places.)
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 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 smaller.
  – Multiplying each data value by the same constant c results in the standard deviation being |c| times as large.

  
Given 1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.)
s =   km

 
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In this problem, we explore th

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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.

12, 4, 10, 4, 16

(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 17, 9, 15, 9, 21. 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?
  • A) Adding the same constant c to each data value results in the standard deviation remaining the same.
  • B) Adding the same constant c to each data value results in the standard deviation increasing by c units. 
  • C) Adding the same constant c to each data value results in the standard deviation decreasing by c units.
  • D) There is no distinct pattern when the same constant is added to each data value in a set.
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