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

ID: 3127802 • Letter: I

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 10,16,10,10,11.

a.) Use athe definding formula, the computation formula or calculator to compute s. round answer to one decimal

s=

b.) Multiply each data value by 8 to obtain teh new data set 80,128,80.80,88, compute s round your answer to one decimal place.

Given 1 mile equals close to 1.6klometer, what is the standard deciation in kilometers, enter your answer to two decimal places.

Explanation / Answer

a)

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    57      
As n =    5      
Thus,          
X =    11.4      
          
Setting up tables,          
x   x - X   (x - X)^2  
10   -1.4   1.96  
16   4.6   21.16  
10   -1.4   1.96  
10   -1.4   1.96  
11   -0.4   0.16  
          
Thus, Sum(x - X)^2 =    27.2      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    5      
          
s^2 =    6.8      
          
Thus,          
          
s =    2.607680962 = 2.6 [ANSWER]

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b)

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    456      
As n =    5      
Thus,          
X =    91.2      
          
Setting up tables,          
x   x - X   (x - X)^2  
80   -11.2   125.44  
128   36.8   1354.24  
80   -11.2   125.44  
80   -11.2   125.44  
88   -3.2   10.24  
          
Thus, Sum(x - X)^2 =    1740.8      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    5      
          
s^2 =    435.2      
          
Thus,          
          
s =    20.8614477 = 20.9   [ANSWER]  
      
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C)

s - 20.861 mi = 20.861*1.6 km = 33.38 km [ANSWER]

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