Six different secondyear medical students at Bellevue Hospit

Six different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings (in mmHg) are listed below. Find the range, variance, and standard deviation for the given sample data. If the subject\'s blood pressure remains constant and the medical students correctly apply the same measurement technique, what should be the value of the standard deviation?
120 134 146 127 138 133

Range= _ mmHg ?

Sample variance= _ mmHg² (Round to the nearest tenth as needed.)

Sample standard deviation= _ mmHg (Round to the nearest tenth as needed.)

What should be the value of the standard deviation?

A.Ideally, the standard deviation would be zero because all the measurements should be the same.

B.Ideally, the standard deviation would be one because all the measurements should be the same.

C.Ideally, the standard deviation would be one because this is the lowest standard deviation that can be achieved.

D.There is no way to tell what the standard deviation should be.

Solution

A)

Range = max - min = 146 - 120 = 26 mmHg [ANSWER]

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b)

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    798      
As n =    6      
Thus,          
X =    133      
          
Setting up tables,          
x   x - X   (x - X)^2  
120   -13   169  
134   1   1  
146   13   169  
127   -6   36  
138   5   25  
133   0   0  
          
Thus, Sum(x - X)^2 =    400      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    6      
          
s^2 =    80   [ANSWER, VARIANCE]  

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c)
          
Thus,          
          
s =    8.94427191   [ANSWER, STANDARD DEVIATION]

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d)

A.Ideally, the standard deviation would be zero because all the measurements should be the same.