SOLUTION: A class of 15 kindergarteners had the following weights in pounds: 53 39 46 36 39 52 49 52 46 47 48 51 48 51 41 Find the mean, var

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Question 224587: A class of 15 kindergarteners had the following weights in pounds:
53 39 46 36 39 52 49 52
46 47 48 51 48 51 41

Find the mean, variance, and standard deviation.
(Points: 5)
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
 
A class of 15 kindergarteners had the following weights in pounds:
53    39    46    36    39    52    49    52    
46    47    48    51    48    51    41

Find the mean, variance, and standard deviation.
  (Points: 5)
 
List them in a column with heading X, add them and divide by the
number of numbers, which is 15.  That is the mean:
        X
       53    
       39    
       46    
       36    
       39    
       52    
       49    
       52    
       46    
       47    
       48    
       51    
       48    
       51    
       41
      ---
   15)698
_     ---  
X = 46.5333···

Subtract that mean from each of the numbers and place in
another column headed with X-X
                 _
        X      X-X
       53   -6.4666...  
       39   -7.5333... 
       46   -0,5333... 
       36  -10.5333... 
       39   -7.5333...  
       52    5.4666... 
       49    2.4666...
       52    5.4666...
       46   -0.5333... 
       47    0.4666...
       48    1.4666...
       51    4.4666...
       48    1.4667...
       51    4.4666...
       41   -5.5333...
      ---
   15)698
_     ---  
X = 46.5333···
           _
The mean = X = 46.5333...


Now square all those in that list and place them
                            _
in a third column headed (X-X)², add that column and
divide by one less than 15, or 14
                 _             _ 
        X      X-X          (X-X)²   
       53   -6.4666...    41.81777...
       39   -7.5333...    56.75111...
       46   -0.5333...      .28444...
       36  -10.5333...   110.95111...
       39   -7.5333...    56.75111... 
       52    5.4666...    29.88444...
       49    2.4666...     6.08444... 
       52    5.4666...    29.88444...
       46   -0.5333...     0.28444...
       47    0.4666...     0.21777...
       48    1.4666...     2.15111... 
       51    4.4666...    19.95111... 
       48    1.4667...     2.15111...
       51    4.4666...    19.95111...
       41   -5.5333...    30.61777...
      ---                ------------
   15)698             14)407.73333...
_     ---                ------------
X = 46.5333···         s²=29.12380952...

s² is the variance = 29.12380952...

s is the standard deviation = ...

Edwin
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