68 54 57 61 59 what is the median mode range and standard de

68   54   57   61   59

what is the median, mode, range, and standard deviation?

Solution

Ordering the data,

54
57
59
61
68

Thus, the median is the middle (3rd) term,

Median = 59 [ANSWER]

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There is no mode, as all numbers appear once. [ANSWER]

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Range = max - min = 68 - 54 = 14 [ANSWER]

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Getting the mean, X,      
      
X = Sum(x) / n      
Summing the items, Sum(x) =    299  
As n =    5  
Thus,      
X =    59.8  
      
Setting up tables,      
x   x - X   (x - X)^2
54   -5.8   33.64
57   -2.8   7.84
59   -0.8   0.64
61   1.2   1.44
68   8.2   67.24
      
Thus, Sum(x - X)^2 =    110.8  
      
Thus, as       
      
s^2 = Sum(x - X)^2 / (n - 1)      
      
As n =    5  
      
s^2 =    27.7  
      
Thus,      
      
s =    5.263078947   [ANSWER, STANDARD DEVIATION]

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