1 For the following sample data set find the a mode b median

1. For the following sample data set find the:

a) mode b) median c) mean d) range e) standard deviation f) variance

Use the formulas and show your work for each one.

The following are seven random numbers generated by my calculator

16 20 15 8 17 8 14

Again, please solve and show your work, thank you so much.

Solution

1.

a)

Ordering the data

8
8
14
15
16
17
20

Thus, the mod is the most frequent,

Mode = 8 [ANSWER]

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b)

The median is the middle (4th) term,

Median = 15 [ANSWER]

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c)

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    98      
As n =    7      
Thus,          
X =    14   [ANSWER]

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d)

Range = max - min = 20 - 8 = 12 [ANSWER]

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e)  
          
Setting up tables,          
x   x - X   (x - X)^2  
8   -6   36  
8   -6   36  
14   0   0  
15   1   1  
16   2   4  
17   3   9  
20   6   36  
          
          
Thus, Sum(x - X)^2 =    122      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    7      
          
s^2 =    20.33333333      
          
Thus,          
          
s =    4.509249753   [ANSWER, STANDARD DEVIATION]

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F)

variance = s^2 = 20.33333333   [ANSWER]