Question 1: Monthly stock prices for two competing firms are as follows: a. Calc

Question

Question 1: Monthly stock prices for two competing firms are as follows:

a. Calculate the sample mean, sample variance, sample standard deviation and sample coefficient of variation for each fund.(Round your answers to 2 decimal places.)

b. Which firm had the higher stock price over the time period?

Firm A or Firm B

c-1. Which firm's stock price had greater variability as measured by standard deviation?

Firm A or Firm B

c-2. Which firm's stock price had the greater relative dispersion?

Firm A or Firm B

Month Firm A Firm B January $28 $21 February 31 24 March 32 24 April 35 27 May 34 25 June 28 20

Explanation / Answer

a)

a)
For Firm A:

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    188      
As n =    6      
Thus,          
X =    31.33333333      
          
Setting up tables,          
x   x - X   (x - X)^2  
28   -3.333333333   11.11111111  
31   -0.333333333   0.111111111  
32   0.666666667   0.444444444  
35   3.666666667   13.44444444  
34   2.666666667   7.111111111  
28   -3.333333333   11.11111111  

Thus, Sum(x - X)^2 =    43.33333333      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    6      
          
s^2 =    8.666666667      
          
Thus,          
          
s =    2.943920289      

coefficient of variation = s/mean =    0.093954903

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For Firm B:

Getting the mean, X,          
          
X = Sum(x) / n          
Summing the items, Sum(x) =    141      
As n =    6      
Thus,          
X =    23.5      
          
Setting up tables,          
x   x - X   (x - X)^2  
21   -2.5   6.25  
24   0.5   0.25  
24   0.5   0.25  
27   3.5   12.25  
25   1.5   2.25  
20   -3.5   12.25  
          
          
Thus, Sum(x - X)^2 =    33.5      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    6      
          
s^2 =    6.7      
          
Thus,          
          
s =    2.588435821      
          
coefficient of variation = s/mean =    0.110146205      
Hence, the table

[ANSWER]

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b)

FIRM A has the higher mean. [ANSWER]

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c-1.

FIRM A has higher standard deviation.

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C-2.

FIRM B has higher coefficient of variance.

Firm A Firm B Mean 31.33333 23.5 Variance 8.666667 6.7 Standard deviation 2.94392 2.588436 Coeffieceint of variance 0.093955 0.110146

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