Given is the following data set 3 5 8 9 11 17 A Calculate th

Given is the following data set: 3, 5, 8, 9, 11, 17.

A) Calculate the mean.

B) Calculate the median.

C) Calculate the standard deviation.

D) Is the data skewed to the left or skewed to the right? Explain, and use the words mean and median in your answer

SHOW ALL THE FORMULAS AND WORK.

Solution

a)

Mean = Sum(x)/n

= (3+5+8+9+11+17)/6

= 8.833333333 [ANSWER]

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b)

As there are 6 entries here, the median is the average of the two middle terms, the 3rd and fourth:

Median = (8+9)/2 = 8.5 [ANSWER]

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c)

Setting up tables,          
x   x - X   (x - X)^2  
3   -5.833333333   34.02777778  
5   -3.833333333   14.69444444  
8   -0.833333333   0.694444444  
9   0.166666667   0.027777778  
11   2.166666667   4.694444444  
17   8.166666667   66.69444444  
          
Thus, Sum(x - X)^2 =    120.8333333      
          
Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    6      
          
s^2 =    24.16666667      
          
Thus,          
          
s =    4.915960401   [ANSWER]

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d)

As the median < mean, then it is skewed to the right.