response time for seven emergency phone calls in a large met

response time for seven emergency phone calls in a large metropolitan area were measured to the mearest minute and found to be 7 10 8 3 8 4 9. Find the following. (A) Mean (B) Median (c)Mode (D) Range (E) Sample variance (F)Sample standard deviation (G) Q1, Q2, and Q3. (H) IQR (I) Coefficient of Variation (J) Find the z-score of 10 (K) Is 10 and outlier?

Solution

A)

Getting the mean, X,      
      
X = Sum(x) / n      
Sum(x) =    49  
As n =    7  
Thus,      
X =    7   [answer]

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b)

Reordering the data,

3
4
7
8
8
9
10

Thus, the middle entry is the 4th entry,

Median = 8 [ANSWER]

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c)

As we can see, the most frequency score is
Mode = 8 [ANSWER]

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d)

Range = max - min = 10 - 3 = 7 [ANSWER]

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e)

Setting up tables,      
x   x - X   (x - X)^2
3   -4   16
4   -3   9
7   0   0
8   1   1
8   1   1
9   2   4
10   3   9

Thus, as           
          
s^2 = Sum(x - X)^2 / (n - 1)          
          
As n =    7      
          
s^2 =    6.666666667   [VARIANCE]

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F)

Thus,          
          
s =    2.581988897   [STANDARD DEVIATION]  

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