Question Help The owner of two fast food restaurants has rec

Question Help The owner of two fast food restaurants has recorded customer satisfaction ratings for hath locations on a scale of 1 to 5 (5 - Most satisfied). The table linked below summarizes the data. Calculate the mean satisfaction rating at each location. Calculate the standard deviation of each distribution. What conclusions can be drawn from these results?

Solution

a)

FOR RESTAURANT A:

Thus,  
  
Mean = Sum(xf) / Sum(f) =    3.7625 [ANSWER, MEAN FOR RESTAURANT A]

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FOR RESTAURANT B:

Consider:

Thus,  
  
Mean = Sum(xf) / Sum(f) =    2.9 [ANSWER, MEAN FOR RESTAURANT B]

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b)

FOR RESTAURANT A:

Thus,  

Variance = [Sum(x^2f) - Sum(xf)^2/Sum(f)]/[Sum(f)-1] =    1.347943038

Standard deviation = sqrt(Variance) =    1.161009491 [ANSWER, STANDARD DEVIATION FOR RESTAURANT A]

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FOR RESTAURANT B:

Thus,  
  
Variance = [Sum(x^2f) - Sum(xf)^2/Sum(f)]/[Sum(f)-1] =    1.946376812
Standard deviation = sqrt(Variance) =    1.395126092 [ANSWER, STANDARD DEVIATION FOR RESTAURANT B]

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c)

As we can see, restaurant A has a higher mean rating, and it is more consistent as well, as it has lower standard deviation. [ANSWER]

x	f	x f	x^2 f
1	3	3	3
2	13	26	52
3	8	24	72
4	32	128	512
5	24	120	600