# Question 26 (2.8571 points) ) A novel on the Amazon.com web site has the following ratings,...

Question 26 (2.8571 points) ) A novel on the Amazon.com web site has the following ratings, in number of stars, from reviewers: Number of Stars Frequency 1 7 2 4 3 20 4 9 5 10 What is the standard deviation of this distribution? 43 1.25 2.71 3.29

Ans: The correct answer is 1.25

Calculation:

 Ratings (1) Frequency (2) Probability of frequency (3) (1) * (2) (4) (1) - 3.22 (5) (5) * (3) 1 7 7/50 = 0.14 0.14 1-3.22 = 4.93 4.93*0.14= 0.6902 2 4 4/50 = 0.08 0.16 2-3.22 = 1.49 1.49*0.08= 0.1192 3 20 20/50 = 0.40 1.20 3-3.22 = 0.05 0.05*0.40= 0.02 4 9 9/50 = 0.18 0.72 4-3.22 = 0.61 0.61*0.72= 0.1098 5 10 10/50 = 0.20 1 5-3.22 = 3.17 3.17*0.20= 0.634 Total 50 3.22 1.5732

Standard deviation = √1.5732 = 1.25

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