Find the mean of the data summarized in the given frequency

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 51.5 miles per hour. The mean of the frequency distributions is miles per hour. Which of the following best describes the relationship between the computed mean and the actual mean? The computed mean is close to the actual mean because the difference between the means is less than 5%. The computed mean is close to the actual mean because the difference between the means is more than 5%. The computed mean is not close to the actual mean because the difference between the means is less than 5%. The computed mean is not close to the actual mean because the difference between the means is more than 5%.

Solution

a)

Consider:

Thus,  
  
Mean = Sum(xf) / Sum(f) =    47.34615385 = 47.3 [ANSWER]

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Here, the percent difference is

%d = (51.5 - 47.34615385)/51.5*100% = 8.06572068

Hence,

OPTION D: The computed mean is not close to the actual mean because the difference between the means is more than 5%. [CONCLUSION]

x	f	x f
43.5	23	1000.5
47.5	16	760
51.5	7	360.5
55.5	4	222
59.5	2	119