Question

find the mean of the data summarized in the given frequency distribution. compare the computed mean to the actual mean of 51.4 miles per hour. speed (miles per hour) 42 - 45 46 - 49 50 - 53 54 - 57 58 - 61 frequency 21 13 7 4 2 the mean of the frequency distribution is 47.5 miles per hour. (type an integer or decimal rounded to one decimal place as needed.) which of the following best describes the relationship between the computed mean and the actual mean? consider the computed mean as close to the actual mean if the difference is less than 5% of the actual mean. a. the computed mean is close to the actual mean because the difference between the means is less than 5%. b. the computed mean is not close to the actual mean because the difference between the means is less than 5%. c. the computed mean is close to the actual mean because the difference between the means is more than 5%. d. the computed mean is not close to the actual mean because the difference between the means is more than 5%.

Explanation:

Step1: Calculate the difference between means

$|51.4 - 47.5|= 3.9$

Step2: Calculate 5% of the actual mean

$0.05\times51.4 = 2.57$

Step3: Compare the difference with 5% of actual mean

Since $3.9>2.57$, the difference is more than 5% of the actual mean.

Answer:

D. The computed mean is not close to the actual mean because the difference between the means is more than 5%.