Question

find the mean of the data summarized in the given frequency distribution. compare the computed mean to the actual mean of 56.1 degrees.
low temperature (°f) | 40 - 44 45 - 49 50 - 54 55 - 59 60 - 64
frequency | 3 6 10 7 2
the mean of the frequency distribution is 51.8 degrees.
(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 not close to the actual mean because the difference between the means is more than 5% of the actual mean.
b. the computed mean is close to the actual mean because the difference between the means is more than 5% of the actual mean.
c. the computed mean is not close to the actual mean because the difference between the means is less than 5% of the actual mean.
d. the computed mean is close to the actual mean because the difference between the means is more than 5% of the actual mean.

Explanation:

Step1: Calculate the difference between means

$|56.1 - 51.8|=4.3$

Step2: Calculate 5% of the actual mean

$0.05\times56.1 = 2.805$

Step3: Compare the difference and 5% of actual mean

Since $4.3>2.805$, the difference between the means is more than 5% of the actual mean.

Answer:

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