To find out how much greater the mean of the reported heights is compared to the mean of the actual, measured heights, we will go through the following steps:
1. Calculate the mean of the reported heights:
The reported heights are:
[tex]\[
61, 68, 57.5, 48.5, 75, 65, 80, 68, 69, 63
\][/tex]
First, sum the reported heights:
[tex]\[
61 + 68 + 57.5 + 48.5 + 75 + 65 + 80 + 68 + 69 + 63 = 655
\][/tex]
Next, count the number of reported heights, which is 10.
Now, calculate the mean:
[tex]\[
\text{Mean of reported heights} = \frac{655}{10} = 65.5
\][/tex]
2. Calculate the mean of the measured heights:
The measured heights are:
[tex]\[
62, 68, 56.5, 47, 72, 65, 78, 67, 69.5, 62.5
\][/tex]
First, sum the measured heights:
[tex]\[
62 + 68 + 56.5 + 47 + 72 + 65 + 78 + 67 + 69.5 + 62.5 = 647.5
\][/tex]
Next, count the number of measured heights, which is 10.
Now, calculate the mean:
[tex]\[
\text{Mean of measured heights} = \frac{647.5}{10} = 64.75
\][/tex]
3. Calculate the difference between the mean reported height and the mean measured height:
[tex]\[
\text{Mean difference} = 65.5 - 64.75 = 0.75
\][/tex]
Therefore, the mean of the reported heights is [tex]\(0.75\)[/tex] units greater than the mean of the measured heights.
