First, let's list the recorded number of yachts leaving at each lift, including the error:
[tex]\[ 12, 15, 13, 10, 14, 9, 2, 12, 16, 17 \][/tex]
Jack realizes he made an error in the seventh value and should have added 2 more yachts to it. Therefore, the correct number of yachts for the seventh value is:
[tex]\[ 2 + 2 = 4 \][/tex]
So, the corrected list of yachts per lift becomes:
[tex]\[ 12, 15, 13, 10, 14, 9, 4, 12, 16, 17 \][/tex]
Next, to find the mean (average) number of yachts per lift, we need to calculate the sum of these corrected values.
Adding up these numbers:
[tex]\[ 12 + 15 + 13 + 10 + 14 + 9 + 4 + 12 + 16 + 17 = 122 \][/tex]
Now that we have the total number of yachts, which is 122, we need to determine the number of lifts recorded. Here, the total number of lifts is 10.
The mean number of yachts per lift is calculated by dividing the total number of yachts by the total number of lifts:
[tex]\[
\text{Mean} = \frac{\text{Total number of yachts}}{\text{Total number of lifts}} = \frac{122}{10} = 12.2
\][/tex]
Therefore, the mean number of yachts per lift is:
[tex]\[
\boxed{12.2}
\][/tex]
