The problem asks to find the mean of the times from the dot plot provided. The dot plot shows how many players completed the puzzle at different times.

Here are the times based on the dot plot:

• 1 player took 8 minutes
• 1 player took 9 minutes
• 1 player took 12 minutes
• 1 player took 18 minutes
• 1 player took 19 minutes
• 2 players took 20 minutes
• 1 player took 22 minutes

To find the mean (average) time:

1. Add all the times together: $8 + 9 + 12 + 18 + 19 + 20 + 20 + 22 = 128$

2. Count the number of players (data points): $8 \text{ players total}$

3. Now, divide the sum of the times by the number of players: $\text{Mean} = \frac{128}{8} = 16 \text{ minutes}$

So, the mean time is 16 minutes.

Would you like any further details or have any questions?

Here are five questions to expand your understanding:

1. What does the mean represent in this context?
2. How would the mean change if one of the times were much larger?
3. Can the median of the times give more insight in this case?
4. How do outliers affect the calculation of the mean?
5. How would the mean differ if the dataset had fewer values but the same sum?

Tip: The mean is sensitive to extreme values (outliers), so sometimes the median might be a better indicator of the "typical" data value.