Leslie is training to compete in a marathon (a $26.2$-mile race). She has been running the entire marathon route each week and keeping track of her times. The times she has recorded are $237$ minutes, $241$ minutes, $242$ minutes, $238$ minutes, and $234$ minutes.

1. Calculate the mean, median, and mode of Leslie's times.

   Hint (a):

   If you need more help with the mean, median, and mode, refer to the Math Notes box from Lesson 1.3.3.

   More Help (a):

   It would be helpful to put Leslie's time in order from least to greatest. This will make it easier to analyze the data.

   Answer (a):

   Leslie's running time mean is $238.4$ minutes, the median is $238$ minutes, and there is no mode.

2. Leslie is hoping to complete the race in less than four hours. Do you think she has a chance? Explain.

   Hint 1(b):

   It may be helpful to know that $4$ hours are equal to $240$ minutes.

   Hint 2(b):

   Try looking closely at the average, or mean, of Leslie's times.

3. If Leslie does one more practice run and it takes her $237$ minutes, explain without doing any calculations how her mean, median, and mode should change.

   Hint (c):

   If Leslie did one more practice time and it took her $241$ minutes, the mean and median would be greater than those calculated in part (a). Also, there would be a new mode. Does this give you any clues as to how to solve this problem?