Final answer:
The mean shoe size for the provided data set, where all shoe sizes are 7, is actually 7. The reference values for the mean, median, and mode do not apply as the set consists of identical numbers, resulting in all three measures of central tendency equaling 7.
Step-by-step explanation:
To answer the student's question, we need to calculate the mean of the shoe sizes given. The mean, also known as the average, is found by summing all the values in a data set and then dividing by the number of values. In this case, all the recorded shoe sizes are 7, with ten occurrences of this value:
- 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 70
- 70 / 10 = 7
Therefore, the mean shoe size is 7.
The values given for the mean (7.7), median (7.5), and mode (seven) in the reference do not correspond to the provided data set, where all shoe sizes are 7. Normally, the mean reflects the skewing the most, but since in this simple example there is no variation in the data, the mean, median, and mode are all the same, being 7.