Final answer:
The mean, median, mode, and range for the tennis players' practice times are 33.7 minutes, 32 minutes, 41 minutes, and 33 minutes, respectively. The mean is the best measure of center for this symmetric data without outliers.
Step-by-step explanation:
To answer the student's question, we need to calculate the mean, median, mode, and range of the data from a stem-and-leaf plot.
Part A: Calculate the Measures
The stem-and-leaf plot gives us the following data: 19, 22, 26, 29, 30, 34, 41, 41, 43, 52. First, we add all the numbers together to find the mean:
Mean = (19 + 22 + 26 + 29 + 30 + 34 + 41 + 41 + 43 + 52) / 10 = 337 / 10 = 33.7 minutes
Median: To find the median, we put the numbers in order and locate the middle value. Since we have an even number of data points, the median is the average of the two middle numbers, which are 30 and 34.
Median = (30 + 34) / 2 = 64 / 2 = 32 minutes
Mode: The mode is the value that occurs most frequently. In this case, 41 appears twice, so the mode is 41 minutes.
Range: The range is the difference between the highest and lowest value in the data set.
Range = 52 - 19 = 33 minutes
Part B: The Best Measure of Center
Considering the data is moderately symmetric and without outliers, the mean can be considered the best measure of center as it takes into account every value.
Part C: Justification
In the context of time spent practicing tennis serving skills, the mean offers a balanced representation of the overall practice time among all players.