Question

The stem-and-leaf plot displays the amount of time, in minutes, that 10 players spent practicing their serving skills for an upcoming tennis tournament.

1 2, 2, 9
2 0, 2, 6
3 1, 1
4 0
5
6 8
Key: 3|1
means 31


Part A: Calculate the mean, median, mode, and range for the data given. Show your work. (8 points)

Part B: Should the tennis players report the mean or median value to show they are less prepared for the tournament? Explain based on the scenario. (4 points)

Answer 1

Part A:

To calculate the mean, we add up all the values and divide by the total number of values:

12 + 12 + 19 + 20 + 22 + 26 + 31 + 31 + 40 + 68 = 281

Mean = 281 / 10 = 28.1

To find the median, we need to find the middle value. Since there is an even number of values, we take the average of the two middle values:

Median = (22 + 26) / 2 = 24

The mode is the value that appears most frequently. In this case, there is no mode as no value appears more than once.

The range is the difference between the highest and lowest values:

Range = 68 - 12 = 56

Part B:

The median may be a better measure of central tendency in this scenario as there is an outlier value of 68 that can skew the mean. Since outliers can have a significant impact on the mean, reporting the median may give a better representation of the typical amount of time spent practicing for the tournament. Therefore, the tennis players should report the median value.