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 15 20,1,4 32,7 48 527 60 key 32 means 32 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 more prepared for the tournament? explain based on the scenario. (4 points)

Answer 1

The mean, median, mode, and range can be calculated for the given data. The choice between reporting the mean or median value depends on the presence of outliers and the skewness of the distribution.

Step-by-step explanation:

To calculate the mean, median, mode, and range for the given data, we first need to organize the data in ascending order: 1, 4, 7, 15, 20, 27, 32, 32, 48, 52, 57, 60. Now we can find the mean by summing up all the data points and dividing by the total number of data points: (1 + 4 + 7 + 15 + 20 + 27 + 32 + 32 + 48 + 52 + 57 + 60)/12 = 359/12 = 29.92 (rounded to two decimal places). The median is the middle value in the data set, which in this case is 32. The mode is the most frequently occurring value, which is also 32. The range is the difference between the largest and smallest values, which is 60 - 1 = 59.

In terms of reporting the mean or median value to show their preparedness for the tournament, it depends on the scenario. If there are no outliers or extreme values in the data set and the distribution is relatively symmetric, the mean can be a good representation of the average practice time for the players. However, if there are outliers present or the distribution is skewed, the median may be a better measure of central tendency as it is less influenced by extreme values.