Final answer:
After calculating the mean by adding all swim times and dividing by the number of attempts, ordering the data to find the median, and identifying the most frequent values for the mode, the correct mean is 2.6 minutes, the median is 2.6 minutes, and the mode includes both 2.5 and 2.6 minutes.
Step-by-step explanation:
The question at hand involves calculating the mean, median, and mode for a given data set of swimming times. To find the mean, we add all the times together and divide by the number of attempts. For the median, we order the data from least to greatest and find the middle value. The mode is the value that occurs most frequently in the data set. Let's begin by calculating each.
For the mean:
(2.8 + 2.5 + 2.6 + 2.8 + 2.5 + 2.6 + 2.6 + 2.4 + 2.5 + 2.7) / 10 = 26 / 10 = 2.6 minutes
For the median, we arrange the times: 2.4, 2.5, 2.5, 2.5, 2.6, 2.6, 2.6, 2.7, 2.8, 2.8. Since there are 10 data points, the median will be the average of the 5th and 6th values: (2.6 + 2.6) / 2 = 5.2 / 2 = 2.6 minutes.
For the mode, we look at the values that appear most frequently. We can see that 2.5 and 2.6 each appear three times, making them both modes.
Therefore, the correct option showing the mean, median, and mode of the distribution is:
c.) Mean: 2.6 Median: 2.6 Mode: 2.5 and 2.6