To determine which data set is Diego's, we need to find the data set that has a mean of 11 minutes. Let's evaluate each data set to identify the correct one:
Data Set A: 9, 11, 13, 10, 12
Data Set B: 8, 10, 12, 14, 16
Data Set C: 10, 10, 10, 10, 10
Data Set D: 11, 11, 11, 11, 11
To find the mean, we sum up all the values in each data set and divide by the number of values:
Data Set A: (9 + 11 + 13 + 10 + 12) / 5 = 11 minutes
Data Set B: (8 + 10 + 12 + 14 + 16) / 5 = 12 minutes
Data Set C: (10 + 10 + 10 + 10 + 10) / 5 = 10 minutes
Data Set D: (11 + 11 + 11 + 11 + 11) / 5 = 11 minutes
Comparing the mean of each data set to 11 minutes, we can see that only Data Set A and Data Set D have a mean of 11 minutes. However, to prove that our choice is correct, we need to analyze the individual values in the data set.
In Data Set A, we can observe that the values are relatively close to 11 minutes, with some values slightly above and below. This variation suggests a realistic scenario where Diego's walk to school might take slightly different amounts of time each day.
In Data Set D, all the values are exactly 11 minutes. While it is not impossible for Diego's walk to consistently take exactly 11 minutes each day, it seems less likely than having some variation in the durations.
Based on these observations, we can conclude that the most plausible data set for Diego is:
Data Set A: 9, 11, 13, 10, 12
This data set has a mean of 11 minutes and exhibits a realistic variation in walk durations, making it the most likely choice for Diego's recorded lengths.