1. Two groups of students were given introduction to statistics examination and tested to find out which group is faster to finish the examination. For the two groups the following information was given.
Value Group one Group two
Mean 10.4 min 11.9 min
Standard deviation 1.2 min 1.3 min
Relatively speaking:
a) Which group is more consistent in its performance?
b) Suppose Yacob from group one take 9.2 minutes while Melat from group two take 9.3 minutes, who was faster in performing the task? Why
a) To determine which group is more consistent in its performance, we need to compare the standard deviations. The group with the smaller standard deviation is considered more consistent. In this case, group one has a standard deviation of 1.2 minutes, while group two has a standard deviation of 1.3 minutes. Therefore, group one is more consistent in its performance.
b) To determine who was faster in performing the task, we need to compare the individual times to the respective group means. Yacob from group one took 9.2 minutes, which is less than the mean of group one (10.4 minutes), indicating that Yacob was faster in performing the task. Similarly, Melat from group two took 9.3 minutes, which is also less than the mean of group two (11.9 minutes), indicating that Melat was also faster in performing the task. Both Yacob and Melat were faster in performing the task compared to their respective groups' means.