Student Group A: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
Student Group B: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
The data shows the number of seconds it took two randomly selected groups to thread a needle. Compare the measures of center and variability of these data sets. Which of the following statements about these data sets is false?
The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
The mean time taken by Group A is higher than that of Group B.
The amount of variability of the time taken by Group A to thread a needle is higher than the amount of variability of the time taken by Group B.
The ranges of the time taken by Group A and Group B are the same.
The statement "The ranges of the time taken by Group A and Group B are the same" is false.
To compare the measures of center, we can look at the median and mean of each group. The median time taken by Group A is 29, while the median time taken by Group B is 19. Therefore, the first statement is true.
The mean time taken by Group A is (56+14+26+28+29+45+32+80+3+10)/10 = 35.3, while the mean time taken by Group B is (27+24+18+19+5+16+22+10+6+20)/10 = 16.7. Therefore, the second statement is also true.
To compare the variability, we can look at the range and interquartile range (IQR) of each group. The range of Group A is 80-3=77, while the range of Group B is 27-5=22. Therefore, the third statement is false. Group A has a larger range, indicating more variability in the data.
We can also calculate the IQR for each group. The IQR for Group A is the difference between the 75th percentile (45) and the 25th percentile (14), which is 31. The IQR for Group B is the difference between the 75th percentile (23.75) and the 25th percentile (9.25), which is 14.5. This confirms that Group A has a larger amount of variability in the data.