To determine which statement is true about the difference between the mean times and the mean absolute deviations (MAD) of the individual times of the relay swim teams, let's follow these steps:
1. Calculate the difference between the means for Team A and Team B:
Mean for Team A = 127.9 seconds
Mean for Team B = 127.4 seconds
Difference in means = [tex]\(127.9 - 127.4 = 0.5 \)[/tex] seconds
2. Calculate the mean of the mean absolute deviations for both teams:
MAD for Team A = 0.26 seconds
MAD for Team B = 0.23 seconds
Mean of MADs = [tex]\(\frac{0.26 + 0.23}{2} = 0.245 \)[/tex] seconds
3. Calculate how many times the difference in means is compared to the mean of MADs:
Ratio = [tex]\(\frac{0.5}{0.245} \approx 2.0408163265306123 \)[/tex]
Now, considering the calculated ratio, we can compare it with the given options:
- The difference between the mean times is about equal to the mean absolute deviation of the data sets.
(This is not true; the ratio is around 2.04, not close to 1.)
- The difference between the mean times is about 2 times the mean absolute deviation of the data sets.
(This statement is true; the ratio is approximately 2.04, which is very close to 2.)
- The difference between the mean times is about 5 times the mean absolute deviation of the data sets.
(This is not true; the ratio is around 2.04, not close to 5.)
- The difference between the mean times is about 16 times the mean absolute deviation of the data sets.
(This is not true; the ratio is around 2.04, not close to 16.)
Therefore, the true statement is:
The difference between the mean times is about 2 times the mean absolute deviation of the data sets.
