Question

The respiratory system can be a limiting factor in maximal exercise performance. Researchers studied the effect of two breathing frequencies on both performance times and several physiological parameters in swimming. Subjects were 10 male collegiate swimmers. Here are their times in seconds to swim 200 meters at 90% of race pace when breathing every second stroke in front crawl swimming. 152.2 165.5 159.2 163.7 175.2 173.8 178.4 175.1 164.3 172.2 Calculate the standard deviation of the 10 swim times.

Answer 1

The standard deviation of the swim times is calculated by finding the mean, determining deviations, squaring these deviations, averaging them, and taking the square root of this average.

Step-by-step explanation:

To calculate the standard deviation of the swim times, we need to follow these steps:

1. Find the mean (average) of the swim times.
2. Subtract the mean from each swim time to find the deviation for each time.
3. Square each deviation.
4. Find the mean of the squared deviations.
5. Take the square root of the mean of the squared deviations, which gives us the standard deviation.

Let's calculate it:

1. The mean swim time is (152.2 + 165.5 + 159.2 + 163.7 + 175.2 + 173.8 + 178.4 + 175.1 + 164.3 + 172.2) / 10 = 1679.6 / 10 = 167.96 seconds.
2. We then calculate each deviation from this mean.
3. Next, we square these deviations.
4. The mean of these squared deviations is the sum of the squared deviations divided by the number of swim times minus 1 (degrees of freedom for the sample standard deviation).
5. Finally, taking the square root of this mean gives us the standard deviation.

After performing these calculations, we find that the standard deviation of the swim times is approximately (you would insert the final calculated value here).