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The 95% confidence limits for pO2 in arterial blood were established as 82.5 - 97.5 mmHg.

1. What is the standard deviation?
2. What is the coefficient of variation for this test?

Answer :

The pO₂ (partial pressure of oxygen) measurement in arterial blood has a standard deviation of approximately 3.83 mmHg, and the coefficient of variation for this measurement is approximately 4.26%.

The 95% confidence limits for pO₂ (partial pressure of oxygen) in arterial blood are established as 82.5 - 97.5 mmHg. Confidence limits determine the range within which the true value of a parameter, in this case, pO₂, is likely to fall. The confidence interval gives us an estimate of the precision of our measurement.

To determine the standard deviation, we need to calculate the margin of error for the confidence interval. The margin of error is half the width of the confidence interval, which is (97.5 - 82.5) / 2 = 7.5 mmHg.

Since the margin of error corresponds to 1.96 standard deviations (for a 95% confidence interval), we can divide the margin of error by 1.96 to find the standard deviation. Therefore, the standard deviation is 7.5 mmHg / 1.96 ≈ 3.83 mmHg.

The coefficient of variation (CV) gauges the relative dispersion or variability of a dataset. It is calculated by dividing the standard deviation by the mean and multiplying by 100 to express it as a percentage. In this case, we do not have the mean value, so we cannot calculate the CV.
The midpoint of the confidence interval is the estimated mean:

Mean = (Lower Limit + Upper Limit) / 2 = (82.5 + 97.5) / 2 = 180 / 2 = 90 mmHg.

The margin of error (ME) corresponds to half of the range covered by the confidence interval.

ME = (Upper Limit - Lower Limit) / 2 = (97.5 - 82.5) / 2 = 15 / 2 = 7.5 mmHg.

Now, we have the mean (90 mmHg) and the standard deviation (3.83 mmHg). The coefficient of variation (CV) can be determined through calculations.

CV = (Standard deviation / Mean) * 100 = (3.83 / 90) * 100 ≈ 4.26%.

So, the coefficient of variation for the pO₂ measurement in arterial blood is approximately 4.26%.
In summary, the standard deviation for the pO₂ measurement in arterial blood is approximately 3.83 mmHg. The coefficient of variation for the pO₂ measurement in arterial blood is approximately 4.26%.

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