Your team performed replicate analyses of a sample and obtained an average 18.54 mM concentration with a relative standard deviation of 4.0%. If you later discover that a systematic error was made by a factor of 2 and the mean concentration should have been 9.27 mM, what is the correct relative standard deviation?

Question

Your team performed replicate analyses of a sample and obtained an average 18.54 mM concentration with a relative standard deviation of 4.0%. If you later discover that a systematic error was made by a factor of 2 and the mean concentration should have been 9.27 mM, what is the correct relative standard deviation?

Answer 1

To calculate the correct relative standard deviation, we first need to understand the concept of relative standard deviation itself.

Relative standard deviation (RSD) is a measure of the precision or variability of a set of values. It is expressed as a percentage and is calculated by dividing the standard deviation of a dataset by its mean and then multiplying by 100.

In this case, we are given that the original dataset had an average concentration of 18.54 mM and a relative standard deviation of 4.0%. However, we now know that there was a systematic error, and the mean concentration should have been 9.27 mM.

To find the correct relative standard deviation, we need to adjust the original dataset by dividing it by the factor of 2 because the mean concentration was underestimated by a factor of 2. Therefore, the adjusted dataset would have the same values but each divided by 2.

Let's calculate the correct relative standard deviation by following these steps:

Step 1: Calculate the standard deviation of the original dataset.

Step 2: Adjust the original dataset by dividing it by 2 to correct the systematic error.

Step 3: Calculate the new mean concentration using the adjusted dataset.

Step 4: Calculate the standard deviation of the adjusted dataset.

Step 5: Calculate the correct relative standard deviation by dividing the updated standard deviation by the new mean concentration and multiplying by 100.

Let's perform the calculations:

Step 1: Calculate the standard deviation of the original dataset.
- Since we are not provided with the standard deviation, we cannot calculate it. Please provide the standard deviation value.

Once we have the standard deviation, we can move on to the next steps and calculate the correct relative standard deviation.

Answer 2

(s/mean)*100 = RSD

You know RSD and mean, solve for s, then use s and the same formula with the new mean to solve for new RSD. I think the answer is 8.0%