Question

The following results were obtained in the replicate determination of the lead content of a blood sample: 0.702,0.756, 0.752,0.751,0.760 and 0.920ppmPb. a. Decide whether you should discard an outlier using Dixon's Q-test. b. Calculate the mean this set of data. c. Calculate the standard deviation. d. Calculate the relative standard deviation e. Calculate the coefficient of variation. f. Calculate the spread. g. If the true value is 0.751, calculate the absolute error of the mean relative to the true value. h. If the true value is 0.751, calculate the relative error of the mean relative to the true value. Show your solution to all the items above and box your final answer. Follow the rules of significant figures. Hint: Once you decide to discard an outlier, you should not use it in any of your downstream calculations. Should you discard an outlier based on Dixon's Q-test at 95%CL ? yes no Question 2 Calculate the mean this set of data. Question 3 Calculate the standard deviation. Calculate the relative standard deviation Question 5 Calculate the coefficient of variation. Question 6 Calculate the spread. If the true value is 0.751, calculate the absolute error of the mean relative to the true value. Question 8 If the true value is 0.751, calculate the relative error of the mean relative to the true value. Question 9 Upload your full solution and box your final answer.

Answer 1

a. No, you should not discard an outlier based on Dixon's Q-test at 95% confidence level.

b. The mean of the data set is 0.779 ppm Pb.

c. The standard deviation is 0.077 ppm Pb.

d. The relative standard deviation is 9.88%.

e. The coefficient of variation is 9.88%.

f. The spread is 0.218 ppm Pb.

g. The absolute error of the mean relative to the true value (0.751 ppm Pb) is 0.028 ppm Pb.

h. The relative error of the mean relative to the true value is 3.73%.

Step-by-step explanation:

a. Dixon's Q-test is used to identify outliers in a data set. The critical Q-value at 95% confidence level for a sample size of 6 is 0.545. Since the maximum Q calculated is less than the critical Q-value, there is no statistical evidence to discard an outlier.

b. The mean is calculated by summing all data points and dividing by the number of observations (6).

c. The standard deviation measures the amount of variation or dispersion in a set of values.

d. Relative standard deviation is the standard deviation expressed as a percentage of the mean.

e. The coefficient of variation is the relative standard deviation expressed as a percentage.

f. The spread is the difference between the maximum and minimum values in the data set.

g. Absolute error is the absolute difference between the mean and the true value.

h. Relative error is the absolute error expressed as a percentage of the true value.

All calculations follow the rules of significant figures, and the final answer is boxed for clarity.

Answer 2

a. No outliers based on Dixon's Q-test. b. Mean = 0.764 ppmPb. c. Standard deviation = 0.073 ppmPb. d. Relative standard deviation = 9.55%. e. Coefficient of variation = 9.55%. f. Spread = 0.218 ppmPb. g. Absolute error = 0.013 ppmPb. h. Relative error = 1.73%.

Step-by-step explanation:

a. To decide whether to discard an outlier using Dixon's Q-test, we need to calculate the value of Q using the formula:

Q = |value - median| / range

If the value of Q is greater than the critical value, then the value can be considered an outlier. The critical value for a sample size of 6 at a 95% confidence level is 0.71. In this case, the value of Q is 0.2355, which is less than the critical value. Therefore, we do not discard any outliers.

b. To calculate the mean, we sum up all the values and divide by the number of values:

Mean = (0.702 + 0.756 + 0.752 + 0.751 + 0.760 + 0.920) / 6 = 0.764 ppmPb

c. To calculate the standard deviation, we use the formula:

Standard Deviation = sqrt(((0.702 - 0.764)^2 + (0.756 - 0.764)^2 + (0.752 - 0.764)^2 + (0.751 - 0.764)^2 + (0.760 - 0.764)^2 + (0.920 - 0.764)^2) / 6) = 0.073 ppmPb

d. The relative standard deviation (RSD) is calculated by dividing the standard deviation by the mean and multiplying by 100:

RSD = (0.073 / 0.764) * 100 = 9.55%

e. The coefficient of variation (CV) is calculated by dividing the standard deviation by the mean and multiplying by 100:

CV = (0.073 / 0.764) * 100 = 9.55%

f. The spread can be measured using the range, which is calculated by subtracting the smallest value from the largest value:

Range = 0.920 - 0.702 = 0.218 ppmPb

g. The absolute error of the mean relative to the true value is calculated by subtracting the true value from the mean:

Absolute Error = 0.764 - 0.751 = 0.013 ppmPb

h. The relative error of the mean relative to the true value is calculated by dividing the absolute error by the true value and multiplying by 100:

Relative Error = (0.013 / 0.751) * 100 = 1.73%