# Lowest standard deviation of measurements

As the Quality Control Manager of a chemical company, you are asked to decide between several process methods that are supposed to uniformly mix 37.4 milligrams into a chemical solution. The resulting solutions from each process are sample tested for uniformity. The test samples yielded the following results of percentage powder mixed in the solution:

Method A: 0.13%, 0.21%, 0.009%, 0.014%

Method B: 0.10%, 0.006%, 0.015%, 0.11%, 0.16%

Method C: 0.006%, 0.09%, 0.07%

Method D: 0.18%, 0.16%, 0.19%, 0.17%

Which method would be the best choice to provide a uniform mixture??? (Hint: The best selection would be that resulting in the lowest standard deviation of measurements

Method A

Method B

Method C

Method D

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#### Solution Preview

Standard Deviation:

The standard deviation is the square root of the average squared deviation from the mean.

Method A: Consider the observations: 0.13%, 0.21%, 0.009%, 0.014%

1. First, calculate the mean and determine N.

2. Remember, the mean is the sum of scores divided by N where N is the number of samples.

3. Therefore, the mean = (.13 + .21 + .009+ .014) / 4 or .09075

4. Then, calculate the standard deviation as illustrated below.

squared

sample mean ...

#### Solution Summary

The lowest standard deviation of measurements is calculated. The excel calculations are copied into a word document which is also in the solution text box.

Compute the Arithmetic Annual Rate of Return

During the past five years you owned two stocks that had the following annual rates of return:

Year Stock A Stock B

1 0.18 0.09

2 0.6 0.04

3 -0.15 -0.11

4 -0.01 0.04

5 0.11 0.05

a) compute the arithmetic annual rate of return for each stock. Which stock is most desirable by this measure?

b) Compute the standard deviation of th annual rate of return for each stock. (Use Chapter 1 Appendix if necessary). By this measure, which is the preferable stock?

c) Compute the coeficient of variation for each stock. By this relative measure of risk, which stock is preferable?

d) Compute the geometric mean rate of retrun for each stock. Discuss the difference between the arithmetic mean return and the geometric mean return for each stock.

Discuss the differences in the mean returns relative to the standard deviation of the return for each stock.