QUESTIONS

1- For the standard deviation, when do we use standard deviation based on a sample and when do we use standard deviation based on the population?

2- Explain why the standard deviation is a better measure to use than the variance.

3-The coefficient of variation (CV) measures relative variability equal to the ratio between the standard deviation divided by the mean and formatted to %. It is regularly used to compare risk (volatility) in investing and is especially useful in comparing data on different scales or with different units of measure. Consider weights of 10 oz, 13.4 oz, 15.1 oz with SD of 2.597 oz. The corresponding weights in pounds 0.625 lb, 0.838 lb, 0.944 lb have SD 0.162 lb. The SDs are not equal, yet the sample and its variability are the same.

- How can the variabilities be compared?

The CV, unlike other measures of variability, does not depend on the units of measurement. The units are divided out by dividing the standard deviation by the mean. For a "rule of thumb," a CV of greater than 5% is considered significant. So, the CV is also used to assess data with no prior history to compare to evaluate any trends.

4-When is the Coefficient of Variation (CV) especially useful?

5-Scenario: A contracted statistician has no prior experience with the company's product. The company has no previous process history and data to compare the sample to evaluate trends. The mode is not especially useful for this data,

but explain why there is or is not a concern with bag weight in terms of the other measures of central tendency.

6- What statistic could be used to assess the variability of the product?

7-Explain why there is or is not a concern with the variability of the product.