Changes in mean and standard deviation?

Question

The company that Amy works for specifies that the mean must be 100 and the standard deviation must be 10 for a set of data. However, when she measures the values for the actual data, she finds that the mean is 106.5 and the standard deviation is 8.4. What does she have to do to the set of data to make it fit the company's criteria?

Answer 1

You don't want to add false data points of course, so maybe the question is asking given this data, how would you get that std dev and mean?

You need to drop the mean, so you would have to drop some higher data points until you get sum/n = 100

To raise the std dev you need the data to be spread out a bit more. Again, it looks like a matter of juggling a few points on the extremes to get the curve to spread out a bit. maybe you could drop a few repeating points because this would increase the spread too.

Answer 2

It does a disservice to the company to "cook" the data. No enlightened company should demand that a set of data meet EXACTLY some parameters. What is needed is a X-bar and R control chart on small samples taken at regular intervals from the process and the sample mean(X-bar) and range (R) are plotted as a function of time. If the sample's X-bar and R remain in between the control limits the process should not be adjusted.
Formulas for calculating control limits can be found in any quality control manual or go to http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc32.htm

Answer 3

Normally sample mean and sample standard deviation will be different from the population mean and population standard deviation.

If your question is just theoretical, she can fiddle with that data and remove some numbers and add some numbers to make it fit the criterion (but that would be unethical).