A Deviation from the Average

• ## A Deviation from the Average

PoW ID: 1110

### Problem Print

Your challenge is to create three distinct datasets, each tailored to have a designated mean and standard deviation.

1. Create a data set that has a mean of 5 and a standard deviation of 1.

2. Create a data set that has a mean of 8 and a standard deviation of 2.

3. Create a data set that has a mean of -10 and a standard deviation of 3.

Explain the process you used to come up with the datasets given the specific statistical properties.

There many possible solutions to this problem. One possibility is sets of {4,6}, {6, 10}, and {-13, -7}. Another is sets of {4,5,6}, {6,8,10}, and {-13,-10,-7}.

• Did you check, once you got the right standard deviation, that your data set still had the right mean?
• Did you use the formula for calculating the population standard deviation? Since you are making up an entire data set, rather than sampling from a larger group, you should use the formula for calculating the population standard deviation, not the sample standard deviation.
• Did you try making up some sample datasets and checking their mean and standard deviation?
• Did you try a working backwards strategy and ask yourself, "in order for the standard deviation calculations to come out to be 1, what must have been true in the previous step?" or "in order for the mean calculations to come out to be 5, what must have been true in the previous step?"
• Did you consider making a data set with just two data points?
• Did you look up the formulas for mean and standard deviation?