Problem II - [18 points] (a) (1) Choose and write down a sample of 12 distinct (different) positive integers (no modes), each less than 100, in a way that your data set would have a range of 90, a mean of 59, and a median of 55 (2) In order not to treat the data as an abstract set, state what your data might represent with an applicable unit. (b) Show your data set and your work to demonstrate that your data set does have the statistical characteristics mentioned. Consider your data set as a sample. (c) (1) Estimate the standard deviation using the "range rule of thumb": four standard deviations practically cover the span of the data (about 95% for normal distributions), when rank ordered. Do not calculate the actual standard deviation value using its formula or technology for this part. The standard deviation found would have the same unit as in Part (a) above; the unit should accompany the value when reported. (2) What would be an estimate for the variance? Do not forget its unit